UTTARANCHAL UNIVERSITY

UTTARANCHAL

UNIVERSITY

UTTARANCHAL UNIVERSITY Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun,

Uttarakhand-248007, INDIA

Detailed Course Structure & Syllabus

of

B.Sc. (Hons.) Mathematics

Applicable for Batch: 2018-21

Under Choice Based Credit System (CBCS)

Course Structure & Syllabus of B.Sc. (Hons.) Mathematics


EVALUATION SCHEME

B.Sc. (Hons.) Mathematics- 3 Years

Under Choice Based Credit System (CBCS)



Semester – I

S.No Code Paper Title Period

L -T -P

Credit

L -T -P

Theory Practical

Total Total

Credit End

sem Sess

End

sem Sess

1.

TBHM/

PBHM

- 101

Calculus 4-0-2 4-0-1 60 40 25 25 150 5

2. TBHM-

102 Algebra 4-1-0 4-1-0 60 40 ----- ------ 100 5

3.

TBHG/

PBHG-

103

Generic

Elective-1

(GE-1)

4-0-4 4-0-2 60 40 25 25 150 6

4.

TBEC -

104

or

TBES -

104

English

Communicati

on/

Environmenta

l Science

2-0-0 2-0-0 60 40 ---- ------ 100 2

5. PBHA-

105

Educational

Visit/Activiti

es*

0-0-2 0-0-1 ----- ------ 25 25 50 1

Total 14-1-8 14-1-4 550 19

*Eco-Club/ Mathematics Club/ NSS activities etc.



Semester – II

S.

No

Code Paper Title Period

L-T-P

Credit

L-T-P

Theory Practical Total Total

Credit End

sem.

Sess. End

sem

Sess.

1. TBHM-

201 Real Analysis 4-1-0 4-1-0 60 40 ----- ------ 100 5

2.

TBHM/P

BHM-

202

Differential

Equations 4-0-2 4-0-1 60 40 25 25 150 5

3.

TBHG/

PBHG-

203

Generic Elective-

2

(GE-2)

4-0-4 4-0-2 60 40 25 25 150 6

4.

TBEC -

204

or

TBES -

204

English

Communication/

Environmental

Science

2-0-0 2-0-0 60 40 ----- ------ 100 2

5. TBHE-

205

Human Ethics

and Professional

Values

2-0-0 2-0-0 60 40 ----- ------ 100 2

Total 16-1-6 16-1-3 600 20

Total for 1 & 2

Sem. 30-2-14 30-2-7 1150 39



Semester – III S.

No


L-T-P

Credit

L-T-P


Credit End

sem

Sess End

sem

Sess

1. TBHM-

301

Theory of

Real

Functions

4-1-0 4-1-0 60 40 ------ ----- 100 5

2. TBHM-

302

Group Theory

- I 4-1-0 4-1-0 60 40 ------ ----- 100 5

3.

TBHM/

PBHM -

303

PDE and

Systems Of

ODE

4-0-2 4-0-1 60 40 25 25 150 5

4. TBHG-

304

Generic

Elective-3

(GE-3)

4-1-0 4-1-0 60 40 ------ ----- 100 5

5.

TBHM-

305

Skill

Enhancement

Course – 1

(SEC-1)

2-0-0 2-0-0 60 40 ------ ----- 100 2

6 PBHS-

306 Seminar* 0-0-2 0-0-1 ----- ------ 25 25 50 1

Total 18-3-4 18-3-2 600 23

Total for 1, 2

& 3 Sem. 48-5-18 48-5-9 1750 62

* Seminar will be based on topic allotted by the Coordinator/HOD.



Semester – IV

S.

No


L-T-P

Credit

L-T-P


Credit End

sem.

Sess. End

sem.

Sess.

1. TBHM/

PBHM-

401

Numerical

Methods

4-0-2 4-0-1 60 40 25 25 150 5

2. TBHM-

402

Riemann

Integration

and Series of

Functions

4-1-0 4-1-0 60 40 ----- ------ 100 5

3. TBHM-

403

Ring Theory

& Linear

Algebra - I

4-1-0 4-1-0 60 40 ----- ------ 100 5

4. TBHG-

404

Generic

Elective-4

(GE-4)

4-1-0 4-1-0 60 40 ----- ------ 100 5

5. TBHM-

405

Skill

Enhancement

Course – 2

(SEC-2)

2-0-0 2-0-0 60 40 ----- ------ 100 2

6. PBHW-

406

Workshop/

Activity*

0-0-2 0-0-1 ----- ------ 25 25 50 1

Total 18-3-4 18-3-2 600 23

Total for

1,2,3 & 4

Sem.

66-8-22 66-8-11 2350 85

*Participation in activities like workshop/ model making/ poster making or any other assigned activity.



Semester – V

S.

No


L-T-P

Credit

L-T-P


Credit End

sem.

Sess End

sem.

Sess

1. TBHM

-501

Multivariate

Calculus 4-1-0 4-1-0 60 40 ------ ----- 100 5

2. TBHM

-502

Group

Theory – II 4-1-0 4-1-0 60 40 ------ ----- 100 5

3. TBHM

-503

Discipline

Specific

Elective – 1

(DSE-1)

4-1-0 4-1-0 60 40 ------ ----- 100 5

4. TBHM

-504

Discipline

Specific

Elective – 2

(DSE-2)

4-1-0 4-1-0 60 40 ------ ----- 100 5

5. PBSM

-505 Seminar* 0-0-3 0-0-2 ----- ----- 50 50 100 2

Total 16-4-3 16-4-2 500 22

Total for

1,2,3,4 & 5

Sem.

82-12-

25 82-12-13 2850 107

* Seminar will be based on SWYAM/ MOOC Courses/ UGC Open Courses or any other.



Semester – VI

S.

No Code Paper Title

Period

L-T-P

Credit

L-T-P

Theory Practical

Total Total

Credit End

sem. Sess

End

sem. Sess.

1. TBHM-

601

Metric

Spaces and

Complex

Analysis

4-1-0 4-1-0 60 40 ----- ------ 100 5

2. TBHM-

602

Ring Theory

and Linear

Algebra - II

4-1-0 4-1-0 60 40 ----- ------ 100 5

3. TBHM-

603

Discipline

Specific

Elective – 3

(DSE-3)

4-1-0 4-1-0 60 40 ----- ------ 100 5

4. TBHM-

604

Discipline

Specific

Elective – 4

(DSE-4)

(Viva/

Dissertation)

4-1-0 4-1-0 60 40 ----- ------ 100 5

5. ADP-

605

Aptitude &

Reasoning

Skills

0-0-2 0-0-1 ------ ----- 25 25 50 1

Total 16-4-2 16-4-1 450 21

Total for

1,2,3,4,5 &

6 Sem.

98-16-27 98-16-14 3300 128

* Wherever there is a practical there will be no tutorial and vice-versa



1. Evaluation Scheme for Internal Practical:

Practical Performance & Viva

During the Semester (10 Marks)

Attendance

Viva

Total

Internal Experiment File work

(5 Marks) (5 Marks) (5 Marks) (10 Marks) (25 Marks)

2. Evaluation Scheme for External Practical:

Experiment File Work Viva Total External

(10 Marks) (5 Marks) (10 Marks) (25 Marks)

3. Evaluation Scheme for Dissertation:

Dissertation Performance &

Presentation During the Semester Attendance Total Internal

(30 Marks) (10 Marks)

(40 arks)

4. External Evaluation (100 marks)

Thesis

Evaluation

Papers presented/Published in

conferences/Journals

Presentation &

Viva Total External

(15 Marks) (15 Marks) (30 Marks)

(60 Marks)



LIST OF CORE COURSES (CC) (All 14 courses are compulsory)

S.

No. Course Code Course Name Credits Remarks

1 TBHM/ PBHM – 101 Calculus 5

2 TBHM-102 Algebra 5

3 TBHM-201 Real Analysis 5

4 TBHM/ PBHM-202 Differential Equations 5

5 TBHM-301 Theory of Real Functions 5

6 TBHM-302 Group Theory – I 5

7 TBHM/PBHM -303 PDE and Systems Of ODE 5

8 TBHM/PBHM-401 Numerical Methods 5

9 TBHM-402 Riemann Integration and Series of

Functions 5

10 TBHM-403 Ring Theory & Linear Algebra – I 5

11 TBHM-501 Multivariate Calculus 5

12 TBHM-502 Group Theory – II 5

13 TBHM-601 Metric Spaces and Complex

Analysis 5

14 TBHM-602 Ring Theory and Linear Algebra – II 5



LIST OF ABILITY ENHANCEMENT COMPULSORY COURSES

S.No Course Code Course Name Credits Remarks

1. TBEC-104 English Communication 2

2. PBHA-105 Educational Visit/Activities 1

3. TBES-104 Environmental Science 2

4. TBHE-205 Human Ethics and Professional

Values 2

5. PBHS-306 Seminar 1

6. PBHW-406 Workshop/Activity 1

7. PBSM-505 Seminar 2

8. ADP-605 Aptitude & Reasoning Skills 1



ELECTIVE COURSES

• List of Generic Elective (GE) Courses

S.

No. Course Code Course Name Credits Remarks

1

TBHG/PBHG- 103(1)-(2)

Fundamentals of Computers (P)

6 Choose any

One 2

Object Oriented Programming

in C++ (P)

1

TBHG/PBHG- 203(1)-(2)

Concepts of Programming (P)

6 Choose any

One 2

DBMS and Networking

Concepts (P)

1

TBHG/PBHG- 304(1)-(4)

Total Quality Management

5 Choose any

One 2 Intellectual Property Rights

3 Statics

1

TBHG/PBHG- 404(1)-(3)

Non-Conventional Energy

Resources

5 Choose any

One 2 Data Structure

3 Dynamics



• List of Skill Enhancement Courses (SEC)

S. No Course Code Course Name Credits Remarks

1 TBHM-305

Logic and Sets 2

Choose any

One 2 Computer Graphics

1

TBHM-405

Graph Theory

2 Choose any

One 2 Combinatorial Mathematics

3 Applications of Algebra

• List of Discipline Specific Electives (DSE) Courses

S.No Course Code Course Name Credits Remarks

1.

TBHM-503

Portfolio Optimization

5 Choose any

One 2. Number Theory

3. Boolean Algebra and Automata Theory

4.

TBHM-504

Theory of Equations

5 Choose any

One 5. Analytical Geometry

6. Probability and Statistics

7.

TBHM-603

Industrial Mathematics

5 Choose any

One 8. Bio-Mathematics

9. Linear Programming

10.

TBHM-604

Mathematical Modelling

5 Choose any

One 11. Mechanics

12. Differential Geometry

13 Dissertation

UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)

(Uttarakhand Act No. 11 of 2013)

Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand

PROGRAM EDUCATIONAL OBJECTIVES (PEOs), PROGRAM

OUTCOMES (POs) and PROGRAM SPECIFIC OUTCOMES (PSOs)

for





PROGRAM EDUCATIONAL OBJECTIVES (PEOs)

PEO 1. To equip students with knowledge, abilities and insight in mathematics and related fields

and enable them to work as a mathematical professional.

PEO 2. To develop the ability to utilize the mathematical problem-solving methods such as analysis,

modelling, and programming and mathematical software applications in addressing the practical

and heuristic issues.

PEO 3. Graduates will develop the skill to write entrance exam conducted by various Universities

and organizations to pursue higher studies/competent career.

PEO 4. Graduates will use their course as a training ground to develop their positive attitude, skills which

will enable them to become a multi facet personality shining in any chosen field.

PEO 5. The graduates will work and communicate effectively in inter-disciplinary environment, either

independently or in a team, and demonstrate leadership qualities.

PROGRAM OUTCOMES (POs)

PO 1. Disciplinary knowledge: Communicate various concepts of mathematics effectively in the

core subject of mathematics though various medium such as seminars, workshop,

presentations.

PO 2. Critical thinking and analytical reasoning: Analyze the results and apply them in various

problems appearing in different branches of mathematics.

PO 3. Problem solving: Provide new solutions using the domain knowledge of mathematics

acquired during this programme.

PO 4. Research-related skills: Inquiring about appropriate questions and advances relating to the

concepts in various fields of mathematics.

PO 5. Information/digital literacy: Create, select, and apply appropriate techniques, resources,

and modern scientific and IT tools with their limitations.

PO 6. Self-directed learning: Work independently and do in-depth study of various notions to

effectively enhance the communication skills.

PO 7. Moral and ethical awareness/reasoning: Educate the students about human values &

professional ethics related to society and environment.

PO 8. Lifelong learning: Prepare graduates according to broadest context of technological

change and ability to work independently and in group with lifelong learning skills in

society and Industry.




PROGRAM SPECIFIC OUTCOMES (PSOs)

PSO 1. Acquire knowledge pertaining to concepts of mathematics and widespread specific disciplines

including Calculus, Mathematical Analysis, Abstract Algebra, Number theory, Statics, LPP,

Statistics, Numerical analysis, logic & sets etc. along with allied fields including environment

science, computer fundamental and human ethics.

PSO 2. Strong foundation of Differential Equation, Linear algebra Mathematical modeling,

Dynamics, Graph theory and Operation Research which have strong link and application

in engineering, technology and physical sciences.

PSO 3. Identify the potential and applicability of concepts of applied mathematics to design/ drive

a solution to complex problems pertaining to industry, society and multidisciplinary

environment and simultaneously enhancing their critical thinking, practical, presentation,

communication and professional skills.

PSO 4. Enhance eligibility and increase competence to appear in various competitive examinations

for higher studies and pursue career in academia, industry, organizations etc.




COMPREHENSIVE TABLE

for B.Sc. (Hons.) Mathematics- 3 Years




S.N

o.

Course

Code

Course

Name

P

O1

P

O2

P

O3

P

O4

P

O5

P

O6

P

O7

P

O8

PS

O1

PS

O2

PS

O3

PS

O4

1 TBHM –

101 Calculus 2 2.5 2.5 1.5 2.5 - -

1.7

5 2.5 - 2 1.5

2 PBHM -

101 Calculus Lab 2 2.6 2 2 1.7 - - 1.5 2.6 - 2.3 2

3 TBHM-

102 Algebra 3 2.3 2 2 2.3 - - 1.5 2 1.7 1.5 1.8

4

TBHG-

103 (GE-

1)

Fundamental

of Computers - - - - 1.2 0.6 0.6 0.8 - - 0.2 0.4

5

PBHG-

103 (GE-

1)

Fundamental

of Computers

(Lab)

0.5 - - - 1.5 0.2 0.7 1.5 - - 0.5 0.75

6

TBHG-

103 (GE-

1)

Object

Oriented

Programming

in C++

2.4 2.2 1.8 2.2 2.4 - - - 2.2 - 2 -

7

PBHG-

103 (GE-

1)

Object

Oriented

Programming

in C++ (Lab)

- - - - 1.5 0.2 0.7 1.5 - - 0.5 0.75

8 TBEC -

104

English

Communicati

on

3 - 1 - - 3 - - 1 - 2 1

9 PBHA-

105

Educational

Visit 2 2 2.2 2 - 2 2 2 - - 1.5 -

10 TBHM-

201 Real Analysis

1.7

5 2 1 - 3 - - 2 2 - 2 2

11 TBHM-

202

Differential

Equations

2.2

5

2.2

5 2

1.7

5 1.5 - 2 2 2 2 - 2

12 PBHM –

202

Differential

Equations Lab 2

2.3

3 2

2.3

3 2 2 2 2 2 2.33 2 2

13

TBHG-

203 (GE-

2)

Concepts of

Programming 0.2 - - 0.2 1 - 1 1.2 - - 0.4 0.6

14

PBHG-

203 (GE-

2)

Concepts of

Programming

(Lab)

- - 0.3 0.3 1.3 0.3 0.6 1.3 - - 0.6 1

15

TBHG-

203 (GE-

2)

DBMS and

Networking

Concepts

1 1 2 1.5 2 - - - 2 1 1.5 1.2

16

PBHG-

203 (GE-

2)

DBMS and

Networking

Concepts

(Lab)

1 1 2 1 1.7

5 - - - 1 1 1.6 1.6

17 TBES-

204

Environmenta

l Science 2 - - - - 1 1 2 1 -- - 2

18 TBHE -

205

Human Ethics

&

Professional

Values

- - - - - - 3 - 1 - - -

19 TBHM-

301

Theory of

Real

Functions

3 2.5 2.3 1.8 1 2.3 2.5 2 2.3 1.8

20 TBHM-

302

Group

Theory-I 2.3 2.3 1.7 1 2 - - 1.8 3 - 1.5

1.8




21 TBHM-

303

PDE and

system of

ODE

2.5 2.5 2 2 2.3 - - 2 - 2.5 2.2 1

22 PBHM -

303

PDE and

Systems of

ODE Lab

2.6 2 2 1 2 - - 1.5 - 2.33 2.5 2

23

TBHG-

304 (GE-

3)

Total Quality

Management 1 2 2.3 1 2 3 2 2.75

24

TBHG-

304 (GE-

3)

Intellectual

Property

Rights

1 1 1 1

25

TBHG-

304 (GE-

3)

Statics 3 2 2 1.7 2.3 - 1 1.5 1.8 1.5 1.5 1.8

26

TBHM-

305

(SEC-1)

Logic and

Sets 3 2.5 2.5 2.5 2 - - 2 2.8 2.3 2.5 2.3

27

TBHM-

305

(SEC-1)

Computer

Graphics 1

1.2

5 1.5 1.5

2.2

5 - - - 1.5 1 1 1.5

28 PBHS-

306 Seminar 1.5 2 - 2 3 1 2 - 2 1.7 2

29 TBHM-

401

Numerical

Methods 3 1.8 1.8 2 1.3 - 1 1.8 2.5 1.5 1 1.5

30 PBHM-

401

Numerical

Methods Lab 3 1.3 2 1.7 2 - - 1.7 2.7 1.5 2.7 1.7

31 TBHM-

402

Riemann

Integration

and Series of

Functions

2 2 2 1.5 1.5 - - 1.5 2 - 2 2

32 TBHM-

403

Ring Theory

and Linear

Algebra – I

2.3 2.3 2.5 1.7 2 - - 1.8 1.3 1.7 1.8 1.5

33

TBHG-

404 (GE-

4)

Non-

Conventional

Energy

Resources

2 1.5 1.2

5 2 2 1 2 - 1 2.25 2.5 2

34

TBHG-

404 (GE-

4)

Data Structure 1 1.2

5 1.5 1.5

2.2

5 - - - 1.5 1 1 1.5

35

TBHG-

404 (GE-

4)

Dynamics 3 2.8 2.5 2.3 1 - - 2.5 2 3 2.3 2

36

TBHM-

405

(SEC-2)

Graph Theory 3 1.5 2 1.5 2 - - 2 - 2.3 1.67 1.67

37

TBHM-

405

(SEC-2)

Combinatorial

Mathematics 3 1.8 1.8 2 1.3 - 1 1.8 2.5 1.5 1 1.5

38

TBHM-

405

(SEC-2)

Applications

of Algebra 2.5 2.7 2.5 1.5 1.3 - - 2.2 2 2 2.25 2

39 PBHW-

406

Workshop/Act

ivities 1.5 2 - 2 3 1 2 - - 2 1.7 2

40 TBHM-

501

Multivariate

Calculus 2.5 2.8 1.8 1.3 1 - - 2 2.5 1 2 1.5

41 TBHM-

502

Group Theory

– II 1.8 2 2.3 2.3 2.5 - - 1.3 2.3 - 2

2.3




42

TBHM-

503

(DSE-1)

Portfolio

Optimization 2 2 2 1.5 1.5 - - 1.5 2 - 2 2

43

TBHM-

503

(DSE-1)

Number

Theory 3 1.5 2 1.3 2.3 - 1 1.8 2.3 - 1.7 1.5

44

TBHM-

503

(DSE-1)

Boolean

Algebra and

Automata

Theory

3 2 2 1.5 1.8 - 1 1.8 3 2.3 1.5 1.8

45

TBHM-

504

(DSE-2)

Theory of

Equations 2 1.7 1.3 1.5 1.8 - 1 1.5 3 1.7 1.5 1.5

46

TBHM-

504

(DSE-2)

Analytical

Geometry 3 1.3 1.5 1.5 1.3 - 1 2 3 1.7 1.5 1.3

47

TBHM-

504

(DSE-2)

Probability

and Statistics 1.7 2 1.5 2 2.3 - - 2 2.25 - 1.5 2.25

48 PBSM-

505 Seminar 1.5 2 - 2 3 1 2 - - 2 1.7 2

49 TBHM-

601

Metric Spaces

and Complex

Analysis

2.7 2.2 2 1.5 1.2 - - 1.7 3 - 2.7 2

50 TBHM-

602

Ring Theory

and Linear

Algebra – II

- 1.6

7

2.2

5 2 2.3 - - 1.7 2 2 1.5 2

51

TBHM-

603

(DSE-3)

Industrial

Mathematics 3 1.7 1.5 1 1 - 1 2.3 2.5 1.7 1.3 1.8

52

TBHM-

603

(DSE-3)

Bio-

Mathematics 3 1.7 1.3 1.5 1.8 - 1 2 - 1.7 1.5 1.8

53

TBHM-

603

(DSE-3)

Linear

Programming

problems

2.5 2.7 2.5 1.5 1.3 - - 2.2 2 2 2.25 2

54

TBHM-

604

(DSE-4)

Mathematical

Modeling 3 2 2 1.5 1.8 - 1 1.8 3 2.3 1.5 1.8

55

TBHM-

604

(DSE-4)

Mechanics 3 2 2 1.5 1.8 - 1 1.8 3 2.3 1.5 1.8

56

TBHM-

604

(DSE-4)

Differential

Geometry 3 2 2 1.5 1.8 - 1 1.8 3 2.3 1.5 1.8

57

TBHM-

604

(DSE-4)

Dissertation

1.5 2.5 3 - 3 1.5 2 - 2 2.5 3 2

58 ADP-

605

Aptitude &

Reasoning

Skills

3 2 2 1.5 1.8 - 1 1.8 3 2.3 1.5 1.8




Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)

SYLLABUS

of






SEMESTER -I





Programme Name B.Sc. (Hons.) Mathematics Programme Code 26

Course Code TBHM – 101 Credit 4

Year/Sem 1/1 L-T-P 4-0-0

Course Name Calculus

Objectives of the Course:

1. To learn the basic techniques of differentiation and integration.

2. To develop the concept of Leibnitz rule, curve tracing, asymptotes and its applications.

3. To derive parametric representations for plane curves, compute length for parametric

curves, use polar coordinates, and its conversion.

4. To identify the polar equations for lines, circles and conics. Learn to use the techniques

of Dirichlet’s integrals and Liouville’s extension.

UNIT-I (Total Topics- 8 and Hrs.- 9)

Hyperbolic functions, higher order derivatives, Leibniz rule and its applications to problems

of type𝑒𝑎𝑥+𝑏𝑠𝑖𝑛𝑥, 𝑒𝑎𝑥+𝑏𝑐𝑜𝑠𝑥, (𝑎𝑥 + 𝑏)𝑛𝑠𝑖𝑛𝑥, (𝑎𝑥 + 𝑏)𝑛𝑐𝑜𝑠𝑥.

UNIT -II (Total Topics -8 and Hrs-9)

Concavity and inflection points, asymptotes, curve tracing in Cartesian coordinates, tracing

in polar coordinates of standard curves, L’ Hospital’s rule, applications in business,

economics and life sciences.

UNIT- III (Total Topics -9 and Hrs-9)

Reduction formulae, derivations and illustrations of reduction formulae of the type

∫ sin 𝑛𝑥𝑑𝑥 , ∫ cos 𝑛𝑥𝑑𝑥 , ∫ tann 𝑛𝑥𝑑𝑥 , ∫ sec 𝑛𝑥𝑑𝑥 , ∫(log 𝑥)𝑛𝑑𝑥 , ∫ 𝑠𝑖𝑛𝑛𝑥𝑠𝑖𝑛𝑚𝑥𝑑𝑥

volumes by slicing, disks and washers methods, volumes by cylindrical shells, parametric

equations.

UNIT-IV (Total Topics -10and Hrs-9)

Parameterizing a curve, arc length, arc length of parametric curves, area of surface of

revolution. Techniques of sketching conics, reflection properties of conics, rotation of axes

and second-degree equations, classification into conics using the discriminant, polar

equations of conics.

UNIT-V (Total Topics -7 and Hrs-9)

Triple product, introduction to vector functions, operations with vector-valued functions,

limits and continuity of vector functions, differentiation and integration of vector functions,

tangent and normal components of acceleration.

Course Outcomes (COs):

TBHM- 101 CO 1.Acquire the sound knowledge of nth derivatives of the product of two

function, reduction formula. Scientifically and graphically comprehend the nature of

function.

TBHM- 101 CO 2.Develop key ideas of Leibnitz rule, learn applications of asymptotes,

concavity & point of inflexion in curve tracing to examine the real-world situations.

TBHM- 101 CO 3.Elaborate the standards of essential to take care of an assortment of

fundamental issues such as length of parametric curves, polar co-ordinates in sciences.

TBHM- 101 CO 4.Propose the solution of Dirichlet’s integrals and Liouville’s extension

and its formulation.





References:

1. Thomas, G.B. and Finney, R.L., Calculus, Pearson Education, Delhi, 2005, 9th Ed.

2. Strauss, M.J., Bradley, G.L. and Smith, K. J., Calculus, Dorling Kindersley (India) P.

Ltd. (Pearson Education), Delhi, 2007, 3rdEd.

3. Anton, H., Bivens, I. and Davis, S., Calculus, John Wiley And Sons (Asia) P. Ltd.,

Singapore, 2002, 7th Ed.

4. Courant R., and John, F., Introduction to Calculus and Analysis (Volumes I & II),

Springer- Verlag, New York, Inc., 1989.

CO-PO Matrix Calculus TBHM-101

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBHM-

101CO1 2 3 3 2 3 _ _ 2 3 _ 2 2

TBHM-

101CO2 2 3 2 1 2 _ _ 2 2 _ 2 1

TBHM-

101CO3 2 2 2 1 2 _ _ 1 2 _ 3 1

TBHM-

101CO4 2 2 3 2 3 _ _ 2 3 _ 1 2

Average CO

(TBHM-101) 2 2.5 2.5 1.5 2.5 _ _

1.7

5 2.5 _ 2 1.5

Mode of Evaluation

Internal (MM-40) External (MM-60)

Component Sessional -1 Sessional -2 Assignments End Semester Examination

Weightage 10 10 20 60






Course Code PBHM - 101 Credit 1


Course Name Calculus Lab


1. To visualize and to draw curve through curve tracing, concavity and convexity. Plotting

of graph of complex functions.

2. To sketch and evaluate arc length. Obtain area of surface of revolution through graphical

methods.

3. Classification and properties of conics and sketching of conics.

List of Practical’s

(i) Plotting of graphs of function eax + b, log (ax + b), 1/ (ax + b), sin (ax + b), cos (ax + b),

|ax + b| and to illustrate the effect of a and b on the graph.

(ii) Plotting the graphs of polynomial of degree 4 and 5, the derivative graph, the second

derivative graph and comparing them.

(iii) Sketching parametric curves (Eg. Trochoid, cycloid, epicycloids, hypocycloid).

(iv) Obtaining surface of revolution of curves.

(v) Tracing of conics in Cartesian coordinates/ polar coordinates.

(vi) Matrix operation (addition, multiplication, inverse, transpose).


PBHM- 101 CO 1. Construction of the graph of function to demonstrate the outcome of

different parameters to diagram.

PBHM- 101 CO 2. Sketch and trace the cartesian, parametric and polar curve with the

method of POSTAR by using the imagination capabilities.

PBHM- 101 CO 3. Improve the capacity of utilizing geometrical understanding of

mathematics in examining true issues of science and innovation.

References:

1. Thomas, G.B. and Finney, R.L., Calculus, Pearson Education, Delhi, 2005, 9th Ed.

2. Strauss, M.J., Bradley, G.L. and Smith, K. J., Calculus, Dorling Kindersley (India) P.

Ltd. (Pearson Education), Delhi, 2007, 3rd Ed.

3. Anton, H., Bivens, I. and Davis, S., Calculus, John Wiley and Sons (Asia) P. Ltd.,

Singapore, 2002, 7th Ed.

4. Courant R., and John, F., Introduction to Calculus and Analysis (Volumes I & II),

Springer- Verlag, New York, Inc., 1989.





CO-PO Matrix Calculus Lab PBHM-101

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

PBHM-

101CO1 2 2 2 1 1 _ _ _ 3 _ 3 2

PBHM-101

CO2 2 3 2 2 2 _ _ 2 2 _ 2 2

PBHM-101

CO3 2 3 2 3 2 _ _ 1 3 _ 2 _

Average CO

(PBHM-101) 2 2.6 2 2 1.7 _ _ 1.5 2.6 _ 2.3 2

Mode of Evaluation

Internal Practical (MM-25) External Practical (MM-25)

Internal Assessment External Assessment

Weightage 25 25





Programme Name B.Sc (Hons.) Mathematics Programme Code 26

Course Code TBHM-102 Credit 5


Course Name Algebra


1. To develop the basic concept of graphical representation of complex numbers.

2. To identify the relations and Functions, and its applications.

3. To derive the Division and Euclidean algorithms and evaluate the Congruence relation

between integers.

4. To learn the concept of Systems of linear equations and Provide the knowledge to find

Eigen values, and Eigen Vectors and its applications.

UNIT- I (Total Topics- 4 and Hrs- 8)

Polar representation of complex numbers, nth roots of unity, De Moivre’s theorem for rational

indices and its applications.


Equivalence relations, Functions, Composition of functions, Invertible functions, One to one

correspondence and cardinality of a set, Well-ordering property of positive integers.


Division algorithm, Divisibility and Euclidean algorithm, Congruence relation between

integers, Principles of Mathematical Induction, statement of Fundamental Theorem of

Arithmetic.

UNIT-IV (Total Topics -8 and Hrs-9)

Systems of linear equations, row reduction and echelon forms, vector equations, the matrix

equation Ax = b, solution sets of linear systems, applications of linear systems, linear

Independence.


Introduction to linear transformations, matrix of a linear transformation, inverse of a matrix,

characterizations of invertible matrices. Subspaces of 𝑅𝑛, dimension of subspaces of 𝑅𝑛and

rank of a matrix, Eigen values, Eigen Vectors and Characteristic Equation of a matrix.


TBHM-102 CO 1.Acquire the basic knowledge of arithmetic operations on complex number

and evaluated the argument of Complex numbers by using appropriate techniques.

TBHM-102 CO 2.Apply the matrix principle to examine the quantitative & qualitative

aspects of resolutions of mathematical models in scientific areas. & understand the concept

of different algebraic systems of equations.

TBHM-102 CO 3.Develop the critical thinking skills by using Principles of mathematical

induction and fundamental theorem of arithmetic.

TBHM-102 CO 4.Acquire knowledge of equivalence relations on sets and various types of

functions with application in real word.

References:

1. Andreescu, T. and Andrica D.,Complex Numbers from A to Z, Birkhauser.





2. Goodaire, E.G. and Parmenter M. M., Discrete Mathematics with Graph Theory, Pearson

Education (Singapore) P. Ltd., Indian Reprint, 3rd Ed.

3. Lay ,D.C., Linear Algebra and its Applications, Pearson Education Asia, Indian Reprint,

2007, 3rdEd.

CO-PO Matrix Algebra TBHM-102

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBHM-102

CO1 3 - 2 2 3 - - 1 3 - 1 2

TBHM-102

CO2 3 2 2 2 2 - - 2 1 2 1 2

TBHM-102

CO3 3 3 - - - - - 1 1 1 3 1

TBHM-102

CO4 3 2 2 2 2 - - 2 3 2 1 2

Average CO

(TBHM-102) 3.0 2.3 2.0 2.0 2.3 - - 1.5 2.0 1.7 1.5 1.8

Mode of Evaluation









Course Code TBHG-103 Credit 4


Course Name Fundamental of Computers


1. To describe the organization and operation of acomputer system, primary and secondary

memory, input, output devices.

2. To discuss the basic concepts of DOS and windows operating system.

3. Toidentify the various computer networks and the components used for networking.

4. To understand thefundamentals of number system like binary decimal, octal and

hexadecimal.

UNIT- I (Total Topics- 15 and Hrs.- 8)

Basics of Hardware and Software

Introduction to computers, primary memory, secondary memory, hardware, software, types

of software-system software, application software, history of computers, data and

information, input devices, output devices, generation of computer languages, compiler,

assembler, interpreter.

UNIT- II (Total Topics -18 and Hrs-10)

Operating System and its Functions

Introduction to DOS, operating system, types of operating system-batch processing system,

real time operating system, need of operating system, multitasking, introduction to DBMS,

concept of primary key, candidate key, super key, data redundancy, inconsistency, DBMS

v\s file system, applications of DBMS, types of attributes, integrity constraint, domain

constraint.


Number System

Introduction to number system, binary number system, octal number system, hexa-decimal

number system, interconversion of number system, 1’s complement, 2’s complement, logic

gates, binary addition, subtraction, BCD & gray codes.


Fundamentals of Computer Network

Introduction to computer networks, client-server architecture, LAN, MAN, WAN,

advantages of computer network, modes of transmission, protocols, network topologies,

Introduction to transmission media, OSI reference model, functions of various layers of OSI.

UNIT-5: (Total Topics -12 and Hrs-8)

Basics of Software Engineering

Introduction to software engineering, software development life cycle, software development

models-water fall model, prototype model, types of software testing-black-box testing, white

box testing, alpha testing, beta testing, acceptance testing.






TBHG-103 CO 1.Acquire the knowledge about basic concepts of hardware and software

components and the role of these components in professional life as well as in daily life.

TBHG-103 CO 2.Know the difference between DOS and windows operating system.

TBHG-103 CO 3.Solve numerical problems by using binary subtraction, binary addition

and interconversion of binary number system.

TBHG-103 CO 4.Analyze the knowledge regarding computer networks, different

components of networking and also get to know various internet related concepts.

TBHG-103 CO 5.Attain knowledge and apply software development models and techniques

to implement, design, maintain and test a software system.

References:

1. Sinha , P. K. , Computer Fundamentals , BPB publications.

2. Rajaraman ,V. , Fundamentals of Computers, Prentice Hall.

3. Goel , A., Computer Fundamentals, Pearson.

4. Thareja , R., Computer fundamentals and programming in C, Oxford Publication.

5. Balagurusamy, E., Computer Fundamentals and C Programming, TMH.

6. Silveschatza, P. J., Operating System Concepts , Willey.

7. Das,S., Unix Concepts and applications, TMH, 2003.

CO-PO Matrix Fundamental of Computers TBHG-103

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBHG-

103CO1

- - - - 1 1 1 - - - 1 1

TBHG-

103 CO2

- - - - 1 - - 1 - - - -

TBHG-

103 CO3

- - - - 1 1 - 1 - - - -

TBHG-

103 CO4

- - - - 2 - 1 1 - - - -

TBHG-

103 CO5

- - - 1 1 1 1 - - - 1

Average

CO

(TBHG-

103)

- - - - 1.2 0.6 0.6 0.8 - - 0.2 0.4

Mode of Evaluation




https://www.google.co.in/search?tbo=p&tbm=bks&q=inauthor:%22V.+Rajaraman%22

https://www.google.co.in/search?tbo=p&tbm=bks&q=inauthor:%22Prentice+Hall+India+Pvt.,+Limited%22





Programme Name B. Sc (H) Mathematics Programme Code 26

Course Code PBHG-103 Credit 2


Course Name Fundamental of Computers (Lab)


1. To provide basic ideas related to operating system, DOS commands, use of operating

systems.

2. To familiarize students with installation of operating system and the use of system tools.

3. To provide knowledge about different computer application MS-Word, MS-Power point,

MS-Excel.

Experiments: At least 08 experiments from the following:

1. Getting familiar with Operating System

2. Creating File & folders, Renaming files, performing various operations on the file

3. DOS commands- CD, MKDIR, DATE, DIR, TIME, CALANDER, HELP CAT, TYPE,

MV CP, RENAME, BREAK etc.

4. Creating slides using Power points.

5. Creating resume using MS-word & practice on all other formatting system

6. Creating the Excel sheets &apply the basic formulas.

7. Creating E-mail account, Sending & receiving mail, File attachments.

8. Installation of Operating System

9. How to make Bootable Storage device

10. How to make a static web page using HTML.


PBHG-103 CO 1. Demonstrate and understanding the fundamental of software installation,

E-mail account and apply application software in an office environment.

PBHG-103 CO 2. Apply various HTML/CSS tags for creating webpages.

PBHG-103 CO 3. Identify the different types of operating system and their functions. Which

will be used in skill development.

PBHG-103 CO 4. Create documents that makes student efficient in the use of word

documents, spreadsheets and presentation applications.

References:

1. Rajaraman, V., Fundamentals of Computers, PHI,2004,4thEd.

2. Sinha, P.K and Priti, Computer fundamentals , BPB , 2003, 6thEd.





CO-PO Matrix Fundamental of Computers PBHG-103

Course Outcome P

O1

P

O2

P

O3

P

O4

P

O5

P

O6

P

O7

P

O8

PS

O1

PS

O2

PS

O3

PS

O4

PBHG-103CO1 - - - - 1 1 1 2 - - - -

PBHG-103 CO2 - - - - 1 - - 1 - - - -

PBHG-103 CO3 - - - - 2 - 1 2 - - 1 1

PBHG-103 CO4 2 - - - 2 - 1 1 - - 1 2

Average CO

(PBHG-103)

0.5 - - - 1.5 0.2 0.7 1.5 - - 0.5 0.75

Mode of Evaluation



Weightage 25 25








Course Name Object Oriented Programming in C++


1. To provide thorough knowledge of Object-Oriented Programming Using C++ and

2. To enhance the programming skills of the students by giving practical assignments to be

done in labs.

UNIT- I (Total Topics- 7 and Hrs.- 8)

OOP Paradigm: Comparison of Programming paradigms, Characteristics of Object-Oriented

Programming Languages, Object-based programming languages C++.


Brief History of C++, Structure of a C++ program, Difference between C and C++ - cin,

cout, new, delete operators, ANSI/ISO Standard C++, Comments, Working with Variables

and const Qualifiers.


Enumeration, Arrays and Pointer. Implementing oops concepts in C++ Objects, Classes,

Encapsulation, Data Abstraction, Inheritance, Polymorphism, Dynamic Binding, Message

Passing, Default Parameter Value,Using Reference variables with Functions.


Abstract data types, Class Component, Object & Class, Constructors Default and Copy

Constructor, Assignment operator deep and shallow coping, Access modifiers – private,

publicand protected. Implementing Class Functions within Class declaration or outside the

Class declaration. instantiation of objects, Scope resolution operator, Working with Friend

Functions,

UNIT-5: (Total Topics -13 and Hrs-10)

Using Static Class members. Understanding Compile Time Polymorphism function

overloading Rules of Operator Overloading (Unary and Binary) as member function/friend

function, Implementation of operator overloading of Arithmetic Operators, Overloading

Output/Input,Prefix/ Postfix Increment and decrement Operators, Overloading comparison

operators, Assignment, subscript and function call Operator , concepts of namespaces.


TBHG-103 CO 1. Assess an object – oriented approach to the development of software

based on modelling objects from the real world.

TBHG-103 CO 2. Categorize a set of OOPs concepts and a language-independent graphic

notation, the Object Modeling method which can be used to analyze problem requirements,

propose a solution to the problem and then implement the solution in a programming

language.

TBHG-103 CO 3. Formulate an OO software development methodology from analysis,

through design, to implementation and comparison of high-level, conceptual analytics and

design processes.





TBHG-103 CO 4. Construct an abstract way of thinking about a problem using concepts of

the real world, rather than computer concepts.

TBHG-103 CO 5. Illustrate the logic of overloading and overriding, functions, inheritance,

polymorphism and file handling. Contrast the major OOPs strategies for implementation of

programs using C++.

References:

1. Venugopal, A. R., Rajkumar, and Ravishanker, T. Mastering C++, TMH, 1997.

2. Lippman, S. B. and Lajoie, J.,C++ Primer, Addison Wesley, 2000,3rd Ed.

3. Eckel, B,Thinking in C++, President, Mindview Inc., Prentice Hall,2nd Ed.

4. Parasons, D.,Object Oriented Programming with C++, BPB Publication.

5. Stroustrup,,The C++ Programming Language, Addison Welsley, 3rd Ed.

CO-PO Matrix Object Oriented Programming in C++

TBHG-103

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBHG-

103CO1 3 3 2 2 3 - - - 3 - 1 -

TBHG-103

CO2 2 3 2 3 3 - - - 2 - 3 -

TBHG-103

CO3 2 1 1 2 2 - - - 2 - 2 -

TBHG-103

CO4 2 2 2 1 2 - - - 2 - - -

TBHG-103

CO5 3 2 2 3 2 - - - 2 - 2 -

Average CO

(TBHG-103) 2.4 2.2 1.8 2.2 2.4 - - - 2.2 - 2 -

Mode of Evaluation








Programme Name B. Sc (H) Mathematics Programme Code 26



Course Name Object Oriented Programming in C++ (Lab)


1. To evaluate the problem-solving techniques by using the basic concepts of C ++

language.

2. To understand the fundamental of flowchart and algorithm to develop the programs and

to solve the problems.

3. To acquire knowledge about C++ language program structure.

1. Simple C++ Programs to Implement “If and loop” Control Structures.

2. Write a C++ program to show the use of object and classes.

3. Write a C++ program to show the concept of inheritance.

4. Write a C++ program to demonstrate the concept of constructor and destructor.

5. Write a C++ program to show function overloading

6. Write a C++ program to show the implementation of function overriding.

7. Write a C++ program to Understand Friend Function & Friend Class.

8. Write a C++ program to show the use of copy constructor


PBHG-103 CO 1. Create the C++ program for given algorithm and flowchart.

PBHG-103 CO 2. Solve real time problems by using objects and classes.

PBHG-103 CO 3. Create any application by applying logics and concepts of C++ language

like constructor, function overloading and Inheritance.

References:

1. Venugopal, A. R., Rajkumar, and Ravishanker, T. Mastering C++, TMH, 1997.

2. Lippman, S. B. and Lajoie, J.,C++ Primer, Addison Wesley, 2000,3rd Ed.

3. Eckel, B,Thinking in C++, President, Mindview Inc., Prentice Hall,2nd Ed.

4. Parasons, D.,Object Oriented Programming with C++, BPB Publication.

5. Stroustrup,,The C++ Programming Language, Addison Welsley, 3rd Ed.





CO-PO Matrix Object Oriented Programming in C++Lab PBHG-103

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

PBHG-

103CO1

- - - - 1 1 1 2 - - - -

PBHG-103

CO2

- - - - 1 - - 1 - - - -

PBHG-103

CO3

- - - - 2 - 1 2 - - 1 1

Average CO

(PBHG-103)

- - - - 1.5 0.2 0.7 1.5 - - 0.5 0.75

Mode of Evaluation



Weightage 25 25






Course Code TBEC -104 Credit 2


Course Name English Communication


The specific objectives of this course are to develop in the student the ability to demonstrate

the following:

1. Understanding of the process of communication and its classification

2. Writing,Listening and Speaking skills

3. Assessment and critical analysis of literary texts

4. Reflect effective communication and overcome the barriers to communication enable

self-directed learning

5. Proper usage of language skills to communicate in professional situations to enhance the

competency.

UNIT- I (Total Topics- 7and Hrs- 5)

English Writing Skills

Grammar& Vocabulary:

1.1 Parts of Speech

1.2 Tenses

1.3 Agreement of Verb with Subject

1.4 Antonym and synonym

1.5 One word substitution

1.6 Homophones

1.7 Jargons, Prefix and Suffix


Reading Skills:

2.1 Process of Reading skills, Importance of Reading skills, Methods to improve reading

skills.

Some Literature based reading:

Poem:

2.2 “If” by Rudyard Kipling

2.3 “Stopping by the woods on a snowy evening” by Robert Frost

Stories:

2.4 “Under a Banyan tree” by R.K.Narayan

2.5 “The Eyes are not here” by Ruskin Bond

Value based Prose:

2.6 Abraham Lincoln’s Letter to his son’s teacher

2. 7 “I Have a Dream” by Martin Luther king

UNIT- III (Total Topics 4- and Hrs-10)

Business Correspondence:

3.1 Memorandum, Notice, Agenda, Minutes of the meeting





3.2 Business letters: Sales, Inquiry, Complaint

3.3 Job Application and Resume writing

3.4 Report writing : Feature, Structure, Types


Communication:

4.1 Communication: Meaning, Types, Process, Barriers

4.2 Listening skills, Process,types, Methods to improve listening skills

4.3 Speaking skills, Conversation, Stress, Intonation.


TBEC -104 CO 1.Understand the meaning and the process of communication along with its

types and barriers.

TBEC -104 CO 2.Develop proficiency in English Language through vocabulary building

and correct use of grammar.

TBEC -104 CO 3.Acquire competency in reading and listening by understanding the skills

involved and assessing &analyzing literary texts critically.

TBEC -104 CO 4.Form a clear concept of writing style in technical communication and

develop technical writing skills.

TBEC -104 CO 5.Develop speaking skills by understanding the basic concepts and enhance

proficiency in verbal and non- verbal communication.

References:

1. Revathi, S., Communicating Effectively in English, Book-I ,Abhishek Publications,

Chandigarh.

2. Sasikumar ,V. and Dhamija, P.V., Spoken English, Tata McGraw Hill.

3. Aslam, M., Introduction of English Phonetics and Phonology, Cambridge.

4. Pal and Rorualling , Essentials of Business Communication , Sultan Chand and Sons.

5. Kohli ,A.L., New Design English Grammar, Reading and Writing Skills ( Course A

and Course B ), Kohli Publishers, 34 Industrial Area Phase- II, Chandigarh.

6. Raina, M.K., Developing English Communication, Orient Blackswan.

7. Krishna Mohan and Banerji, M., Developing Communication Skills, MacMillan

India

8. Sharma ,S.D., Communication Skills,Natraj Publishing House, Karnal

9. Thomson and Marlinet, A Practical English Grammar.

10. Wren and Martin , High School Grammar and Composition, S. Chand & Company

Ltd., Delhi





CO-PO Matrix English Communication TBEC-104

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBEC-104

CO1 3 - - - - 3 - - 1 - 2 1

TBEC-104

CO2 3 - - - - 3 - - 1 - 2 1

TBEC-104

CO3 3 - - - - 3 - - 1 - 2 1

TBEC-104

CO4 3 - 1 - - 3 - -- 1 - 2 1

TBEC-104

CO5 3 - - - - 3 - - 1 - 2 1

Average CO

(TBEC-104) 3 - 1 - - 3 - - 1 - 2 1

Mode of Evaluation









Course Code PBHA-105 Credit 1


Course Name Educational Visit


1. To widen the understudy's frame of reference and worldwide social mindfulness through

connection with the expert specialists.

2. To provide students a chance to relate the study to the present reality circumstances.

3. To supplement class room program with field visits and profession centered agenda.

4. To enable the students to recognize and explore the non-test research.

Students will visit the scientific and educational places and will study the impact of different

aspects socially and economically and will prepare summary report.


PBHA-105 CO 1.Analyze many ground real factors and a chance to associate and talk about

with the business heads/academicians.

PBHA-105 CO 2.Carries to all the students to a typical stage independent of their social,

monetary and cultural foundation.

PBHA-105 CO 3.Appraise to discover answers for genuine issues and makes them inventive.

PBHA-105 CO 4.Opportunity to advance and be on their own which improves relational

abilities and makes them all the more explorative.

CO-PO Matrix Educational Visit PBHA -105

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

PBHA-105

CO1 2 2 2 _ _ 2 2 2 _ _ 1 _

PBHA-105

CO2 2 2 2 2 _ 2 2 _ _ _ 2 _

PBHA-105

CO3 2 2 3 2 _ 2 _ 2 _ _ 2 _

PBHA-105

CO4 2 2 2 2 _ 2 2 2 _ _ 1 _

Average CO

(PBHA -105) 2 2 2.2 2 _ 2 2 2 _ _ 1.5 _

Mode of Evaluation



Weightage 25 25





SEMESTER -II








Course Name Real Analysis


1. To demonstrate the Algebraic properties & order properties of Real Numbers.

2. To develop a basic knowledge of important mathematical concepts in real analysis such

as neighborhood, isolated point, bounded or unbounded sets and limit point.

3. To acquire the knowledge of completeness property of Real numbers for rational and

irrational number.

4. To learn the concept of Sequence and series and their tests for convergence or

divergence.

UNIT-I (Total Topics- 14 and Hrs- 9)

Review of Algebraic and Order Properties of R, 𝛿-neighborhood of a point in R, Idea of

countable sets, uncountable sets and uncountability of R. Bounded above sets, Bounded

below sets, Bounded Sets, Unbounded sets, Suprema and Infima.


The Completeness Property of R, TheArchimedean Property, Density of Rational (and

Irrational) numbers in R, Intervals. Limit points of a set, Isolated points, Illustrations of

Bolzano-Weierstrass theorem for sets.


Sequences, Bounded sequence, Convergent sequence, Limit of a sequence. Limit Theorems,

Monotone Sequences, Monotone Convergence Theorem.


Subsequences, Divergence Criteria, Monotone Subsequence Theorem (statement only),

Bolzano Weierstrass Theorem for Sequences. Cauchy sequence, Cauchy’s Convergence

Criterion.


Infinite series, convergence and divergence of infinite series, Cauchy Criterion, Tests for

convergence: Comparison test, Limit Comparison test, Ratio Test, Cauchy’s nth root test,

Integral test, Alternating series, Leibniz test, Absolute and Conditional convergence.


TBHM-201 CO 1.Enhance the knowledge regarding basic properties of the field of real

numbers and improved and outline the logical thinking.

TBHM-201 CO 2.Define and recognized the series of real numbers and convergence and

enhanced the critical thinking ability.

TBHM-201 CO 3.Acquire the knowledge of convergence and divergence of series using

interpretation of data and appropriate tools and techniques.

TBHM-201 CO4.Apply the application of real analysis in multidisciplinary environment.

References:

1. Bartle,R.G.andSherbert, D. R., Introduction to Real Analysis, John Wiley and Sons

(Asia) Pvt. Ltd., Singapore, 2002, 3rd Ed.





2. BilodeauG. G., Thie ,P. R., Keough, G. E., An Introduction to Analysis, Jones & Bartlett,

2010, 2nd Ed.

3. Thomson, B. S., Bruckner, A.M. and Bruckner, J. B., Elementary Real Analysis, Prentice

Hall, 2001.

4. Berberian, S.K., A First Course in Real Analysis, Springer Verlag, New York, 1994.

CO-PO Matrix (Real Analysis) TBHM-201

Course

Outcom

e

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBHM-

201CO1 2 _ _ _ _ _ _ 2 3 _ 1 3

TBHM-

201CO2 2 _ _ _ _ _ _ 2 2 _ 2 2

TBHM-

201CO3 1 2 1 _ 3 _ _ 2 2 _ _ 2

TBHM-

201CO4 2 2 1 _ _ _ _ _ 1 _ 3 1

Averag

e CO

(TBHM

-201)

1.7

5 2 1 _ 3 _ _ 2 2 _ 2 2

Mode of Evaluation











Course Name Differential Equations


1. To identify a differential equation and evaluate by apply appropriate analytical

techniques.

2. To understand DE’s of 1st order as well as separable, exact, homogeneous and linear &

compute existence and uniqueness of differential equations.

3. To solve higher order linear D. E’s. Determine central solutions and independence using

the Wronskian.

4. To create and analyze mathematical models.

UNIT-I (Total Topics- 15 and Hrs.- 10)

Differential equations and mathematical models. General, particular, explicit, implicit and

singular solutions of a differential equation. Exact differential equations and integrating

factors, separable equations and equations reducible to this form, linear equation and

Bernoulli equations, special integrating factors and transformations.


General solution of homogeneous equation of second order, principle of super position for

homogeneous equation, Wronskian: its properties and applications.


Linear homogeneous and non-homogeneous equations of higher order with constant

coefficients, Euler’s equation, method of undetermined coefficients, method of variation of

parameters.


Introduction to compartmental model, exponential decay model, lake pollution model (case

study of Lake Burley Griffin), drug assimilation into the blood (case of a single cold pill,

case of a course of cold pills).


Exponential growth of population, limited growth of population, limited growth with

harvesting.


TBHM-202 CO 1.Develop critical thinking by identifying, analyzing and afterward

evaluate physical conditions whose comportment could defined by ODE’s.

TBHM-202 CO 2.Elaborate the use of appropriate techniques such as existence and

uniqueness theorems.

TBHM-202 CO 3.Propose the solution of higher order differential equations and explain

importance of technique’s as Wronskian.

TBHM-202 CO 4.Determine the solution and formulation of mathematical models using

differential equations.

References:





1. Barnes,B. and Fulford,G.R, Mathematical Modeling with Case Studies, A Differential

Equation Approach using MAPLE and MATLAB, Taylor and Francis group, London

and New York, 2009, 2nd Ed.

2. Edwards C.H., and Penny, D.E., Differential Equations and Boundary Value problems

Computing and Modeling, Pearson Education, India, 2005.

3. Ross, S.L., Differential Equations, John Wiley and Sons, India, 2004,3rd Ed.

4. Abell, M.L., Braselton, J.P., Differential Equations with MATHEMATICA, Elsevier

Academic Press, 2004, 3rdEd.

CO-PO Matrix Differential Equations TBHM-202

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBHM-

202CO1 3 3 2 2 1 _ 2 3 2 2 _ 2

TBHM-202

CO2 2 2 2 1 2 _ _ 1 2 2 _ _

TBHM-202

CO3 2 2 1 2 2 _ _ 1 2 2 _ _

TBHM-202

CO4 2 2 3 2 1 _ 2 3 2 2 _ 2

Average CO

(TBHM-202)

2.2

5

2.2

5 2

1.7

5 1.5 _ 2 2 2 2 _ 2

Mode of Evaluation









Course Code PBHM – 202 Credit 1


Course Name Differential Equations Lab


1. To design and develop the various mathematical models and construct the differential

equation and propose solutions.

2. To sketch the graphical representations of integral surfaces of PDE.

3. To determine the convergence of sequences through graphical representations.


1. Plotting of second order solution family of differential equation.

2. Plotting of third order solution family of differential equation.

3. Growth model (exponential case only).

4. Decay model (exponential case only).

5. Lake pollution model (with constant/seasonal flow and pollution concentration).

6. Case of single cold pill and a course of cold pills.

7. Limited growth of population (with and without harvesting).

8. Battle model (basic battle model, jungle warfare, long range weapons).

9. Plotting of recursive sequences.

10. Study the convergence of sequences through plotting.

11. Cauchy’s root test by plotting nth roots.

12. Ratio test by plotting the ratio of nth and (n+1)th term.


PBHM-202 CO 1.Create, identify, analyze and solve the mathematical models to

understand the real-world problems.

PBHM-202 CO 2.Elaborate appropriate techniques such as characteristics method, method

of separation of variables to sketch the graph of integral surfaces of PDE.

PBHM-202 CO 3.Enhance advance knowledge and critical thinking ability by graphing

the ratios of sequence and series.

References:

1. Barnes, B. and Fulford, G.R., Mathematical Modeling with Case Studies, A Differential

Equation Approach using MAPLE and MATLAB, Taylor and Francis group, London

and New York, 2009, 2nd Ed.

2. Edwards C.H., and Penny, D.E., Differential Equations and Boundary Value problems

Computing and Modeling, Pearson Education, India, 2005.

3. Ross, S.L., Differential Equations, John Wiley and Sons, India, 2004, 3rd Ed.

4. Abell, M.L., Braselton, J.P., Differential Equations with MATHEMATICA, Elsevier

Academic Press, 2004, 3rd Ed.





CO-PO Matrix Differential Equations Lab PBHM-202

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

PBHM-

202CO1 2 3 2 3 2 _ 2 3 2 3 2 2

PBHM-202

CO2 2 2 2 2 2 _ _ 1 _ 2 2 _

PBHM-202

CO3 2 2 2 2 2 _ _ 2 _ 2 2 _

Average CO

(PBHM-202) 2

2.3

3 2

2.3

3 2 2 2 2 2 2.33 2 2

Mode of Evaluation



Weightage 25 25








Course Name Concepts of Programming


1. To understand the basic concepts of C language.

2. To understand the fundamental of flowchart and algorithmto develop logics and design

new ideas.

3. To acquire knowledge about C language syntax, declaration of variables and different

data types.

UNIT-I (Total Topics- 10and Hrs.- 12)

OOPs and Basics of C Introduction to C, variables, constants, keywords, conditional

statements, procedural language, object oriented language, features of OOPs, data types,

format specifiers, flow-chart, algorithms, operator precedence and associativity, complexity

of algorithm, factors influencing complexity of algorithm.


Fundamentals of loops

Introduction to loops, use of for, while, do-while loop, relational and logical operators,

Introduction to printf () and scanf () functions, nesting of loops, switch statement, difference

between while and do-while loop.


Functions

Introduction to functions, advantages of function, types of function: function with no return

type and no argument, function with no return type with argument, function with return type

and no argument, function with return type and with argument, storage classes, recursion.


Array and structures

Array, structures, advantages of structure over array, strings, string handling functions, use

of gets() and puts, difference between gets and scanf().


Pointers and dynamic memory allocation

Introduction to pointers, call by value and call by reference, static memory allocation,

dynamic memory allocation, memory allocation using calloc(), malloc() and realloc(),

printing a string using pointers, pointers and arrays, pointers and structures, 2-D array.


TBHG-203CO 1. Create the flowchart and an algorithm to develop C program for any

problem.

TBHG-203CO 2. Solve real time problems by using user defined functions.

TBHG-203CO 3. Construct any applicationby applying logics and concepts of C language

like conditional statements and iterative statements.

TBHG-203CO 4. Acquire knowledge about the use of pointers,strings, functions and arrays.





TBHG-203CO 5. Compose C program and familiar with the concept of structures and

unions.

References:

1. BalaGuruswamy, E.,Programming In C,TMH Publications.

2. Kanetkar, Let us C.

CO-PO Matrix Concepts of Programming TBHG-203

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBHG-

203CO1 1 - - 1 1 - 1 1 - - 1 1

TBHG-203

CO2 - - - - 1 - 1 1 - - - 1

TBHG-203

CO3 - - - - 1 - 1 2 - - 1 1

TBHG-203

CO4 - - - - 1 - 1 1 - - - -

TBHG-203

CO5 - - - - 1 - 1 1 - - - -

Average CO

(TBHG-203 ) 0.2 - - 0.2 1 - 1 1.2 - - 0.4 0.6

Mode of Evaluation








Programme Name B.Sc.(H) Math’s Programme Code 26



Course Name Concepts of Programming (Lab)


1. To evaluate the problem-solving techniques by using the basic concepts of C language.

2. To understand the fundamental of flowchart and algorithm to develop the programs and

to solve the problems.

3. To acquire knowledge about C language program structure.

At least 14 experiments from the following:

1. WAP to check that the given number is even or odd.

2. WAP of swapping two numbers without using third variable.

3. WAP to find the fibonacci series up to the given limit.

4. WAP to find that the given year is leap year or not.

5. WAP to find that the given number is prime or not.

6. WAP to insert and delete number from given array.

7. WAP to find the factorial of a given number using function.

8. WAP to check for armstrong number.

9. WAP to add two numbers using pointers.

10. WAP to read and print name and other details of 50 students using Structure.

11. WAP in c to print any string using pointers.

12. WAP in c to find factorial of any number using recursion.

13. WAP in c to show nesting of loops.

14. WAP in c to swap two numbers using call by reference.

15. WAP in c to show the use of string handling functions.


PBHG-203CO 1.Create the C program for given algorithm and flowchart.

PBHG-203CO 2.Solve real time problems by using arrays, pointers and structures.

PBHG-203CO 3.Create any application by applying logics and concepts of C language like

derived data types, operators

References:

1.BalaGuruswamy, E.,Programming In C, TMH, 2003,3rd Ed..

2.Thareja, R., Computer fundamentals and programming in C, Oxford, 2016, 2nd Ed.

3.Kanetkar, Yashwant ,Let us C, BPB , 2017 , 4th Ed.





CO-PO Matrix Concepts of Programming (Lab)PBHG-203

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

PBHG-

203CO1 - - 1 - 1 - 1 2 - - 1 1

PBHG-

203CO2 - - - - 1 - 1 1 - - 1 1

PBHG-

203CO3 - - - 1 2 1 - 1 - - - 1

Average CO

(PBHG-203 ) - - 0.3 0.3 1.3 0.3 0.6 1.3 - - 0.6 1

Mode of Evaluation



Weightage 25 25








Course Name DBMS and Networking Concepts


1. To present an introduction to database management systems, with an emphasis on how

to organize, maintain and retrieve - efficiently, and effectively - information from a

DBMS.

2. Also, it includes learning about computer network organization and implementation,

obtaining a theoretical understanding of data communication and computer networks,

3. Gaining practical experience in installation, monitoring, and troubleshooting of current

LAN systems


Introduction: An overview of database management system, database system Vs file system,

Database system concepts and architecture, data models schema and instances, data

independence and data base language and interfaces, Data definitions language, DML, Data

Modeling using the Entity Relationship Model: ER model concepts, notation for ER diagram,

mapping constraints, keys, Concepts of Super Key, Candidate key, primary key, weak entity

sets, reduction of an ER diagrams to tables, Extended ER features.


Relational data Model and Language: Relational data model concepts, integrity constraints:

entity integrity, referential integrity, Keys constraints, Domain constraints, relational

algebra, Introduction to SQL: Characteristics of SQL. Advantage of SQL. SQL data types

and literals. Types of SQL commands. SQL operators and their procedure. Tables, views,

Queries and subqueries. Aggregate functions. Insert, update and delete operations. Joins,

Unions, Intersection, Minus.


History of Internet, Introduction to web(www), protocols governing the web- HTTP-SMTP

etc., web development strategies, Web applications, web project, web team. Interactive and

social web: Blogs, wikis, and social networking sites – The technology behind these

applications.


Introduction Concepts: Goals and Applications of Networks, Network structure and

architecture, Network categories(LAN, MAN, WAN), The OSI reference model, services,

Network Topologies, Back Bone Design. Physical Layer Transmission Media, ISDN.


TBHG-203CO 1. Discover the challenges of Database and classify different DBMS services

and deployment models.

TBHG-203CO 2. Find importance of E-R model along with their notations in DBMS.

TBHG-203CO 3. Create, select, and apply appropriate queries to analyze different type of

information.

TBHG-203CO 4. Survey of modern challenges in networking technologies.





References:

1. Date, C.J. An Introduction to Database Systems, Pearson Education; (2006) 8 edition.

2. Andrew S. T., Computer Networks, Pearson; (27 September 2010) 5 edition

3. Forouzan,B. A.,Data Communications And Networking (Sie) Paperback – 20 May 2006

4. SilberschatzDatabase System Concepts Paperback – 1 Dec 2013,Korth, McGraw Hill

Education India Private Limited; (1 December 2013), Sixth edition.

CO-PO Matrix DBMS and Networking ConceptsTBHG-203

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBHG-

203CO1

1 1 - 1 1 - - - 2 - 1 1

TBHG-203

CO2

1 1 3 1 - - - - 1 1 2 1

TBHG-203

CO3

1 1 1 - 2 - - - 2 - 2 2

TBHG-203

CO4

1 1 - 1 3 - - - 3 1 1 1

Average CO

(TBHG-203 )

1 1 2 1.5 2 - - - 2 1 1.5 1.2

Mode of Evaluation




http://www.amazon.in/Andrew-S.-Tanenbaum/e/B000AQ1UBW/ref=dp_byline_cont_book_1

http://www.amazon.in/s/ref=dp_byline_sr_book_1?ie=UTF8&field-author=Behrouz+A.+Forouzan&search-alias=stripbooks

http://www.amazon.in/s/ref=dp_byline_sr_book_1?ie=UTF8&field-author=Silberschatz&search-alias=stripbooks





Programme Name B.Sc.(Hons.) Mathematics Programme Code 26



Course Name DBMS and Networking Concepts (Lab)


1. Learn basic concepts of computer networking and acquire practical notions of protocols

with the emphasis on TCP/IP.

2. A lab provides a practical approach to Ethernet/Internet networking: networks are

assembled, and experiments are made to understand the layered architecture and how do

some important protocols work.

3. Objective of this lab includes to provide a strong formal foundation in database

concepts, technology and practice to the participants to groom them into well-informed

database application developers.

1. Write the queries for Data Definition and Data Manipulation Language.

2. Write SQL queries using logical operations (=, <,>, etc)

3. Write SQL queries using SQL operators

4. Write SQL query using character, number, date and group functions

5. Execute the following Network Oriented Commands (with all their options) and observe

their Output:

a. PING

b. TRACERT

c. ROUTE

d. IPCONFIG

e. ARP

f. NETSTAT

g. NBTSTAT

h. HOSTNAME

i. NETSEND

j. DNS Configuration

6. Formation of data cable.


PBHG-203CO 1. Write the queries for Data Definition and Data Manipulation Language.

PBHG-203CO 2. Write SQL queries using SQL operators as well as Logical Operators

(=,>, <) etc.

PBHG-203CO 3. Write SQL queries for relational algebra and referential Integrity.

PBHG –204 CO4: Write SQL queries for extracting data from more than one table.

PBHG –204 CO5: Execute network-oriented commands-Netstat, Ping, Route, Ipconfig,

ARP.

References:

1. Date, C.J. An Introduction to Database Systems, Pearson Education; (2006) 8 edition.





2. Andrew S. T., Computer Networks, Pearson; (27 September 2010) 5 edition

3. Forouzan, B. A., Data Communications And Networking (Sie) Paperback – 20 May 2006

4. Silberschatz Database System Concepts Paperback – 1 Dec 2013,Korth, McGraw Hill

Education India Private Limited; (1 December 2013), Sixth edition.

CO-PO Matrix DBMS and Networking Concepts (Lab)PBHG-203

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

PBHG-

203CO1

1 1 - 1 1 - - - 1 - 2 2

PBHG-

203CO2

1 1 2 - 2 - - - - 1 2 1

PBHG-

203CO3

1 1 2 - 2 - - - 1 - 1 2

PBHG-

203CO4

1 1 2 - 2 - - - - - 1 2

PBHG-

203CO5

1 1 - - - - - - - - 2 1

Average

CO

(PBHG-

203 )

1 1 2 1 1.7

5

- - - 1 1 1.6 1.6

Mode of Evaluation



Weightage 25 25

http://www.amazon.in/Andrew-S.-Tanenbaum/e/B000AQ1UBW/ref=dp_byline_cont_book_1

http://www.amazon.in/s/ref=dp_byline_sr_book_1?ie=UTF8&field-author=Behrouz+A.+Forouzan&search-alias=stripbooks

http://www.amazon.in/s/ref=dp_byline_sr_book_1?ie=UTF8&field-author=Silberschatz&search-alias=stripbooks






Course Code TBES-204 Credit 2


Course Name Environmental Science


1. Fundamental concepts related to Environmental Studies to be introduced in a simple

manner.

2. To make students aware of natural resources, their importance, and problems of

environmental pollution.

3. To create awareness about environmental acts related to wildlife, forest etc.

UNIT-I (Total Topics- 16 and Hrs- 8)

Introduction to environmental studies & Natural Resources, Multidisciplinary nature of

environmental studies, Scope and importance: Concept of sustainability and sustainable

development., Land resources: Land degradation, soil erosion and desertification.

Deforestation: Causes and impacts due to mining, dams- benefits and problems

Water: Use and over--‐exploitation of surface and ground water, floods, droughts, conflicts

over water (international & inter--‐state).

UNIT-II Ecosystem& Biodiversity (Total Topics – 14 and Hrs-7)

Ecosystem & Biodiversity

Ecosystem- Structure and function of ecosystem; Energy flow in an ecosystem: food chains,

food webs Ecological Pyramids. Biodiversity: Classification: genetic, species and ecosystem

diversity. Values of Biodiversity. Biogeographic zones of India; Hot spots of India, India as

a mega-biodiversity nation; Endangered and endemic species of India.

Threats to biodiversity: Habitat loss, poaching of wildlife, man--‐wildlife conflicts,

Conservation of biodiversity: In-situ and Ex-situ conservation of biodiversity.

UNIT- III Environmental Pollution (Total Topics -8 and Hrs-8)

Environmental Pollution

Environmental pollution: Air Pollution: causes, effects and control measures.

Water Pollution: Sources, effects and control measures.

Noise Pollution: causes effects and Limits of noise as prescribed by CPCB

Nuclear hazards and Human health risks

Solid waste management: Control measures of urban and industrial waste.


Environmental Issues: Climate change, Global warming, Ozone layer depletion, Acid rain

Disaster management: floods, earthquake, cyclones and landslides.


Environmental Ethics, Policies & Practices

Environmental Ethics, Environmental movements: Chipko, Silent valley, Bishnois of

Rajasthan, Environment Laws: Environment Protection Act; Wildlife Protection Act; Forest

Conservation Act. International agreements: Montreal and Kyoto protocols.

Course Outcomes (COs)





TBES-204CO 1. Master foundational knowledge enabling them to have life –long learning

related to one’s surroundings.

TBES-204CO 2. Develop critical thinking skills in relation to environmental affairs and

articulate multidisciplinary context of the subject.

TBES-204CO 3. Acquire knowledge about natural resources and assess aesthetic and

ethical importance of all the living flora and fauna.

TBES-204CO 4. Interpret and propose solutions for effective management of different

types of environmental pollution

TBES-204CO 5. Keep updated and communicate knowledge regarding social issues and

laws related to environment.

References:

1. Kaushik, A., Environmental Studies.

2. Barucha ,E., Environmental Studies.

3. Deswal&Deswal, Environmental Studies.

CO-PO Matrix Environmental Science TBES-204

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBES-204

CO1

2 - - - - 1 1 2 1 - - 2

TBES-204

CO2

2 - - - - 1 1 2 1 - - 2

TBES-204

CO3

2 - - - - 1 1 2 1 - - 2

TBES-204

CO4

2 - - - - 1 1 2 1 - - 2

TBES-204

CO5

2 - - - - 1 1 2 1 - - 2

Average CO

(TBES-204)

2 - - -- - 1 1 2 1 -- - 2

Mode of Evaluation









Course Code TBHE -205 Credit 2


Course Name Human Ethics & Professional Values


1. To enable the students to understand the significance of Values and Ethical Behavior in

the personal and Professional lives.

2. To understand the correct appraisal of human needs by learning about self and body.

3. To appreciate family values and also to learn how to establish and develop harmony in

family and society.

4. To appreciate the significance of universal order by understanding harmony in nature.

5. To address the ethical issues that arises in the work environment and also to understand

the importance of a Holistic perspective in human life

6. To develop ability to develop scope and characteristics of eco friendly techniques.

UNITI (Total Topics- 3 and Hrs- 5)

Course Introduction &self-exploration: Need, Basic Guidelines, Content and Process for

Value Education, Relationship and Physical Facilities- the basic requirements for fulfillment

of aspirations of every human being with their correct priority, Understanding Happiness

and Prosperity correctly- A critical appraisal of the current scenario

UNIT II (Total Topics -3 and Hrs-5)

Understanding of human being as a co-existence of the sentient ‘I’ and the material ‘Body’:

Understanding the needs of Self (‘I’) and ‘Body’ - Sukh and Suvidha. Understanding the

harmony of I with the Body: Sanyam and Swasthya; correct appraisal of Physical needs,

meaning of Prosperity in detail


Understanding Harmony in the Family and Society: Harmony in Human-Human

Relationship, Trust (Vishwas) and Respect (Samman) as the foundational values of

relationship, Understanding the meaning of Samman, Difference between respect and

differentiation, Visualizing a universal harmonious order in society- concept of Undivided

Society (Akhand Samaj).


Understanding Harmony in the Nature and Existence:Whole existence as Co-existence,

(Sah-astitva

UNIT: 5 (Total Topics -4 and Hrs-5)

Implications of Holistic Understanding of Harmony on Professional Ethics:

Ability to identify the scope and characteristics of people-friendly and eco-friendly

production systems, technologies and management models, Natural acceptance of human

values, Definitiveness of Ethical HumanConduct, Basis for Humanistic Education,

Humanistic Constitution and Humanistic Universal Order. Competence in Professional

Ethics. Ability to identify the scope and characteristics of people-friendly and eco-friendly

production systems, technologies and management models






TBHE -205CO 1. Recognize the role of ethics in human life and to apply creative thinking

to fulfill the aspirations of every human being.

TBHE -205CO2.Understand the dimension of ethical human conduct and to determine how

values can be converted to rules of behavior that can be derived as ethics. Understand the

correct appraisal of physical needs.

TBHE -205CO3. Delineate the difference between respect and differentiation and analyze

the concept of undivided society in real life.

TBHE -205CO4. Describe how different orders in nature have mutually fulfilling

coexistence, develop the ability of identifying people-friendly and eco-friendly production

systems, and understand the implication of holistic understanding of harmony on

professional ethics.

References:

1. Gaur, R.R,Sangal,R,Bagaria,G.P., A Foundation Course in Human Values and

Professional Ethics, Excel Books, New Delhi, 2009.

2. Nagraj, A.,JeevanVidyaEkParichay,Divya Path Sansthan, Amarkantak, 1998.

3. Tripathy, A.N. , Human Values, New Age International Publishers, 2003.

4. Seebauer,E.G.& Berry, R.L., Fundamentals of Ethics for Scientists & Engineers,

Oxford University Press ,2000.

CO-PO Matrix Human Ethics and Professional Values (TBHE-205)

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBHE-

205C01 - - - - - - - - 1 - - -

TBHE-

205C02 - - - - - - - - 1 - - -

TBHE-

205C03 - - - - - - 3 - 1 - - -

TBHE-

205C04 - - - - - - 3 - 1 - - -

Average

CO(TBH

E-205)

- - - - - - 3 - 1 - - -

Mode of Evaluation








SEMESTER -III








Course Name Theory of Real Functions


1. To expose the student to fundamental properties of real number.

2. To develop the deep understanding of limit, continuity and differentiability of functions.

3. To improve the ability to solve critical problems in mathematical analysis.

4. To assess of fundamental properties of real function in basic research and scientific

problems.

UNIT- I (Total Topics- 10 and Hrs-09)

Limits of functions ( 𝜖 − 𝛿 approach), sequential criterion for limits, divergence criteria.

Limit theorems, one sided limits. Infinite limits and limits at infinity. Continuous functions,

sequential criterion for continuity and discontinuity.


Algebra of continuous functions. Continuous functions on an interval, intermediate value

theorem, location of roots theorem, preservation of intervals theorem. Uniform continuity,

non-uniform continuity criteria, uniform continuity theorem.


Differentiability of a function at a point and in an interval, Caratheodory’s theorem, algebra

of differentiable functions. Relative extrema, interior extremum theorem.


Rolle’s theorem, Mean value theorem, intermediate value property of derivatives, Darboux’s

theorem. Applications of mean value theorem to inequalities and approximation of

polynomials, Taylor’s theorem to inequalities.


Cauchy’s mean value theorem. Taylor’s theorem with Lagrange’s form of remainder,

Taylor’s theorem with Cauchy’s form of remainder, application of Taylor’s theorem to

convex functions, relative extrema. Taylor’s series and Maclaurin’s series expansions of

exponential and trigonometric functions, ln (1 + x), 1/ ax+b and (1 + 𝑥)𝑛.


TBHM-301CO 1. Acquire the knowledge about fundamental properties of the real numbers

and that lead to the formal development of pure mathematics.

TBHM-301 CO 2. Demonstrate deep understanding of limits, continuity and

differentiability of real function in abstract ways and how they are applicable in engineering

and scientific problems.

TBHM-301 CO 3. Develop the logical thinking to proof the basic and standard results of

mathematical analysis.

TBHM-301 CO 4. Create and analyze theories, methods and interpretations that develop

critical thinking skills and advance mathematical knowledge.

References:

1. Bartle, R. and Sherbert ,D.R., Introduction to Real Analysis, John Wiley and Sons.

2. Ross, K.A., Elementary Analysis: The Theory of Calculus, Springer, 2004.





3. Mattuck, Introduction to Analysis, Prentice Hall, 1999.

4. Ghorpade, S.R. and Limaye, B.V.,A Course in Calculus and Real Analysis, Springer.

CO-PO Matrix-Theory of Real Functions TBHM-301

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PS

O4

TBHM-

301CO1

3 2 2 2

2 3

2 2

TBHM-

301CO2

3 3 3 1 1

3 3 2 3 2

TBHM-

301CO3

3 2 2 2

2 2

1 1

TBHM-

301CO4

3 3 2 2

2 2

3 2

Average

CO

(TBHM-

301)

3.0 2.5 2.3 1.8 1.0

2.3 2.5 2.0 2.3 1.8

Mode of Evaluation








Programme Name B. Sc (Hons.) Mathematics Programme Code 26



Course Name Group Theory-I


1. To develop the relationships between basic abstract algebraic structures and number

systems.

2. To develop a basic knowledge of important mathematical concepts in abstract algebra

such as group, subgroup, cyclic group and order of group.

3. To be familiar with normal subgroups, quotient group, permutation group and Abelian

group and understand the structure and characteristics of these groups.

4. To understand the important concepts of homeomorphisms and isomorphism in group

theory

UNIT-I (Total Topics- 06 and Hrs-09)

Symmetries of a square, Dihedral groups, definition and examples of groups including

permutation groups and quaternion groups (illustration through matrices), elementary

properties of groups.


Subgroups and examples of subgroups, centralizer, normalizer, center of a group, product of

two subgroups.


Properties of cyclic groups, classification of subgroups of cyclic groups. Cycle notation for

permutations, properties of permutations, even and odd permutations, alternating group.


properties of cosets, Lagrange’s theorem and consequences including Fermat’s Little

theorem. External direct product of a finite number of groups, normal subgroups, factor

groups, Cauchy’s theorem for finite abelian groups.


Group homomorphisms, properties of homomorphisms, Cayley’s theorem, properties of

isomorphism, First, Second and Third isomorphism theorems.


TBHM-302 CO 1. Identify and analyze the properties of algebraic structure called group.

TBHM-302 CO 2. Acquire the basic knowledge of Cyclic Groups, Normal Subgroup and

Quotient group.

TBHM-302 CO 3. Analyze the notion of permutations graphically and analytically.

TBHM-302 CO 4. Develope the capability of critical thinking about isomorphism and

homomorphism and analyzed its applications

References:

1. Fraleigh, J.B., A First Course in Abstract Algebra, Pearson, 2002, , 7th Ed.

2. Artin, M., Abstract Algebra, Pearson, 2011, 2nd Ed.

3. Gallian, J. A., Contemporary Abstract Algebra , Narosa Publishing House, New Delhi,

1999, 4th Ed.





4. Rotman, J. J., An Introduction to the Theory of Groups, Springer Verlag, 1995, 4th Ed.

5. Herstein, I.N., Topics in Algebra, Wiley Eastern Limited, India, 1975.

CO-PO Matrix (Group Theory-I) TBHM-302

Course

Outcome

PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PSO1 PSO2 PSO3 PSO4

TBHM-

302 CO1

2 2 1 1 _ _ _ 2 3 _ 2 2

TBHM-

302 CO2

3 _ _ 1 _ _ _ 1 3 _ 1 2

TBHM-

302 CO3

1 2 2 _ 2 _ _ 1 3 _ 1 1

TBHM-

302 CO4

3 3 2 1 2 _ _ 3 3 _ 2 2

Average

CO

(TBHM-

302)

2.3 2.3 1.7 1.0 2.0 _ _ 1.8 3.0 _ 1.5 1.8

Mode of Evaluation











Course Name PDE and system of ODE


1. To be competent in solving applied problems associated to various form of PDE.

2. To develop the use of appropriate techniques such as analytical and numerical methods.

3. To obtain the solution of heat’s equation, wave’s equation & Laplace’s equation.

4. To describe canonical forms and systems of linear differential equations.


Partial Differential Equations – Basic concepts and Definitions, Mathematical Problems.

First-Order Equations: Classification, Construction and Geometrical Interpretation. Method

of Characteristics for obtaining General Solution of Quasi Linear Equations. Canonical

Forms of First-order Linear Equations. Method of Separation of Variables for solving first

order partial differential equations.


Derivation of Heat equation, Wave equation and Laplace equation. Classification of second

order linear equations as hyperbolic, parabolic or elliptic. Reduction of second order Linear

Equations to canonical forms.


The Cauchy problem, the Cauchy-Kowaleewskaya theorem, Cauchy problem of an infinite

string. Initial Boundary Value Problems, Semi-Infinite String with a fixed end, Semi-Infinite

String with a Free end, Equations with non-homogeneous boundary conditions, Non-

Homogeneous Wave Equation.


Method of separation of variables, Solving the Vibrating String Problem, Solving the Heat

Conduction problem.


Systems of linear differential equations, types of linear systems, differential operators,

anoperator method for linear systems with constant coefficients, Basic Theory of linear

systems in normal form, homogeneous linear systems with constant coefficients: Two

Equations in two unknown functions, The method of successive approximations, the Euler

method, the modified Euler method, The Runge-Kutta method.


TBHM-303 CO 1.Develop critical thinking by identifying, analyzing& subsequently

explaining physical circumstances by using PDE & ODE.

TBHM-303 CO 2.Elaborate the use of appropriate techniques such as analytical and

numerical.

TBHM-303 CO 3.Evaluate practical problems of ODE & PDE and Learn to create

mathematical models.

TBHM-303 CO 4.Propose the solutions and classifications of PDE through initial and

boundary situations and its reduction to canonical forms.





References:

1. Tyn,M.U. and Debnath,L,Linear Partial Differential Equations for Scientists and

Engineers, Springer, Indian reprint, 2006, 4th Ed..

2. Ross, S.L., Differential equations, John Wiley and Sons, India, 2004, 3rd Ed.

3. Abell M. L. and Braselton J.P., Differential equations with MATHEMATICA, Elsevier


CO-PO Matrix PDE and System of ODE TBHM-303

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PS

O1

PS

O2

PS

O3

PS

O4

TBHM-

303CO1 3 3 2 2 _ _ _ 2 _ 3 2 1

TBHM-

303CO2 2 2 2 2 2 _ _ 2 _ 2 2 1

TBHM-

303CO3 3 2 2 2 3 _ _ 2 _ 3 2 1

TBHM-

303CO4 2 3 2 2 2 _ _ 2 _ 2 3 1

Average CO

(TBHM-303) 2.5 2.5 2 2 2.3 _ _ 2 _ 2.5 2.2 1

Mode of Evaluation









Course Code PBHM - 303 Credit 1


Course Name PDE and Systems of ODE Lab


1. To obtain the solution of Cauchy problem for first order PDE and to find its characteristic

equations.

2. To identify the various form of PDE and to plot the integral surfaces of PDE.

3. To propose the solution of Heat equation and Wave equation with various associated

conditions.



PBHM-303 CO 1.Create, identify, analyze and solve the heat equation, wave equation &

Laplace equation to understand the real-world problems.

PBHM-303 CO 2.Discuss appropriate techniques such as characteristics method, method

of separation of variables to sketch the graph of integral surfaces of PDE.

PBHM-303 CO 3.Enhance critical thinking ability by solving Cauchy initial value and

boundary value problems.

References:

1. Tyn, M.U. and Debnath, L, Linear Partial Differential Equations for Scientists and

Engineers, Springer, Indian reprint, 2006, 4th Ed.





2. Ross, S.L., Differential equations, John Wiley and Sons, India, 2004, 3rd Ed.

3. Abell M. L. and Braselton J.P., Differential equations with MATHEMATICA, Elsevier


CO-PO Matrix PDE and System of ODE Lab PBHM-303

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

PBHM-303

CO1

3 2 2 1 1 _ _ 2 1 3 3 2

PBHM-303

CO2

2 2 2 1 3 _ _ 1 _ 2 2 _

PBHM-303

CO3

3 2 2 1 2 _ _ _ _ 2 _ _

Average CO

(PBHM-303)

2.6 2 2 1 2 _ _ 1.5 _ 2.33 2.5 2

Mode of Evaluation



Weightage 25 25








Course Name Total Quality Management


1. To appraise the students about concept of ISO & various standards.

2. To appraise management systems with documentation required for development of

organization with its sustainability.

3. To appraise about regulatory bodies with specifications requirements for environment

protection.

4. To do assessment and analysis of data by using modern tools like statistical methods

for problem analysis

UNIT- I (Total Topics-12 and Hrs-08)

TQM & QMS

Definition of quality, quality product, General introduction about ISO & History, various

standards, TQM definition, Introduction about QMS-ISO 9001 General, Scope &

Applications of QMS, Terms & definitions used in QMS, Process approach(PDCA

cycle),General Requirements of ISO 9001, Documentation , Quality Policy, Quality

objectives, customer satisfaction, Nonconformance of product ,corrective and preventive

action.

UNIT-II (Total Topics -15 and Hrs-08)

EMS & OHSAS

Scope & Applications of EMS & OHSAS, Terms & definitions used in EMS & OHSAS ,

General & Legal Requirements of ISO 14001 & ISO 18001, Documentation, EIA,

significant aspect-impact analsyis, introduction about EPA, . Introduction about regulatory

bodies, CPCB & SPCB. EPA /CPCB Standards for discharge of effluents from common

chemical industries. , Training & Emergency Preparedness, non-conformance & corrective

action


Other ISO standards

Introduction about ISO 22000(FSMS) , 27000(ISMS) & 50000( Energy Management

System) . Hazard Analysis and Critical Control Points (HACCP),ISO for Food Industry,

introduction about GMP(good manufacturing process), cGMP& Concept of house keeping

(5S), Concept of six sigma in Industry.


Measurement & Analysis of data -1 Statistical Analysis of data Statistical methods of

analysis of data, mean, mode, median, standard deviation, standard error, t-test, chi-square





test, correlation& regression. Statistical quality control, introduction about SPSS. Concept

of control charts. Use of computers for analysis of data.


Measurement & Analysis of data -2

General definition, concept of Permutation (nPr) concept of combination (nCr) and

Probability. Applications of permutation, combination and probability.


TBHG-304CO 1. Understanding of concept of quality, ISO & various standards.

TBHG-304 CO 2. Learning of various management systems with SOPs, six sigma & 5S

TBHG-304 CO 3. Well verse with regulatory bodies and environmental standards for

environment protection.

TBHG-304 CO 4. Knowledge about assessment and analysis of data by using modern

computational & statistical methods for problem solution.

References:

1. Singh, A, Total Quality Management and Outlook on TQM,Vani Publication.

2. Evans, J.R. and Lindsay, W.M., Total Quality Management, ,Cengage Learning.

CO-PO Matrix Total Quality Management TBHG-304

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBHG-

304CO1

1 2

1

2

TBHG-

304CO2

3 2

3

TBHG-

304CO3

3

3

TBHG-

304CO4

1 1 2

2

3

3

Average CO

(TBHG-304)

1 2 2.3 1

2

3 2

2.75

Mode of Evaluation











Course Name Intellectual Property Rights


1. To explain about Intellectual Property and Copyrights

2. To explain about software patents and their importance.

3. To gain knowledge about trade marks

4. To layout design of integrated circuits and Industrial Designs

5. To Illustrate layout design and Different International Agreements


Introduction to Intellectual Property: Historical Perspective, Different Types of IP,

Importance of protecting IP.

Copyrights: Introduction, How to obtain, Differences from Patents.


Trade Marks: Introduction, How to obtain, Different types of marks – Collective marks,

certification marks, service marks, Trade names, etc, Differences from Designs.

Patents: Historical Perspective, Basic and associated right, WIPO, PCT system, Traditional

Knowledge, Patents and Healthcare-balancing promoting innovation with public health,

Software patents and their importance for India.


Geographical Indications: Definition, rules for registration, prevention of illegal

exploitation, importance to India.

Industrial Designs: Definition, How to obtain, features, International design registration.

Layout design of integrated circuits: Circuit Boards, Integrated Chips, Importance for

electronic industry.


Trade Secrets: Introduction and Historical Perspectives, Scope of Protection, Risks

involved and legal aspects of Trade Secret Protection.


(a) Word Trade Organization (WTO):

(i) General Agreement on Tariffs & Trade (GATT), Trade Related Intellectual Property

Rights (TRIPS) agreement

(ii) General Agreement on Trade related Services (GATS),

(iii) Madrid Protocol

(iv) Berne Convention, (v) Budapest Treaty

(b) Paris ConventionWIPOand TRIPS, IPR and Plant Breeders Rights, IPR and Biodiversity

IP Infringement issue and enforcement – Role of Judiciary, Role of law enforcement

agencies – Police, Customs etc. Economic Value of Intellectual Property – Intangible assets

and their valuation, Intellectual Property in the Indian Context – Various laws in India

Licensing and technology transfer.


TBHG-304CO 1. Acquire knowledge about Intellectual property rights, copyrights,

trademarks and patents.





TBHG-304 CO 2. Appraise about geographical indications, industrial designs, trade secrets

and different international agreements including paris convention, Budapest treaty etc.

TBHG-304 CO 3. Analyze layout designs of integrated circuits, risks involved in trade

secret protection, international design registration, rules for registration of geographical

indications etc.

TBHG-304 CO 4. Assess introduction and historical perspectives of trade secrets, working

of WTO, Madrid protocol, different type of IPs, trademarks, copyrights etc.

References:

1. Acharya, N.K.: Textbook on intellectual property rights, Asia Law House (2001).

2. Guru, M,&Rao, M.B., Understanding Trips: Managing Knowledge in Developing

Countries, Sage Publications (2003).

3. Ganguli, P. ,Intellectual Property Rights: Unleashing the Knowledge Economy, Tata

McGraw-Hill (2001),71

4. Miller,A,R,MichealH.Davis; Intellectual Property: Patents, Trademarks and Copyright

in a Nutshell, West Group Publishers (2000).

5. Watal, J., Intellectual property rights in the WTO and developing countries, Oxford

University Press, Oxford.

CO-PO Matrix Intellectual Property RightsTBHG-304

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBHG-304

CO1

1

1

2 1

TBHG-304

CO2

2

1

1 2

TBHG-304

CO3

1

1

1 1

TBHG-304

CO4

1

1

1 1

Average

CO

(TBHG-

304)

1

1

1 1

Mode of Evaluation











Course Name Statics


1. To derive principle of virtual work, Work done by the tension and thrust of an extensible

string and its applications.

2. To provide knowledge of stable and unstable equilibrium position.

3. To develop important concepts of centre of gravity and catenary and its applications

4. To identify an equilibrium of forces in three dimensions.


Virtual Works: Definitions of virtual displacement and virtual work done, Difference

between work done and virtual work done with examples, The principle of virtual work,

Work done by the tension and thrust of an extensible string during a small displacement,

Some solved problems.


Equilibrium: Stable and unstable equilibrium, Moments and couples and Varignon’s

theorem of moments and some solved problems


Centre of Gravity: Definition centre of gravity (C.G.) and examples, A system of particles

lying in a line, A number of particles lying in a plane, Compound body, Remainder body,

Uniform plane curve, Plane area, An area enclosed between two curves and solved problems


Strings in Two Dimensions: Definition and examples of catenary, Definitions axis of the

catenary, Vertex of the catenary, Parameter of the catenary, Directrix of the catenary, Span

and Sag of the catenary. Intrinsic and cartesian equations of common catenary, Some

important relations for the common catenary, Approximation to the common catenary and

sag of tightly stretched wires (definitions and examples).


Equilibrium in Three Dimensions: Equilibrium of forces in three dimensions, Wrench and

screw, Pitch of the wrench and solved problems.


TBHG-304CO 1. Acquire the basic knowledge of resultant, component of a force, coplanar

forces, moment of a force and couple with examples, virtual work, virtual displacement for

extensible and inextensible string and thrust and its applications in real life and engineering

problems.

TBHG-304 CO 2. Develop critical thinking skills and apply the statics to precise advance

problems in math’s, engineering, physics or in additional areas..

TBHG-304 CO 3. Acquire the basic knowledge of centre of gravity for a system of particles

lying in line, plane, and compound body, uniform plane curve, enclosed by two curves and

applied in mechanical and civil engineering for real life problems.





TBHG-304 CO 4. Propose the ideas of equilibrium for two and three dimensions, stable and

unstable, and its applications in society.

References:

1. Verma, R. S., A Text Book on Statics, PothishalaPvt. Ltd., Allahabad.

2. Loney, S. L., An Elementary Treatise on Statics, Kalyani Publishers, New Delhi.

CO-PO Matrix Statics TBHG-304

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PS

O1

PS

O2

PS

O3

PS

O4

TBHG-304CO1 3 - 2 2 3 - - 1 3 1 1 2

TBHG-304CO2 3 3 2 - - - - 1 1 - 3 1

TBHG-304CO3 3 2 2 2 2 - - 2 2 2 1 2

TBHG-304CO4 3 1 - 1 2 - 1 2 1 - 1 2

Average CO

(TBHG-304) 3.0 2.0 2.0 1.7 2.3 -

1.0 1.5 1.8 1.5 1.5 1.8

Mode of Evaluation











Course Name Logic and Sets


1. To provide sound knowledge about axiomatic set theory and elementary logics.

2. To expose the student to properties of integers, real or complex numbers, sets, relations,

cardinalities and functions.

3. To understand the construction of un-quantified or quantified arguments by reproducing

valid examples.

4. To develop ability to translate real world problem into mathematical statements and

solution, interpretations of those problems.


Introduction, propositions, truth table, negation, conjunction and disjunction. Implications,

bi-conditional propositions, converse, contra positive and inverse propositions and

precedence of logical operators.


Propositional equivalence: Logical equivalences. Predicates and quantifiers: Introduction,

Quantifiers, Binding variables and Negations.

UNIT-III (Total Topics -13 and Hrs-05)

Sets, subsets, Set operations and the laws of set theory and Venn diagrams. Examples of

finite and infinite sets. Finite sets and counting principle. Empty set, properties of empty set.

Standard set operations. Classes of sets. Power set of a set.


Difference and Symmetric difference of two sets. Set identities, Generalized union and

intersections.


Relation: Product set, Composition of relations, Types of relations, Partitions, Equivalence

Relations with example of congruence modulo relation, Partial ordering relations, binary

relations.


TBHG-305 CO 1.Analyze and determine the truth value of quantified sentences, given its

universal set by constructing truth value table or by applying the concept of solution sets.

TBHG-305 CO 2.Construct un-quantified or quantified arguments by reproducing valid

examples in deducing a tautology or laws of deduction/inference.

TBHG-305 CO 3.Justify propositions related to the properties of integers, real or complex

numbers, sets, relations, cardinalities and functions.

TBHG-305 CO 4.Synthesis symbolic laws of logic to natural science languages and develop

tools and techniques for the application in engineering and technology.

References:

1. Grimaldi, R.P., Discrete Mathematics and Combinatorial Mathematics, Pearson

Education.





2. Kamke, E., Theory of Sets, Dover Publishers, 1950.

CO-PO Matrix- Logic and Sets TBHM-305

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBHM-

305CO1

3 3 3 2

- - 2 3

2 2

TBHM-

305CO2

3 2 3 2 2 - - 2 3 2 3 2

TBHM-

305CO3

3 2 2 3

- - 2 3 2 2 2

TBHM-

305CO4

3 3 2 3 2 - - 2 2 3 3 3

Average CO

(TBHM-

305)

3.0 2.5 2.5 2.5 2.0 - - 2.0 2.8 2.3 2.5 2.3

Mode of Evaluation









Course Code TBHM – 305 Credit 2


Course Name Computer Graphics


1. To introduce the use of the components of a graphics system and become familiar with

building approach of graphics system components and algorithms related with them.

2. To learn the basic principles of 3- dimensional computer graphics.

3. Provide an understanding of how to scan convert the basic geometrical primitives, how

to transform the shapes to fit them as per the picture definition.

4. Provide an understanding of mapping from a world coordinates to device coordinates,

clipping, and projections.


Introduction to computer Graphics: Raster Scan and Random Scan display, aspect ratio,

CRT, displays processors and character generators, color display techniques, interactive

input/output devices.


Points, lines and curves: Scan conversion, line-drawing algorithms, circle and ellipse

generation, polygon filling antialiasing. Two-dimensional viewing: Coordinate systems,

linear transformations, line and polygon clipping algorithms.


TBHM – 305 CO 1. Implement of various scan, convert the basic geometrical primitives,

transformations, Area filling, clipping algorithms.

TBHM – 305 CO 2. Discuss the application of computer graphics concepts for the

development of computer games, information visualization, and business applications.

TBHM – 305 CO 3. Define the fundamentals of animation, virtual reality and its related

technologies.

TBHM – 305CO 4. Describe the significance of viewing and projections in real world

objects.

References:

1. Hearn, D., and Baker, M.P., Computer Graphics, Prentice–Hall of India, 2nd Ed.

2. Rogers, D.F., Procedural Elements in Computer Graphics, McGraw Hill Book

Company, 2001, 2nd Ed.,

3. Rogers, D.F., and Admas, A.J., Mathematical Elements in Computer Graphics, McGraw

Hill Book Company, 1990, 2nd Ed.





CO-PO Matrix-Computer Graphics TBHM-305

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBHM-

305CO1

1 2 - 2 3 - - - 1 2 - 1

TBHM-

305CO2

2 1 2 1 2 - - - 2 - 2 2

TBHM-

305CO3

1 1 2 2 2 - - - 1 1 2 1

TBHM-

305CO4

- 1 2 1 2 - - - 2 1 - 2

Average

CO

(TBHM-

305)

1 1.2

5

1.5 1.5 2.2

5

- - - 1.5 1 1 1.5

Mode of Evaluation









Course Code PBHS-306 Credit 1


Course Name Seminar


1. To provide the detail knowledge for preparing presentation and seminar.

2. To develop the concept of team work, presentation skills of data in conferences,

symposia , seminar etc.

3. To demonstrate knowledge and understand mathematical tools and techniques in

seminar.

Seminar: Participation/ paper presentation in the national /international conferences.


1. PBHS-306CO 1. Developed the idea for preparing presentation for their possible future

profession.

PBHS -306 CO 2. Enhanced the critical thinking skills, communication skills and build

team work for conferences, symposia, seminar etc.

PBHS -306 CO 3. Demonstrate the knowledge of mathematical tools and techniques for

presentations of research data in seminar and conferences.

CO-PO Matrix (Seminar) PBHS-306

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PSO

1

PSO

2

PSO

3

PSO

4

PBHS-

306 CO1 2 _ _ 2 3 _ 2 _ 2 1 2

PBHS -

306 CO2 _ 2 _ 2 3 _ 2 _ 2 2 2

PBHS -

306 CO3 1 _ _ 2 3 1 2 _ 2 2 2

Average

CO

(PBHS -

306)

1.5 2.0 _ 2.0 3.0 1.0 2.0 _ 2.0 1.7 2.0

Mode of Evaluation



Weightage 25 25





SEMESTER -IV








Course Name Numerical Methods


1. To learn the numerical techniques to solve algebraic and transcendental equations and it

applications.

2. To provide knowledge of system of linear equations and its applications

3. To develop the concept of interpolation and numerical integration.

4. To derive the numerical solution of initial value problems.


Algorithms, Convergence, Errors: Relative, Absolute, Round off, Truncation.

Transcendental and Polynomial equations: Bisection method, Newton’s method, Secant

method. Rate of convergence of these methods.


System of linear algebraic equations: Gaussian Elimination and Gauss Jordan methods.

Gauss Jacobi method, Gauss Seidel method and their convergence analysis.


Interpolation: Lagrange and Newton’s methods. Error bounds. Finite difference operators.

Gregory forward and backward difference interpolation.


Numerical Integration Trapezoidal rule, Simpson rule, Simpson 3/8 rule, Boole’s rule,

Midpoint rule, Composite Trapezoidal rule, Composite Simpson rule.


Ordinary Differential Equations: Euler’s method. Runge-Kutta methods of orders two and

four.


TBHM-401CO 1. Analyze the concept of error inherent in different numerical methods for

solution in real world problems.

TBHM-401CO 2. Propose ideas for finding numerical solution of algebraic and

transcendental equation by numerical methods to solve and analyses complex engineering

problems.

TBHM-401CO 3. Acquire the basic knowledge of method of interpolation for scientific

problems with consideration for industry, environment and society.

TBHM-401CO 4. Ability to assess and prepare the numerical solution of differential

equation, integral equation, linear and nonlinear polynomials.

References:

1. Bradie, B., A Friendly Introduction to Numerical Analysis, Pearson Education, India,

2007.





2. Jain, M.K., Iyengar, S.R.K. and Jain, R.K., Numerical Methods for Scientific and

Engineering Computation, New age International Publisher, India6th Ed.

3. Gerald, C.F. and Wheatley, P.O., Applied Numerical Analysis, Pearson Education, India,

2008.

4. Ascher, U. M. and Greif, C., A First Course in Numerical Methods, PHI Learning Private

Limited, 2013, 7th Ed.

5. Mathews, J.H. and Fink, K. D., Numerical Methods using Matlab, PHI Learning Private

Limited, 2012, 4th Ed.

CO-PO Matrix Numerical Methods TBHM-401

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PS

O1

PS

O2

PS

O3

PS

O4

TBHM-

401CO1 3 2 2 2 - - -

2 3 1 1 1

TBHM-

401CO2 3 2 2 2 1 - -

1 2 2 -

1

TBHM-

401CO3 3 1 2 2 2 -

1 2 2 - -

2

TBHM-

401CO4 3 2 1 -

1 - -

2 3 - -

2

Average CO

(TBHM-401) 3.0 1.8 1.8 2.0 1.3 -

1.0 1.8 2.5 1.5 1.0 1.5

Mode of Evaluation









Course Code PBHM-401 Credit 1


Course Name Numerical Methods Lab


1. To learn concept of different numerical methods with the help of C/C++ languages.

2. To provide basic knowledge of system of linear equations with the help of software.

3. To develop the concept of initial value problem, numerical integration and interpolation

with lab knowledge.


(i) Calculate the sum 1/1 + 1/2 + 1/3 + 1/4 + ----------+ 1/ N.

(ii) To find the absolute value of an integer.

(iii) Enter 100 integers into an array and sort them in an ascending order.

(iv) Bisection Method.

(v) Newton Raphson Method.

(vi) Secant Method.

(vii) RegulaiFalsi Method.

(viii) LU decomposition Method.

(ix) Gauss-Jacobi Method.

(x) SOR Method or Gauss-Siedel Method.

(xi) Lagrange Interpolation or Newton Interpolation.

(xii) Simpson’s rule.


PBHM-401CO 1. Application of techniques of different numerical methods for solution in

real world problems.

PBHM-401CO 2. Finding numerical solution of algebraic and transcendental equation by

numerical methods to solve engineering problems.

PBHM-401CO 3. Acquire the basic knowledge of method of interpolation and numerical

solution of differential equations with the help of C/C++ languages.

References:

1. Sharma, J. N., Numerical Methods for Engineers and Scientists, Narosa

2. Grewal, B. S., Numerical Methods for Engineering and Science with Program C & C++,

DhanpatRai

3. Jain, M. K., Iyengar, S. R. K. and Jain, R. K., Numerical Methods for Scientific and

Engineering Computation, 6th Ed., New age International Publisher, India.

4. Gerald, C. F. and Wheatley, P. O., Applied Numerical Analysis, Pearson Education,

India, 2008.

5. Ascher, Uri M. and Greif, Chen, A First Course in Numerical Methods, 7th Ed., PHI

Learning Private Limited, 2013.

6. Mathews, John H. and Fink, Kurtis D., Numerical Methods using Matlab, 4th Ed., PHI

Learning Private Limited, 2012.





CO-PO Matrix Numerical Methods Lab PBHM-401

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

PBHM-

401CO1 3 2 2 1 2 - -

2 3 2 3 2

PBHM-

401CO2 3 1 2 2 2 - -

1 3 1 3 2

PBHM-

401CO3 3 1 2 2 2 - -

2 2 -

2 1

Average CO

(PBHM-401) 3.0 1.3 2.0 1.7 2.0 - -

1.7 2.7 1.5 2.7 1.7

Mode of Evaluation



Weightage 25 25








Course Name Riemann Integration and Series of Functions


1. To understand and illustrate the theory & applications of the Riemann integral and

improper integrals, piece-wise continuous, uniform & point-wise convergence and

monotonic functions.

2. To illustrate a partition of an interval and Riemann sum for a function on a given interval.

3. To state the definitions of fundamental concepts in each integration theory and etc.

4. To learn the concept of Beta and Gamma function and their tests for convergence or

divergence.


Riemann integration; inequalities of upper and lower sums; Riemann conditions of

integrability. Riemann sum and definition of Riemann integral through Riemann sums;

equivalence of two definitions; Riemann integrability of monotone and continuous

functions.


Properties of the Riemann integral; definition and integrability of piecewise continuous and

monotone functions. Intermediate Value theorem for Integrals; Fundamental theorems of

Calculus. Improper integrals; Convergence of Beta and Gamma functions.


Pointwise and uniform convergence of sequence of functions. Theorems on continuity,

derivability and integrability of the limit function of a sequence of functions. Series of

functions.


Theorems on the continuity and derivability of the sum function of a series of functions;

Cauchy criterion for uniform convergence and Weierstrass M-Test.


Limit superior and Limit inferior. Power series, radius of convergence, Cauchy Hadamard

Theorem, Differentiation and integration of power series; Abel’s Theorem; Weierstrass

Approximation Theorem.


TBHM-402CO 1. Develop critical thinking by identifying, analyzing and subsequently

solved Riemann Integration and their applications.

TBHM-402CO 2. Application of appropriate techniques to study uniform &point-wise

convergence of sequence of function and its applications to real world situations.

TBHM-402CO 3. Obtain the idea of integral and its implementation’s, various theorems

and their explanations through their applications in multidisciplinary situation.

TBHM-402CO 4. Enhance critical thinking ability by learning application of Beta-gamma

functions, convergence theorem, piece-wise continuous and monotonic functions and its

advanced knowledge.





References:

1. Ross, K.A., Elementary Analysis, The Theory of Calculus, Undergraduate Texts in

Mathematics, Springer (SIE), Indian reprint, 2004.

2. Bartle, R.G. and Sherbert, D.R., Introduction to Real Analysis, John Wiley and Sons

(Asia) Pvt. Ltd., Singapore, 2002, 3rd Ed.

3. Denlinger, C. G., Elements of Real Analysis, Jones & Bartlett (Student Edition), 2011.

CO-PO Matrix (Riemann Integration and Series of Functions) TBHM-402

Course

Outcom

e

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBHM-

402CO

1 2 2 2 1 1 _ _ 1 3 _ 2 2

TBHM-

402CO

2 3 2 2 2 3 _ _ 1 2 _ _ 2

TBHM-

402CO

3 2 2 2 2 1 _ _ 2 2 _ 2 2

TBHM-

402CO

4 1 2 2 1 1 _ _ 2 1 _ 2 2

Averag

e CO

(TBHM

-402)

2 2 2 1.5 1.5 _ _ 1.5 2 _ 2 2

Mode of Evaluation











Course Name Ring Theory and Linear Algebra – I


1. To analyze the fundamental idea in ring theory and vector space.

2. To create depth knowledge about range, rank and nullity of linear transform.

3. To understand the important concepts of basis and dimension of vector space.

4. To explore the knowledge about ring homomorphism and ring isomorphism.


Definition and examples of rings, properties of rings, subrings, integral domains and fields,

characteristic of a ring. Ideal, ideal generated by a subset of a ring, factor rings, operations

on ideals, prime and maximal ideals.


Ring homomorphisms, properties of ring homomorphisms, Isomorphism theorems I, II and

III, field of quotients.


Vector spaces, subspaces, algebra of subspaces, quotient spaces, linear combination of

vectors, linear span, linear independence, basis and dimension, dimension of subspaces.


Linear transformations, null space, range, rank and nullity of a linear transformation,

matrixrepresentation of a linear transformation, algebra of linear transformations.


Isomorphisms, Isomorphism theorems, invertibility and isomorphisms, change of coordinate

matrix.


TBHM-403CO 1. Analyze the fundamental concepts in ring theory and vector space

TBHM-403CO 2. Application of ring homomorphism to enhance the capability of critical

thinking

TBHM-403CO 3. Application of appropriate techniques to formulate the proof of

theorems in ring theory and vector space

TBHM-403CO 4. Obtain in-depth understanding about range, rank and nullity of linear

transform and its applications

References:

1. Fraleigh, J.B., A First Course in Abstract Algebra, Pearson, 2002, 7th Ed.






3. Friedberg S.H. and Insel A.J., Spence,L.E.,Linear Algebra, Prentice Hall of India

Pvt. Ltd., New Delhi, 2004, 4th Ed.

4. Gallian, J.A., Contemporary Abstract Algebra, Narosa Publishing House, New

Delhi, 1999, 4th Ed.

5. Lang, S., Introduction to Linear Algebra, Springer, 2005,2nd Ed.

6. Strang, G., Linear Algebra and its Applications, Thomson, 2007.

7. Kumaresan, S., Linear Algebra- A Geometric Approach, Prentice Hall of India,1999.

8. Hoffman, K. and Kunze, R.A., Linear Algebra, Prentice-Hall of India Pvt. Ltd., 1971,

2nd Ed.

9. Wallace, D.A.R., Groups, Rings and Fields, Springer Verlag London Ltd., 1998.

CO-PO Matrix (Ring Theory-I) TBHM-403

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBHM-

403 CO1

2 3 2 _ _ _ _ 2 2 2 1 2

TBHM-

403 CO2

3 2 2 2 2 _ _ 1 1 _ 1 1

TBHM-

403 CO3

2 3 3 2 3 _ _ 1 1 1 3 2

TBHM-

403 CO4

2 1 3 1 1 _ _ 3 _ 2 2 1

Average

CO

(TBHM-

403)

2.3 2.3 2.5 1.7 2.0 _ _ 1.8 1.3 1.7 1.8 1.5

Mode of Evaluation











Course Name Non-Conventional Energy Resources


1. To know about non-conventional energy sources.

2. To understand NCER harvesting process.

3. To look out feature scope of renewable energy sources.

4. To analyze various non-conventional energy resources & their applications.


Introduction: Various non-conventional energy resources- Introduction, availability of Solar

Energy, Wind energy, Geothermal energy, Ocean thermal, Tidal and wave energy, Fuel cells,

& Their relative merits and demerits. Waste Recycling Plants.


Solar Cells & Solar Thermal Energy: Theory of solar cells Photovoltaic effect, Efficiency

of solar cells. Solar cell materials, solar cell power plant, limitations. Flat plate collectors

and their materials, applications and performance, focusing of collectors and their materials,

applications and performance; solar thermal power plants, thermal energy storage for solar

heating and cooling & limitations.


Geothermal Energy& Magneto-Hydrodynamics (MHD)

Resources of geothermal energy, Structure of earth’s interior, Site selection for geothermal

power plants, thermodynamics of geo-thermal energy Conversion-electrical conversion,

non-electrical conversion, Problems associated with geothermal conversion. Principle of

working of MHD Power plant, performance, Power output, efficiency and its limitations.


Fuel Cells, Thermo-Electrical and Thermionic Conversions

Principle of operation of an acidic fuel cell, Reusable cells, Ideal fuel cells, other types of

fuel cells and their Comparison, Efficiency and EMF of fuel cells, Operating characteristics

of fuel cells, Advantages of fuel cell power plants. Thermo-Electrical and Thermionic

Conversions- Principle of working, performance and limitations.


Wind Energy: Wind power and its sources, Properties of wind, site selection criterion,

momentum theory, classification of rotors, concentrations and augments, wind

characteristics, performance and limitations of energy conversion systems.

Bio-Mass: Availability of bio-mass and its conversion theory. Problems involved in bio gas

production .Types of Bigas Plant

Wave And Tidal Wave: Principle of working, performance and limitations. Theory of Ocean

Thermal Energy Conversion (OTEC)


TBHG -404CO 1. Understand non conventional Energy Sources.





TBHG -404CO 2. Analyze ample inputs on a various issues in harnessing renewable

Energy.

TBHG -404CO 3. Recognize present and forthcoming role of renewable energy sources.

TBHG -404CO 4. Interpret various renewable energy resources, technologies and their

Applications.

References:

1. Saeed, S.H.,Sharma,D.K., Non Conventional Energy Resources, katsons.

2. Garg, H.P., Reidel D. Advanced in Solar Energy Technology, Publishing Co., Drdricht.

3. Sukhatme, S.P., Solar Energy, Tata McGrew Hill Company Ltd., New Delhi.

4. Twidell&Wier,AW., Renewable energy resources, English Language book, Society I

E&FNSpon (1986).

5. Bansal. N.K., Kleeman M. &MieleeM.,Renewable conversion technology, TataMcGraw

Hill, New Delhi.

6. Duffle and Beckman Solar Thermal Engineering Process, John Wiley & Sons, NewYork

CO-PO Matrix- Non-Conventional Energy Resources TBHG-404

Course Outcome PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PS

O 1

PS

O 2

PS

O 3

PS

O 4

TBHG-404CO1 2 2 1 2 - 1 2 - 1 2 2 2

TBHG-404CO2 2 1 1 1 2 1 2 - 1 2 3 2

TBHG-404CO3 2 2 1 3 - 1 2 - 1 3 2 2

TBHG-404CO4 2 1 2 2 - 1 2 - 1 2 3 2

Average CO

(TBHM-404) 2 1.5

1.2

5 2 2 1 2 - 1 2.25 2.5 2

Mode of Evaluation











Course Name Data Structure


1. To understand the fundamentals of concept and the importance of data structure in

implementing efficient algorithms.

2. Students demonstrate an ability to apply mathematical foundations, algorithmic

principles, and computer science theory in the modelling and design of computer-based

systems.


Introduction to Data Structures

Data structures and Algorithms Introduction: Concept of data structure, types of data

structures, different operations in data structure, Algorithm and its complexity, Time-Space

trade-off.Arrays: Introduction, One Dimensional Arrays, address calculation of a location in

array, Different operations on array: traversal, selection, searching, insertion, deletion,

Spares matrices


Stacks and Queues

Stacks, array representation of stack, operations on stack, applications of stacks, Conversion

of Infix to Prefix and Postfix Expressions, Evaluation of postfix expression using stack,

Recursion in C, example of recursion, Tower of Hanoi, , Array representation of Linear

Queues, Circular Queues,De-queues, priority queues, Applications of Queues.


Pointers and Linked Lists

Pointers: Introduction to pointers, Pointer variables, pointers and Dynamic memory

allocation, Linked Lists: Introduction to linear linked list, Circular linked list, doubly linked

list, operations on linked lists, Concepts of header linked lists, Linked representation of Stack

and its operation, Linked representation of Queues and its operation.


Trees and Graphs

Trees: Introduction to trees, binary tree, representation and traversal of Binary tree,

operations on binary trees, types of binary trees, BST, operations in BST, threaded binary

trees, Balanced search trees, AVL trees, Application of trees.

Graphs: Introduction, terminology, representation, traversal and searching in graph, types of

graphs, Introduction to Minimum Cost Spanning tree, Prims and kruskal method for finding

MCST.

UNIT-V (Total Topics -9and Hrs-9)

Advanced Data Structure/Miscellaneous Top

Searching techniques: Linear search and Binary search, Sorting: Selection sort, bubble





sort,quick sort, Heapsort, insertion sort, Hashing: Hash Table, hash functions, collision

Resolution Strategies, hash table Implementation, Huffman algorithm & Huffman tree.


TBHG -404CO 1. Demonstrate how linked list, stacks, arrays, queues and trees

represented in memory by using algorithms.

TBHG -404CO 2. Demonstrate the efficiency of algorithms for searching and sorting.

TBHG -404CO 3. Evaluate the different methods of traversing trees.

TBHG -404CO 4. Solve the real word problems involving graphs, trees and heaps

References:

1. Lipschuz, S., Data Structure, Schaum’s Outlines Series.

2. Kanetker, Y.. Data Structures Through C, BPB Publication.

CO-PO Matrix-Data Structure TBHG-404

Course Outcome PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PS

O1

PS

O2

PS

O3

PS

O4

TBHG-404CO1 1 2 - 2 3 - - - 1 2 - 1

TBHG-404CO2 2 1 2 1 2 - - - 2 - 2 2

TBHG-404CO3 1 1 2 2 2 - - - 1 1 2 1

TBHG-404CO4 - 1 2 1 2 - - - 2 1 - 2

Average CO

(TBHM-404)

1 1.2

5

1.5 1.5 2.2

5

- - - 1.5 1 1 1.5

Mode of Evaluation











Course Name Dynamics


1. To expose the student to basic principles of kinematics, rectilinear motion in plane.

2. To develop conceptual understanding of simple harmonic motion, cycloid motion and

projectile motion.

3. To provide sound knowledge that how to solve modern dynamical problems related to

Simple harmonic motion and projectile motion.

4. To develop ability to translate real world problem into mathematical problems and



Kinematics: Motion in a straight line and plane and some examples, Radial velocity and

acceleration, Transverse velocity and acceleration with solved problems.


Velocity and Acceleration: Angular velocity and acceleration, Tangential velocity and

acceleration, Normal velocity and acceleration, Rectilinear motion with constant

acceleration and some problems.


Simple Harmonic Motion: Definition of simple harmonic motion (SHM) and examples,

Equation of simple harmonic motion, Hook’s law for horizontal and vertical strings with

solved problems.


Cycloid: Definition of cycloid and examples, Parametric equation of the cycloid, Intrinsic

equation of the cycloid, Cycloid motion with solved problems.


Projectiles: Definitions of projectile (Trajectory, Velocity of projection, Angle of projection,

Point of projection, Range, Time of flight and greatest height), Position of projectile at any

time, Equation of trajectory, Maximum height, Maximum horizontal range of the projectile,

Range and time of flight up an inclined plane and solved problems.


TBHG -404CO 1. Understanding the principles and methods used in analyzing rectilinear

motion of a particle and apply these to solve typical problems by integration to find position,

velocity, acceleration or time.

TBHG -404CO 2. Demonstrate the concept of simple harmonic motion, projectile motion

and cycloid motion and apply these to find solution of problems related to real world.

TBHG -404CO 3. Acquire the knowledge that how to solve modern dynamical problems

with appropriate information, techniques and solution strategy.

TBHG -404CO 4. Translating real world problem into mathematical statements and






References:

1. Loney, S. L., AnElementary Treatise on the Dynamics of a Particle and of Rigid Bodies,

Kalyani Publishers, New Delhi.

2. Ray, M., A Textbook on Dynamics, S. Chand and Company Limited, New Delhi ,13th

Ed..

CO-PO Matrix-Dynamics TBHG-404

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBHG-

404CO1

3 3 2 2 1 - - 2 2 3 2 2

TBHG-

404CO2

3 3 3 2 1 - - 3 2 3 2 2

TBHG-

404CO3

3 2 2 2 1 - - 2 2 3 2 2

TBHG-

404CO4

3 3 3 3 1 - - 3 2 3 3 2

Average CO

(TBHM-404)

3.0 2.8 2.5 2.3 1.0 - - 2.5 2.0 3.0 2.3 2.0

Mode of Evaluation











Course Name Graph Theory


1. To provide the basic of graph theory and its properties.

2. To gain the knowledge of graphs, theorems and algorithms for set up the solution.

3. To assess different type of problems like Chinese postman problems, travelling

salesman’s problem etc.


Definition, examples and basic properties of graphs, pseudo graphs, complete graphs, bi-

partite graphs, isomorphism of graphs, paths and circuits.


Eulerian circuits, Hamiltonian cycles, the adjacency matrix, weighted graph, travelling

salesman’s problem, shortest path, Dijkstra’s algorithm, Floyd-Warshall algorithm.


TBHM-405CO 1. Knowledge of graphs and its properties and its application on different

problems of graph theory.

TBHM-405CO 2. Ability to assess the isomorphism of graph, path, circuits, Dijkstra’s and

Floyd-Warshall algorithm for solution of real life problems.

TBHM-405CO 3. Enhance understanding of graphs such as Euler graph, Hamiltonian

cycles, and travelling salesman problem for solution of engineering problems.

References:

1. Davey, B.A. and Priestley, H.A., Introduction to Lattices and Order, Cambridge

University Press, Cambridge, 1990.

2. Goodaire, E. G. and Parmenter, M.M., Discrete Mathematics with Graph Theory,

Pearson Education (Singapore) P. Ltd., Indian Reprint 2003, 2nd Ed.

3. Lidl, R. and Pilz, G., Applied Abstract Algebra, Undergraduate Texts in Mathematics,

Springer (SIE), Indian reprint, 2004, 2ndEd.





CO-PO Matrix (Graph Theory) TBHM-405

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBHM-

405CO1 3 _ 2 1 2 _ _ 2 _ 3 2 2

TBHM-

405CO2 3 1 2 _ 2 _ _ 2 _ 2 1 2

TBHM-

405CO3 3 2 2 2 2 _ _ 2 _ 2 2 1

Average CO

(TBHM-405) 3 1.5 2 1.5 2 _ _ 2 _ 2.3 1.67 1.67

Mode of Evaluation











Course Name Combinatorial Mathematics


1. To learn the Basic counting principles, Permutations and Combinations

2. To develop the concept of Generating functions and models

3. To discuss the basic conceptsof Recurrence relations and Solution of recurrence relations

4. To acquire knowledge about Polya theory of counting and Latin squares


Basic counting principles, Permutations and Combinations (with and without repetitions),

Binomial theorem, Multinomial theorem, Counting subsets, Set-partitions, Stirling numbers,

Principle of Inclusion and Exclusion, Derangements, Inversion formulae


Generating functions: Algebra of formal power series, Generating function models,

Calculating generating functions, Exponential generating functions.


Recurrence relations: Recurrence relation models, Divide and conquer relations, Solution of

recurrence relations, Solutions by generating functions, Integer partitions, Systems of

distinct representatives.


Polya theory of counting: Necklace problem and Burnside’s lemma, Cyclic index of a

permutation group, Polya’s theorems and their immediate applications.


Latin squares, Hadamard matrices, Combinatorial designs: t designs, BIBDs, Symmetric

designs.


TBHM -405CO 1. Appraise the concept of Basic counting principles, Permutations and

Combinations

TBHM-405CO 2. Develop the logical thinking about concept of Generating functions and

models

TBHM -405CO 3. Enhance critical thinking ability about Polya theory of counting and Latin

squares

TBHGM-405CO 4. Acquire the knowledge of Recurrence relations and Solution of

recurrence relations.

References:

1. van Lint, J.H., and Wilson, R.M. A Course in Combinatorics, Cambridge University

Press, 2001,2nd Ed.





2. Krishnamurthy, V.,Combinatorics, Theory and Application, Affiliated East-West Press

1985.

3. Cameron, P.J,.Combinatorics, Topics, Techniques, Algorithms, Cambridge University

Press, 1995.

4. Hall, M. Jr.,Combinatorial Theory, John Wiley & Sons, 1986,2nd Ed.

5. Sane, S.S.,Combinatorial Techniques, Hindustan Book Agency, 2013.

6. Brualdi, R.A.,IntroductoryCombinatorics, Pearson Education Inc.,5th Ed.

CO-PO Matrix-Combinatorial Mathematics TBHM-405

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBHM-

405CO1 3 2 2 2 - - - 2 3 1 1 1

TBHM-

405CO2 3 2 2 2 1 - - 1 2 2 - 1

TBHM-

405CO3 3 1 2 2 2 - 1 2 2 - - 2

TBHM-

405CO4 3 2 1 - 1 - - 2 3 - - 2

Average

CO

(TBHM-

405)

3.0 1.8 1.8 2.0 1.3 - 1.0 1.8 2.5 1.5 1.0 1.5

Mode of Evaluation











Course Name Applications of Algebra


1. To learn the concept of Balanced incomplete block designs (BIBD), Balanced

incomplete block designs and finite field

2. To develop the concept of Symmetry groups and permutation groups, groups of

symmetry

3. To discuss the basic concepts. color patterns and, generating functions for non-

isomorphic graphs

4. To acquire knowledge about Coding Theory, Hamming Codes, decoding and cyclic

codes.


Balanced incomplete block designs (BIBD): definitions and results, incidence matrix of a

BIBD, construction of BIBD from difference sets, construction of BIBD using quadratic

residues, difference set families, construction of BIBD from finite fields.

UNIT-II (Total Topics -7and Hrs-5)

Coding Theory: introduction to error correcting codes, linear cods, generator and parity

check matrices, minimum distance, Hamming Codes, decoding and cyclic codes.

UNIT-III (Total Topics -5and Hrs-5)

Symmetry groups and color patterns: review of permutation groups, groups of symmetry and

action of a group on a set;


Colouring and colouring patterns, Polya theorem and pattern


Inventory, generating functions for non-isomorphic graphs.


TBHM -405CO 1. Appraise the concept Balanced incomplete block designs(BIBD),

Balanced incomplete block designs and finite field

TBHM-405CO 2. Develop the logical thinking about concept of Symmetry groups and

permutation groups, groups of symmetry

TBHM -405CO 3. Acquire the basic knowledge about color patterns and , generating

functions for non-isomorphic graphs

TBHGM-405CO 4. Enhance critical thinking ability of Coding Theory, Hamming Codes,

decoding and cyclic codes

References:

1. Herstein, I. N. and Winter, D. J., Primer on Linear Algebra, Macmillan Publishing

Company, New York, 1990.





2. Nagpaul, S. R. and Jain, S. K., Topics in Applied Abstract Algebra, Thomson Brooks

and Cole, Belmont, 2005.

3. Klima, R. E. Sigmon, N., Stitzinger, E., Applications of Abstract Algebra with Maple,

CRC Press LLC, Boca Raton, 2000.

4. Lay, D.C., Linear Algebra and its Applications. Pearson Education Asia, Indian Reprint,

2007,3rd Ed.

5. Zhang, F., Matrix theory, Springer-Verlag New York, Inc., New York, 1999.

CO-PO Matrix-Applications of Algebra TBHM-405

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBHM-

405CO1

2 3 2 1 _ _ _ 2 2 2 2 2

TBHM-

405CO2

2 2 2 1 1 _ _ 2 2 2 1 2

TBHM-

405CO3

3 3 3 2 2 _ _ 2 2 2 3 2

TBHM-

405CO4

3 3 3 2 1 _ _ 3 2 2 3 2

Average CO

(TBHM-405)

2.5 2.7 2.5 1.5 1.3 _ _ 2.2 2 2 2.25 2

Mode of Evaluation









Course Code PBHW-406 Credit 1


Course Name Workshop/Activities


1. To encourage students to participate in academic (seminar, conference, workshop) and

extracurricular activities (poster presentation, debates, etc)

2. To enhance their presentation and communication skill through participation in various

activities.

3. To inculcate critical thinking ability through discussions, exploring recent developments

in science, etc

Activities will be based on department allotted by the class Coordinator/HOD.

1. Presentation by students on the topic provided by HOD/ class coordinator.

2. Any social activities

3. Presentation on mathematical Model


PBHW -406CO 1.Demonstrate technical skills for effective preparation of presentations,

write-ups through participant in academic and extracurricular activities.

PBHW -406 CO 2. Exhibit good communication and presentation skills.

PBHW -406 CO 3. Acquire critical thinking ability to analyze and interpret observations,

recent scientific developments, etc.

CO-PO Matrix (Activity) PBHW-406

Course

Outcom

e

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PSO

1

PSO

2

PSO

3

PSO

4

PBHW-

406CO1

2 _ _ 2 3 _ 2 _ 2 1 2

PBHW-

406CO2

_ 2 _ 2 3 _ 2 _ 2 2 2

PBHW-

406 CO3

1 _ _ 2 3 1 2 _ 2 2 2

Average

CO

(PBHW-

406)

1.5 2.0 _ 2.0 3.0 1.0 2.0 _ 2.0 1.7 2.0

Mode of Evaluation



Weightage 25 25





SEMESTER -V





Programme Name B.Sc. (Hons) Mathematics Programme Code 26



Course Name Multivariate Calculus


1. Application of multivariable functions viz. double and triple integrals to solve the

complex variety of practical problems in multidisciplinary environment.

2. Implementation of multi variable calculus in defining the maxima-minima and two

times integrals for binary variable functions in the field of industry and society.

3. Appraise about multi variable functions, fractional derivatives and various properties

connected with by using mathematical techniques and tools.

4. Enhance the critical thinking ability by prove the usage of Multivariate calculus in

defining shape, equilibrium, outline in real world situation.

UNIT- I (Total Topics- 7 and Hrs. - 9)

Functions of several variables, limit and continuity of functions of two variables, Partial

differentiation, total differentiability and differentiability, sufficient condition for

differentiability.

UNIT- II (Total Topics -12and Hrs-6)

Chain rule for one and two independent parameters, directional derivatives, the gradient,

maximal and normal property of the gradient, tangent planes, Extrema of functions of two

variables, method of Lagrange multipliers, constrained optimization problems, Definition of

vector field, divergence and curl.


Double integration over rectangular region, double integration over non-rectangular region,

Double integrals in polar co-ordinates, Triple integrals, Triple integral over a parallelepiped

and solid regions. Volume by triple integrals, cylindrical and spherical co-ordinates.


Change of variables in double integrals and triple integrals. Line integrals, Applications of

line integrals: Mass and Work. Fundamental theorem for line integrals, conservative vector

fields, independence of path.


Green’s theorem, surface integrals, integrals over parametrically defined surfaces. Stoke’s

theorem, The Divergence theorem.


TBHM-501 CO 1.Elaborate multi variable function by using double and triple integrals to

solve the complex problems.





TBHM-501 CO 2.Implement multi variable calculus in defining the minimum – maximum

& double integrals.

TBHM-501 CO 3.Outline functions of multi-variable’s, fractional derivatives and various

properties.

TBHM-501 CO 4.Enhance the critical thinking ability by demonstrating the usage of

Multivariate calculus in real world situation

References:

1. Thomas, G.B. and Finney R.L., Calculus and Analytic Geometry, Pearson Education,

Delhi,2005,9th Ed.

2. Strauss, M.J., Bradley, G.L. and Smith, K.J., Calculus , Dorling Kindersley (India) Pvt.

Ltd. (Pearson Education), Delhi, 2007, 3rdEd.

3. Marsden, E., Tromba, A.J. and Weinstein, A., Basic Multivariable Calculus, Springer

(SIE), Indian reprint, 2005.

4. Stewart, James, Multivariable Calculus, Concepts and Contexts, Cole, Thomson

Learning, USA, 2001, 2nd Ed.

CO-PO Matrix-Multivariate Calculus TBHM-501

Course Outcome PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PS

O 1

PS

O2

PS

O3

PS

O4

TBHM-501CO1 2 2 1 1 _ _ _ 2 3 _ 2 1

TBHM-501CO2 2 3 1 1 1 _ _ 2 2 1 2 1

TBHM-501CO3 3 3 2 1 _ _ 2 2 1 2 2

TBHM-501CO4 3 3 3 2 1 _ _ 2 3 1 2 2

Average CO

(TBHM-501)

2.5 2.8 1.8 1.3 1.0 _ _ 2.0 2.5 1.0 2.0 1.5

Mode of Evaluation








Programme Name B.Sc.(Hons.) Mathematics Programme Code 26



Course Name Group Theory – II


1. Advance knowledge of important mathematical concepts in abstract algebra such as

automorphism, direct product of groups, group action, finite and infinite groups.

2. To understand the important advanced subgroups such as characteristic subgroups,

commutator subgroup and its properties

3. To understand the concepts of class equation and its applications

4. Prove theorems like Cayley’s theorem, Index theorem, Sylow’s theorems and Cauchy’s

theorem


Automorphism, inner automorphism, automorphism groups, automorphism groups of finite

and infinite cyclic groups, applications of factor groups to automorphism groups,

Characteristic subgroups, Commutator subgroup and its properties.


Properties of external direct products, the group of units modulo n as an external direct

product, internal direct products, Fundamental Theorem of finite abelian groups.


Group actions, stabilizers and kernels, permutation representation associated with a given

group action, Applications of group actions: Generalized Cayley’s theorem, Index theorem.

UNIT-IV (Total Topics - 4 and Hrs-9)

Groups acting on themselves by conjugation, class equation and consequences, conjugacy in

Sn.

UNIT-V (Total Topics - 6 and Hrs-9)

p-groups, Sylow’s theorems and consequences, Cauchy’s theorem, Simplicity of An for n ≥

5, non-simplicity tests.


TBHM-502CO 1.Enhance the advance knowledge of automorphism and learned its

applications in field of research and higher studies.

TBHM-502CO 2.Build an idea about group action and direct product.

TBHM-502CO 3.Elaborate the idea of subgroup and order of group using Cauchy theorem

and Sylow’s theorems and analyzed its applications.

TBHM-502CO 4.Application of appropriate technique to formulate the proof of

fundamental theorem of finite group, index theorem and Cayley’s theorem.

References:

1. Fraleigh,J.B., First Course in Abstract Algebra, Pearson, 2002, 7th Ed.


3. Gallian,J.A., Contemporary Abstract Algebra, Narosa Publishing House, 1999, 4th Ed

4. Dummit, D. S. and Foote, R.M., Abstract Algebra, John Wiley and Sons (Asia) Pvt. Ltd.,

Singapore, 2004, 3rd Ed.

5. Durbin, J.R. ,Modern Algebra, John Wiley & Sons, New York Inc., 2000.

6. Wallace, D. A. R. ,Groups, Rings and Fields, Springer Verlag London Ltd., 1998.





CO-PO Matrix (Group Theory-II) TBHM-502

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBHM-

502CO1 2 2 1 3 _ _ _ 2 3 _ 2 3

TBHM-

502CO2 1 _ _ _ _ _ _ _ 2 _ _ 2

TBHM-

502CO3 2 2 3 2 2 _ _ 1 2 _ 2 2

TBHM-

502CO4 2 2 3 2 3 _ _ 1 2 _ 2 2

Average

CO

(TBHM-

502)

1.8 2.0 2.3 2.3 2.5 _ _ 1.3 2.3 _ 2.0 2.3

Mode of Evaluation








Programme Name B.Sc.(Hons) Mathematics Programme Code 26



Course Name Portfolio Optimization


1. To learn the concept of Financial markets. Investment objectives and Measures of return

and risk

2. To develop the concept Mutual funds and Mean-variance portfolio optimization

3. To discuss the basic concepts Capital market theory and Capital assets pricing model

4. To acquire knowledge about Index tracking optimization and Portfolio performance

evaluation measures.


Financial markets. Investment objectives. Measures of return and risk. Types of risks. Risk

free assets.


Mutual funds. Portfolio of assets. Expected risk and return of portfolio. Diversification.

UNIT- III (Total Topics -6and Hrs-9)

Mean-variance portfolio optimization- the Markowitz model and the two-fund theorem, risk-

free assets and one fund theorem, efficient frontier.

UNIT-IV (Total Topics 7and Hrs-9)

Portfolios with short sales. Capital market theory. Capital assets pricing model- the capital

market line, beta of an asset, beta of a portfolio, security market line.


Index tracking optimization models. Portfolio performance evaluation measures.


TBHM-503CO 1. Appraise the concept of Financial markets. Investment objectives and

Measures of return and risk

TBHM-503CO 2. Acquire the knowledge about Index tracking optimization and Portfolio

performance evaluation measures.

TBHM-503CO 3. Enhance critical thinking ability of Capital market theory and Capital

assets pricing model

TBHM-503CO 4. Develop the logical thinking about concept of Mutual funds and Mean-

variance portfolio optimization

References:

1. Reilly, F. K., Brown, K.C., Investment Analysis and Portfolio Management, ,South-

Western Publishers, 2011, 10th Ed.

2. Markowitz, H.M., Mean-Variance Analysis in Portfolio Choice and Capital Markets,

Blackwell, New York, 1987.

3. Best, M.J., Portfolio Optimization, Chapman and Hall, CRC Press, 2010.

4. Luenberger, D.G., Investment Science, Oxford University Press, 2013,2nd Ed.





CO-PO Matrix Portfolio Optimization TBHM-503

Course Outcome PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PS

O 1

PS

O2

PS

O3

PS

O4

TBHM-503CO1 2 2 2 1 1 _ _ 1 3 _ 2 2

TBHM-503CO2 3 2 2 2 3 _ _ 1 2 _ _ 2

TBHM-503CO3 2 2 2 2 1 _ _ 2 2 _ 2 2

TBHM-503CO4 1 2 2 1 1 _ _ 2 1 _ 2 2

Average CO

(TBHM-503) 2 2 2 1.5 1.5 _ _ 1.5 2 _ 2 2

Mode of Evaluation











Course Name Number Theory


1. To assess different types of Linear Diophantine equation and evaluate prime counting

function, and Chinese Remainder theorem. To design the concept of Fermat’s Little

theorem, Number theoretic functions and Wilson’s theorem, and its applications.

2. To develop the concept of Inverse Mobius formula, Dirichlet product and Euler’s phi‐

function, and its applications

3. To identify the primitive roots and primitive roots for primes, and its applications of

number theory in cryptography


Linear Diophantine equation, prime counting function, statement of prime number theorem,

Goldbach conjecture, linear congruences, complete set of residues, Chinese Remainder

theorem.


Fermat’s Little theorem, Wilson’s theorem, sum and number of divisors, totally

multiplicative functions.


Definition and properties of the Dirichlet product, the Mobius Inversion formula, the greatest

integer function, Euler’s phi‐function, Euler’s theorem, reduced set of residues, some

properties of Euler’s phi-function.


Order of an integer modulo n, primitive roots for primes, composite numbers having

primitive roots, Euler’s criterion, the Legendre symbol and its properties,


Quadratic Reciprocity, quadratic congruences with composite moduli. Public key

encryption, RSA encryption and decryption, the equation x2 + y2= z2, Fermat’s Last theorem.


TBHM-503CO 1.Acquire the basic knowledge of Number Theory and Theoretic Problems

in practical situations in real life environment and society.

TBHM-503CO 2.Create the ideas of Fermat’s, Euler’s & Chinese remainder theorems and

evaluated congruence equations ascend in numerous higher-level problems.

TBHM-503CO 3.Acquire the knowledge of number theoretic functions, Dirichlet product,

Mobius inverse formula, linear congruence and residue with some properties and learn its

application to higher studies.

TBHM-503CO 4.Develop the appropriate techniques to find primitive roots, quadratic

reciprocity, public key encryption, RSA encryption and their application in cryptography.

References:

1. Burton,D.M., Elementary Number Theory, Tata McGraw, Hill, Indian reprint, 2007,

6th Ed.





2. Robinns, Neville, Beginning Number Theory, Narosa Publishing House Pvt. Ltd.,

Delhi, 2007, 2nd Ed.

CO-PO Matrix Number Theory TBHM-503

Course Outcome P

O1

P

O2

P

O3

P

O4

P

O5

P

O6

P

O7

P

O8

PS

O1

PS

O2

PS

O3

PS

O4

TBHM-503CO1 3 2 2 1 2 - 1 2 3 - 2 1

TBHM-503CO2 3 1 2 1 3 - - 2 2 - 2 2

TBHM-503CO3 3 1 2 - - - - 1 2 - - 2

TBHM-503CO4 3 2 2 2 2 - - 2 2 - 1 1

Average CO

(TBHM-503) 3.0 1.5 2.0 1.3 2.3 - 1.0 1.8 2.3 - 1.7 1.5

Mode of Evaluation











Course Name Boolean Algebra and Automata Theory


1. To provide sound knowledge about axiomatic set theory and elementary logics.

2. To expose the student to properties lattice, Boolean polynomial and circuit theory.

3. To understand the concept of finite automata, language with valid examples.

4. To develop ability to translate real world problem into mathematical statements and



Definition, examples and basic properties of ordered sets, maps between ordered sets, duality

principle, lattices as ordered sets, lattices as algebraic structures, sublattices, products and

homomorphisms.


Definition, examples and properties of modular and distributive lattices, Boolean algebras,

Boolean polynomials, minimal forms of Boolean polynomials, Quinn‐McCluskey method,

Karnaugh diagrams, switching circuits and applications of switching circuits.


Introduction: Alphabets, strings, and languages. Finite Automata and Regular Languages:

deterministic and non-deterministic finite automata, regular expressions, regular languages

and their relationship with finite automata, pumping lemma and closure properties of regular

languages.


Context Free Grammars and Pushdown Automata: Context free grammars (CFG), parse

trees, ambiguities in grammars and languages, pushdown automaton (PDA) and the language

accepted by PDA, deterministic PDA, Non- deterministic PDA, properties of context free

languages; normal forms, pumping lemma, closure properties, decision properties.


Turing Machines: Turing machine as a model of computation, programming with a Turing

machine, variants of Turing machine and their equivalence. Undecidability: Recursively

enumerable and recursive languages, undecidable problems about Turing machines: halting

problem, Post Correspondence Problem, and undecidability problems About CFGs.


TBHM-503CO 1. Understand Boolean algebra and basic properties of Boolean algebra;

able to simplify simple Boolean functions by using the basic Boolean properties.

TBHM-503CO 2. Able to design simple combinational logics using baisc gates. Able to

optimize simple logic using Karnaugh maps.

TBHM-503CO 3. Acquire a fundamental understanding of the core concepts in automata

theory and formal languages





TBHM-503CO 4. An ability to prove and disprove theorems establishing key properties of

formal languages and automata.

References:

1. Davey, B A. and Priestley, H. A., Introduction to Lattices and Order, Cambridge

University Press, Cambridge, 1990.

2. Goodaire, E. G. and Michael M. Parmenter, Discrete Mathematics with Graph Theory,

Pearson Education (Singapore) P.Ltd., Indian Reprint. (2nd Ed.)

3. Lidl, R. and Pilz, G., Applied Abstract Algebra, Undergraduate Texts in Mathematics,

Springer (SIE), Indian reprint, 2004,2nd Ed.

4. Hopcroft, J. E., Motwani, R. and Ullman, J. D., Introduction to Automata Theory,

Languages, and Computation, Addison-Wesley, 2001, 2nd Ed.

5. Lewis, H.R., Papadimitriou, C.H., Papadimitriou, C., Elements of the Theory of

Computation, Prentice-Hall, NJ, 1997,2nd Ed.

CO-PO Matrix Boolean Algebra and Automata TheoryTBHM-503

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBHM-

503CO1 3 - 2 - 2 - 1 2 - 3 1 1

TBHM-

503CO2 3 2 2 2 2 - - 2 - 2 2 2

TBHM-

503CO3 3 2 2 - 2 - - 1 - 2 1 2

TBHM-

503CO4 3 2 2 1 1 - - 2 3 - 2 2

Average

CO

(TBHM-

503)

3.0 2.0 2.0 1.5 1.8 - 1.0 1.8 3.0 2.3 1.5 1.8

Mode of Evaluation











Course Name Theory of Equations


1. To learn the Descarte’s rule of signs and Transformation of equations

2. To develop the concept of Polynomials and Equation and its properties.

3. To discuss the advanced concepts of Algebraic solutions of the cubic and bi-quadratic.

4. To acquire knowledge about Derived function and Newton’s theorem on the sums of

powers of roots.


General properties of polynomials, Graphical representation of a polynomial, maximum and

minimum values of a polynomials, General properties of equations.


Descarte’s rule of signs positive and negative rule, Relation between the roots and the

coefficients of equations.


Symmetric functions, Applications of symmetric function of the roots, Transformation of

equations. Solutions of reciprocal and binomial equations. Algebraic solutions of the cubic

and biquadratic. Properties of the derived functions.


Symmetric functions of the roots, Newton’s theorem on the sums of powers of roots,

homogeneous products, limits of the roots of equations.


Separation of the roots of equations, Strums theorem, Applications of Strum’s theorem,

Conditions for reality of the roots of an equation and biquadratic. Solution of numerical

equations.


TBHM-504CO 1. Appraise the concept of Derived function and Newton’s theorem on the

sums of powers of roots.

TBHM-504CO 2.Demonstrate deep understanding about Polynomials, Equation and its

properties

TBHM-504CO 3.Demonstrate deep understanding about Polynomials, Equation and its

properties

TBHM-504CO 4. Develop the appropriate techniques to Descarte’s rule of signs and

Transformation of equations

References:

1. Burnside, W.S. and Panton, A.W., The Theory of Equations, Dublin University Press,

1954.

2. MacDuffee, C. C., Theory of Equations, John Wiley & Sons Inc., 1954.





CO-PO Matrix (Theory of Equations) TBHM-504

Course

Outcom

e

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBHM-

504CO

1

3 - 2 - 2 - 1 1 - 1 1 1

TBHM-

504CO

2

3 2 1 2 2 - - 2 - 2 2 2

TBHM-

504CO

3

1 1 1 - 2 - - 1 - 2 1 1

TBHM-

504CO

4

1 2 1 1 1 - - 2 3 - 2 2

Averag

e CO

(TBHM

-504)

2.0 1.7 1.3 1.5 1.8 - 1.0 1.5 3.0 1.7 1.5 1.5

Mode of Evaluation











Course Name Analytical Geometry


1. To develop the concept of Asymptotes and tracing the curves.

2. To discuss the concepts of cylinder and cone and their properties

3. To acquire knowledge about General equation of second degree

4. To assess of fundamental properties of Plane, line and spheres.


General equation of second degree, Pair of lines, Parabola, Tangent, Normal, Pole and Polar

and their properties, Ellipse, Hyperbola, Tangent, Normal, Pole and Polar, Conjugate

diameters.

UNIT- II (Total Topics -9and Hrs-9)

Asymptotes, Conjugate hyperbola and Rectangular hyperbola, Polar equation of a conics,

Polar equation of tangent, normal, polar and asymptotes, Tracing of parabola, Ellipse and

hyperbola.


Review of straight lines and planes, Equation of sphere, Tangent plane, Plane of contact and

polar plane, Intersection of two spheres, radical plane, Coaxial spheres,


Equation of cylinder, Enveloping and right circular cylinders, Equations of central conicoids,

Tangent plane, Normal, Plane of contact and polar plane,


Equation of a cone, Intersection of cone with a plane and a line, Enveloping cone, Right

circular cone, Enveloping cone and enveloping cylinder, Equations of paraboloids and its

simple properties.


TBHM-504 CO1. Appraise the fundamental properties of cylinder, cone and their properties

TBHM-504 CO2. Demonstrate the deep understanding of General equation of second

degree

TBHM-504 CO3.Develop the logical thinking about concept of Asymptotes and tracing the

curves

TBHM-504 CO4.Acquire the knowledge of fundamental properties Plane, line and

spheres

References:

1. Thomas, G.B., and Finney, R.L., Calculus, Pearson Education, Delhi, 2005,9th Ed.

2. Anton, H., Bivens, I., and Davis, S., Calculus, John Wiley and Sons (Asia) Pvt. Ltd.

3. Loney, S.L., The Elements of Coordinate Geometry, McMillan and Company.





4. Bell, R.J.T., Elementary Treatise on Coordinate Geometry of Three Dimensions,

McMillan India Ltd., 1994.

5. BallabhR.: Textbook of Coordinate Geometry, Prakashan Kendra.

6. Jain, P.K. and Ahmad K.: Textbook of Analytical Geometry, New Age International (P)

Ltd. Publishers, 1986.

7. Askwith, E. H.: A Course of Pure Geometry, Merchant Books, 2007.

CO-PO Matrix (Analytical Geometry) TBHM-504

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBHM-504

CO1 3 - 2 - 1 - 1 2 - 1 1 1

TBHM-504

CO2 3 1 1 2 1 - - 2 - 2 2 2

TBHM-504

CO3 3 1 1 - 2 - - 2 - 2 1 1

TBHM-504

CO4 3 2 2 1 1 - - 2 3 - 2 1

Average

CO

(TBHM-

504)

3.0 1.3 1.5 1.5 1.3 - 1.0 2.0 3.0 1.7 1.5 1.3

Mode of Evaluation











Course Name Probability and Statistics


1. To learn Markov Chains, Chapman-Kolmogorov equations, classification of states.

2. To evaluate the correlation, rank correlation and regression lines.

3. To develop the concepts of moments, continuous distribution, discrete distribution, Joint

moment generating function, marginal and conditional Distributions.

4. To understand and illustrate the theory and applications of the probability and sample

space.


Sample space, probability axioms, real random variables (discrete and continuous),

cumulative distribution function, probability mass/density functions, mathematical

expectation, moments, moment generating function, characteristic function.


Discrete distributions: uniform, binomial, Poisson, geometric, negative binomial,

continuous distributions: uniform, normal, exponential.


Joint cumulative distribution function and its properties, joint probability density functions,

marginal and conditional distributions, expectation of function of two random variables,

conditional expectations, independent random variables.


Bivariate normal distribution, correlation coefficient, joint moment generating function

(JMGF) and calculation of covariance from JMGF, linear regression for two variables


Chebyshev’s inequality, statement and interpretation of (weak) law of large numbers and

strong law of large numbers, Central Limit theorem for independent and identically

distributed random variables with finite variance, Markov Chains, Chapman-Kolmogorov

equations, classification of states.


TBHM-504CO 1.Acquire the deep knowledge of various forms of discrete & continuous

probability distribution functions and its application in real world problems.

TBHM-504CO 2.Application of different statistical technique such as correlation &

regression to the actual life arithmetical data.

TBHM-504CO 3.Analysis of statistical data analytically and graphically for real world

problems.

TBHM-504CO 4.Appraise the concept of Markov Chains, Chapman-Kolmogorov

equations, classification of states.

References:

1. Hogg, R. V., McKean, J.W. and Craig, Allen T., Introduction to Mathematical Statistics,

Pearson Education, Asia, 2007, 8th Ed.





2. Miller, I., Miller, M., Freund, J.E., Mathematical Statistics with Applications, Pearson

Education, Asia, 2006, 7th Ed.

3. Ross, S., Introduction to Probability Models, Academic Press, Indian Reprint, 2007,

9thEd.

4. Mood, A.M., Graybill, F. A. and Boes, D. C., Introduction to the Theory of Statistics,

Tata McGraw- Hill, Reprint , 2007, 3rd Ed.

CO-PO Matrix (Probability and Statistics) TBHM-504

Course

Outcom

e

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBHM-

504CO

1

2 2 _ 1 _ _ _ 2 2 _ _ 3

TBHM-

504CO

2

2 2 _ _ 3 _ _ 2 3 _ 1 2

TBHM-

504CO

3

2 2 1 2 2 _ _ 2 2 _ _ 2

TBHM-

504CO

4

1 2 2 3 2 _ _ 2 2 _ 2 2

Averag

e CO

(TBHM

-504)

1.7 2 1.5 2 2.3 _ _ 2 2.25 _ 1.5 2.25

Mode of Evaluation









Course Code PBSM-505 Credit 2


Course Name Seminar


1. To provide the detail knowledge for preparing presentation and seminar.

2. To develop the concept of team work, presentation skills of data in conferences,

symposia, seminar etc.

3. To demonstrate knowledge and understand mathematical tools and techniques in

seminar.

Seminar: Participation/ paper presentation in the seminar


2. PBSM-505 CO 1. Developed the idea for preparing presentation for their possible future

profession.

3. PBSM -505 CO 2. Enhanced the critical thinking skills, communication skills and build

team work for conferences, symposia, seminar etc.

PBSM -505 CO 3. Demonstrate the knowledge of mathematical tools and techniques for

presentations of research data in seminar and conferences.

CO-PO Matrix (Seminar) PBSM-505

Course

Outcom

e

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PSO

1

PSO

2

PSO

3

PSO

4

PBSM-

505 CO1 2 _ _ 2 3 _ 2 _ 2 1 2

PBSM-

505 CO2 _ 2 _ 2 3 _ 2 _ 2 2 2

PBSM-

505 CO3 1 _ _ 2 3 1 2 _ 2 2 2

Average

CO

(PBSM -

505)

1.5 2.0 _ 2.0 3.0 1.0 2.0 _ 2.0 1.7 2.0

Mode of Evaluation



Weightage 50 -





SEMESTER -VI








Course Name Metric Spaces and Complex Analysis


1. To define a metric space, absolute and uniform convergence of power series.

2. To elaborate convergent sequence and demonstrate equivalence of metrics.

3. To illustrate the concepts of Limits, continuity, regions in the complex plane, mappings,

C-R equation’s, sufficient & necessary conditions to differentiability.

4. To examine Liouville’s& Cauchy- Goursat theorem, analyticity & algebraic fundamental

theorem.


Metric spaces: definition and examples. Sequences in metric spaces, Cauchy sequences.

Complete Metric Spaces. Open and closed balls, neighbourhood, open set, interior of a set.

Limit point of a set, closed set, diameter of a set, Cantor’s theorem. Subspaces, dense sets,

separable spaces.


Continuous mappings, sequential criterion and other characterizations of continuity.

Uniform continuity. Homeomorphism, Contraction mappings, Banach Fixed point Theorem.

Connectedness, connected subsets of R.


Limits, Limits involving the point at infinity, continuity. Properties of complex numbers,

regionsin the complex plane, functions of complex variable, mappings. Derivatives,

differentiation formulas, Cauchy-Riemann equations, sufficient conditions for

differentiability.


Analytic functions, examples of analytic functions, exponential function, Logarithmic

function, trigonometric function, derivatives of functions, definite integrals of functions.

Contours, Contour integrals and its examples, upper bounds for moduli of contour integrals.

Cauchy-Goursat theorem, Cauchy integral formula.

UNIT-V (Total Topics - 9 and Hrs-9)

Liouville’s theorem and the fundamental theorem of algebra. Convergence of sequences and

series, Taylor series and its examples. Laurent series and its examples, absolute and uniform

convergence of power series.


TBHM-601CO 1.Develop the concept of compound variable function related to analytic

functions.

TBHM-601CO 2.Learn appropriate techniques such as Cauchy’s Theorem, Liouville’s

Theorem, Laurent’s and Taylor’s Theorem.





TBHM-601CO 3.Setup and verify the solution of a metric space and its application in real

word situations.

TBHM-601CO 4.Enhance critical thinking ability by solving differentiation and

integration of complex functions.

References:

1. Shirali, S.andVasudeva,H.L., Metric Spaces, Springer Verlag, London, 2005.

2. Kumaresan, S. ,Topology of Metric Spaces, Narosa Publishing House, 2nd Ed.

3. Simmons G.F.,Introduction to Topology and Modern Analysis, McGraw Hill Education,

2017, 1st Ed

4. Brown,J.W. and Churchill,R.V., Complex Variables and Applications, McGraw – Hill

International Edition,2009, 8thEd.

5. Bak,J. and Newman,D.J., Complex Analysis, Undergraduate Texts in Mathematics,

Springer-Verlag New York, Inc., NewYork, 1997, 2nd Ed.

CO-PO Matrix Metric Space and Complex Analysis TBHM-601

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBHM-

601CO1

3 2 2 1 1 _ _ 2 3 _ 3 2

TBHM-

601CO2

3 2 2 2 2 _ _ 1 _ _ 2 2

TBHM-

601CO3

2 2 2 1 1 _ _ 3 _ _ 3 2

TBHM-

601CO4

3 3 2 2 1 _ _ 1 3 _ 3 2

Average CO

(TBHM-601)

2.7 2.2 2 1.5 1.2 _ _ 1.7 3 _ 2.7 2

Mode of Evaluation











Course Name Ring Theory and Linear Algebra – II


1. To develop advance knowledge of important mathematical concepts in such as

polynomial ring, irreducibility, Euclidean domain and division algorithm

2. To understand and prove the important theorems such as Cayley-Hamilton theorem,

Bessel’s inequality, projections and Spectral theorem

3. To develop the knowledge about dual space and inner product space

4. To evaluate orthogonal basis through Gram-Schmidt orthogonalization process

UNIT I (Total Topics- 9 and Hrs- 9)

Polynomial rings over commutative rings, division algorithm and consequences, principal

ideal domains, factorization of polynomials, reducibility tests, irreducibility tests, Eisenstein

criterion, unique factorization in Z[x].


Divisibility in integral domains, irreducibles, primes, unique factorization domains,

Euclidean domains.


Dual spaces, dual basis, double dual, transpose of a linear transformation and its matrix in

the dual basis, annihilators, Eigen spaces of a linear operator, diagonalizability, invariant

subspaces and Cayley-Hamilton theorem, the minimal polynomial for a linear operator.


Inner product spaces and norms, Gram-Schmidt orthogonalisation process, orthogonal

complements, Bessel’s inequality, the adjoint of a linear operator, Least Squares

Approximation.


Minimal solutions to systems of linear equations, Normal and self-adjoint operators,

Orthogonal projections and Spectral theorem.


TBHM-602CO 1. Develop advanced knowledge of rings & vector space and its application

in higher studies.

TBHM-602CO 2. Appraise about ring polynomial prime and irreducible elements and its

application.

TBHM-602CO 3. Establish the relationship between matrix and linear transform and

evaluated Eigen value and Eigen vector.

TBHM-602CO 4. Develop the concept of inner product spaces and interpreted the

orthogonality in inner product spaces.





References:

1. Fraleigh, J.B.,A First Course in Abstract Algebra, Pearson, 2002, 7thEd.

2. Artin, M., Abstract Algebra, Pearson, 2011, 2ndEd.

3. Gallian, G.A., Contemporary Abstract Algebra, Narosa Publishing House, 1999, 4th Ed.

4. Friedberg, S.H., Insel, A. J. and Spence, L.E., Linear Algebra, Prentice Hall of India Pvt.

Ltd., New Delhi, 2004, 4th Ed.

5. Lang, S., Introduction to Linear Algebra, Springer, 2005, 2ndEd.

6. Strang, G., Linear Algebra and its Applications, Thomson, 2007.

7. Kumaresan, S, Linear Algebra- A Geometric Approach, Prentice Hall of India.

8. Hoffman, K and Kenneth, R.A., Linear Algebra, Prentice-Hall of India Pvt. Ltd., 1978,

2nd Ed.

CO-PO Matrix (Ring Theory-II) TBHM-602

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBHM-

602CO1 1 2 1 2 _ _ _ 2 2 2 2 3

TBHM-

602CO2 1 2 3 _ 2 _ _ 1 2 _ 2 2

TBHM-

602CO3 2 _ 3 2 2 _ _ 2 _ 2 1 1

TBHM-

602CO4 1 1 2 2 3 _ _ _ _ 2 1 2

Average

CO

(TBHM-

602)

1.6

7

2.2

5 2 2.3 1.7 2 2 1.5 2

Mode of Evaluation











Course Name Industrial Mathematics


1. To learn about the Medical Imaging, X-ray and CT scan based on the knowledge of

Mathematics

2. To develop the concept of Inverse problems through problems taught in Mathematics.

3. To discuss the basic concepts of Radon Transform and Back Projection.

4. To acquire knowledge about CT Scan using the properties of Fourier and inverse Fourier

transforms and applications of their properties in image reconstruction


Medical Imaging and Inverse Problems. The content is based on Mathematics of X-ray and

CT scan based on the knowledge of calculus, elementary differential equations, complex

numbers and matrices.


Introduction to Inverse problems: Why should we teach Inverse Problems? Illustration of

Inverse problems through problems taught in Pre-Calculus, Calculus, Matrices and

differential equations. Geological anomalies in Earth’s interior from measurements at its

surface (Inverse problems for Natural disaster) and Tomography.


X-ray: Introduction, X-ray behavior and Beers Law (The fundament question of image

construction) Lines in the place.


Radon Transform: Definition and Examples, Linearity, Phantom (Shepp-Logan Phantom -

Mathematical phantoms). Back Projection: Definition, properties and examples.


CT Scan: Revision of properties of Fourier and inverse Fourier transforms and applications

of their properties in image reconstruction. Algorithms of CT scan machine. Algebraic

reconstruction techniques abbreviated as ART with application to CT scan.


TBHM-603 CO 1. Acquire the knowledge about fundamental properties Medical Imaging,

X-ray and CT scan based on the knowledge of Mathematics

TBHM-603CO 2.Enhance critical thinking ability about concept of Inverse problems

through problems taught in Mathematics.

TBHM-603 CO 3. Develop the basic knowledge about Radon Transform and Back

Projection.

TBHM-603 CO 4. Appraise the concept of CT Scan using the properties of Fourier and

inverse Fourier transforms and applications of their properties in image reconstruction





References:

1. Feeman, T. G., The Mathematics of Medical Imaging, A Beginners Guide, Springer

Under graduate Text in Mathematics and Technology, Springer,

2. Groetsch, C.W.,Inverse Problems, Activities for Undergraduates, The Mathematical

Association of America, 1999.

3. Kirsch, A.An Introduction to the Mathematical Theory of Inverse Problems, Springer,

2011, 2nd Ed.

CO-PO Matrix- Industrial Mathematics TBHM-603

Course Outcome P

O1

P

O2

P

O3

P

O4

P

O5

P

O6

P

O7

P

O8

PS

O1

PS

O2

PS

O3

PS

O4

TBHM-603CO1 3 - 1 - 2 - 1 2 2 1 1 1

TBHM-603CO2 3 2 2 1 1 - - 2 - 2 1 2

TBHM-603CO3 3 1 1 - 0 - - 3 - 2 1 2

TBHM-603CO4 3 2 2 1 1 - - 2 3 - 2 2

Average CO

(TBHM-603) 3.0 1.7 1.5 1.0 1.0 - 1.0 2.3 2.5 1.7 1.3 1.8

Mode of Evaluation











Course Name Bio-Mathematics


1. To learn the Mathematical Biology and modeling process.

2. To develop the concept of Prey predator systems and LotkaVolterra equations

3. To discuss the advanced concepts of Spatial Models (one and Two species)and Discrete

Models

4. To acquire knowledge about Numerical solution of the models and its graphical

representation (Steady state solutions, Phase plane methods and qualitative solutions


Mathematical Biology and the modeling process: an overview. Continuous models: Malthus

model, logistic growth, Allee effect, Gompertz growth, Michaelis-Menten Kinetics, Holling

type growth, Bacterial growth in a Chemostat, Harvesting a single natural population.


Prey predator systems and Lotka Volterra equations, Populations in competitions, Epidemic

Models (SI, SIR, SIRS, SIC), Activator-Inhibitor system, Insect Outbreak Model: Spruce

Budworm.


Numerical solution of the models and its graphical representation. Qualitative analysis of

continuous models: Steady state solutions, stability and linearization, multiple species

communities and Routh-Hurwitz Criteria, Phase plane methods and qualitative solutions,

bifurcations and limit cycles with examples in the context of biological scenario.


Spatial Models: One species model with diffusion, Two species model with diffusion,

Conditions for diffusive instability, Spreading colonies of microorganisms, Blood flow in

circulatory system, Travelling wave solutions, Spread of genes in a population. Discrete

Models: Overview of difference equations, steady state solution and linear stability analysis,


Introduction to Discrete Models, Linear Models, Growth models, Decay models, Drug

Delivery Problem, Discrete Prey-Predator models, Density dependent growth models with

harvesting, Host-Parasitoid systems (Nicholson-Bailey model), Numerical solution of the

models and its graphical representation. Case Studies: Optimal Exploitation models, Models

in Genetics, Stage Structure Models, Age Structure Models.


TBHM-603 CO 1.Acquire the knowledge of Mathematical Biology and modeling

process

TBHM-603CO 2.Demonstrate understanding of Prey predator systems and

LotkaVolterraequations





TBHM-603 CO 3. Appraise the concept of Spatial Models (one and Two species)and

Discrete Models

TBHM-603 CO 4. Develop the appropriate techniques to Numerical solution of models ,

Qualitative analysis of continuous models and Routh-Hurwitz Criteria

References:

1. Keshet, L.E.,Mathematical Models in Biology, SIAM, 1988.

2. Murray, J. D.,Mathematical Biology, Springer, 1993.

3. Fung, Y.C.,Biomechanics, Springer-Verlag, 1990.

4. Brauer, F.,PDriessche.,V.D. and Wu, J.,Mathematical Epidemiology, Springer,

5. Kot, M.,Elements of Mathematical Ecology, Cambridge University Press, 2001.

CO-PO Matrix-Bio – Mathematics TBHM-603

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBHM-

603CO1 3 - 2 - 2 - 1 2 - 1 1 1

TBHM-

603CO2 3 2 1 2 2 - - 2 - 2 2 2

TBHM-

603CO3 3 1 1 - 2 - - 2 - 2 1 2

TBHM-

603CO4 3 2 1 1 1 - - 2 - - 2 2

Average

CO

(TBHM-

603)

3.0 1.7 1.3 1.5 1.8 - 1.0 2.0 - 1.7 1.5 1.8

Mode of Evaluation











Course Name Linear Programming problems


1. To develop the fundamental concepts Linear Programming problems

2. To identify and obtain the solution of simplex method and duality

3. To construct the concepts of various type of solution viz. bounded solution, degeneracy

and optimal solution.

4. To solve transportation and assignment problem and create a depth understanding

about Game theory and its applications


Introduction to linear programming problem, Theory of simplex method, optimality and

unboundedness,


The simplex algorithm, simplex method in tableau format, introduction to artificial variables,

two‐phase method, Big‐M method and their comparison.


Duality, formulation of the dual problem, primal‐dual relationships, economic interpretation

of the dual.


Transportation problem and its mathematical formulation, northwest‐corner method least

cost method and Vogel approximation method for determination of starting basic solution,

algorithm for solving transportation problem, assignment problem and its mathematical

formulation, Hungarian method for solving assignment problem.


Game theory: formulation of two person zero sum games, solving two person zero sum

games, games with mixed strategies, graphical solution procedure, linear programming

solution of games.


TBHM-603 CO 1.Develop the fundamental concepts of Linear Programming problems

and its real-life applications.

TBHM-603CO 2.Elaborate the understanding of simplex method and duality

TBHM-603 CO 3.Explain various type of solution in LPP such that unbalanced,

boundedness, degeneracy and optimal solution.

TBHM-603 CO 4.Enhance and propose the idea about transportation, assignment

problem and game theory and its application

References:





1. Bazaraa, M. S., Jarvis,J.J. and Sherali, H. D., Linear Programming and Network Flows,

John Wiley and Sons, India, 2004, 2nd Ed.

2. Hillier, F.S. and Lieberman, G.J., Introduction to Operations Research, Tata McGraw

Hill, Singapore, 2009, 9th Ed.

3. Taha, H.A., Operations Research, An Introduction, PrenticeHall, India, 2006, 8th Ed.

4. Hadley,G.,Linear Programming, Narosa Publishing House, New Delhi ,2002.

CO-PO Matrix-Linear Progamming Problem TBHM-603

Course Outcome P

O1

P

O2

P

O3

P

O4

P

O5

P

O6

P

O7

P

O8

PS

O1

PS

O2

PS

O3

PS

O4

TBHM-603CO1 2 3 2 1 _ _ _ 2 2 2 2 2

TBHM-603CO2 2 2 2 1 1 _ _ 2 2 2 1 2

TBHM-603CO3 3 3 3 2 2 _ _ 2 2 2 3 2

TBHM-603CO4 3 3 3 2 1 _ _ 3 2 2 3 2

Average CO

(TBHM-603)

2.5 2.7 2.5 1.5 1.3 _ _ 2.2 2 2 2.25 2

Mode of Evaluation











Course Name Mathematical Modeling


1. To learn the basic techniques of Power series solution of a differential equation and its

application.

2. To derive the concept Legendre equation, Bessel equation, Laplace transform and

initial value problems.

3. To provide the knowledge of Monte Carlo Simulation Modeling and its applications

4. To develop the concepts ofoptimizationmodeling, Linear Programming, and simplex

method.


Power series solution of a differential equation about an ordinary point, solution about a

regular singular point.


Bessel’s equation and Legendre’s equation, Laplace transform and inverse transform,

application to initial value problem up to second order.


Monte Carlo Simulation Modeling: simulating deterministic behavior (area under a curve,

volume under a surface)


Generating Random Numbers: middle square method, linear congruence, Queuing Models:

harbor system, morning rush hour.


Overview of optimization modeling, Linear Programming Model: geometric solution

algebraic solution, simplex method, sensitivity analysis


TBHM-604CO 1.Acquire the basic knowledge of Power series solution of a ‘DE’ by usual

point and singular point and applications in real life environment and society.

TBHM-604 CO 2.Develop and apply the Simulation Modeling in real life situations

TBHM-604 CO 3.Create the ideas to produce arbitrary numbers: Queuing Models:

morning rush hour, harbor system, middle square method and their applications

TBHM-604 CO 1.Ability to assess and prepare the critical thinking skills of LPP Model:

graphical solution arithmetical solution, simplex method, sensitivity analysis &

optimization modeling.

References:

1. Tyn, M.U. and Debnath,L., Linear Partial Differential Equation for Scientists and

Engineers, Springer, Indian reprint, 2006.





2. Giordano, F. R., Weir,M.D. and Fox,W.P.,A First Course in Mathematical Modeling,

Thomson Learning, London and New York, 2003.

CO-PO Matrix Mathematical Modeling TBHM-604

Course Outcome P

O1

P

O2

P

O3

P

O4

P

O5

P

O6

P

O7

P

O8

PS

O1

PS

O2

PS

O3

PS

O4

TBHM-604CO1 3 - 2 - 2 - 1 2 - 3 1 1

TBHM-604CO2 3 2 2 2 2 - - 2 - 2 2 2

TBHM-604CO3 3 2 2 - 2 - - 1 - 2 1 2

TBHM-604CO4 3 2 2 1 1 - - 2 3 - 2 2

Average CO

(TBHM-604) 3.0 2.0 2.0 1.5 1.8 - 1.0 1.8 3.0 2.3 1.5 1.8

Mode of Evaluation











Course Name Mechanics


1. To learn the basic techniques of Moment of a force about a point and an axis, couple

and couple moment, Moment of a couple about a line, resultant of a force system, and

its application.

2. To derive the concept laws of Coulomb friction, application to simple and complex

surface contact friction problems, transmission of power through belts, screw jack.

3. To provide the knowledge of second moments and the product of area of a plane area,

transfer theorems, Conservative force field, conservation for mechanical energy, work

energy equation, kinetic energy and their applications.

4. To develop the concept of Chasles’ theorem, general relationship between time

derivatives of a vector for different references.

UNIT I (Total Topics-9 and Hrs- 10)

Moment of a force about a point and an axis, couple and couple moment, Moment of a couple

about a line, resultant of a force system, distributed force system, free body diagram, free

body involving interior sections, general equations of equilibrium, two point equivalent

loading, problems arising from structures, static indeterminacy.


Laws of Coulomb friction, application to simple and complex surface contact friction

problems, transmission of power through belts, screw jack, wedge, first moment of an area

and the centroid, other centers.


Theorem of Pappus-Guldinus, second moments and the product of area of a plane area,

transfer theorems, relation between second moments and products of area, polar moment of

area, principal axes.


Conservative force field, conservation for mechanical energy, work energy equation, kinetic

energy and work kinetic energy expression based on center of mass, moment of momentum

equation for a single particle and a system of particles, translation and rotation of rigid

bodies.


Chasles’ theorem, general relationship between time derivatives of a vector for different

references, relationship between velocities of a particle for different references, acceleration

of particle for different references.


TBHM-604CO 1.Acquire the basic knowledge of Moment of a force about a point and an

axis, couple and couple moment, Moment of a couple about a line, resultant of a force

system, and its application in society.





TBHM-604 CO 2. Develop the knowledge of laws of Coulomb friction, application to

simple and complex surface contact friction problems, transmission of power through belts,

screw jack.

TBHM-604 CO 3.Create the ideas of second moments and the product of area of a plane

area, transfer theorems, Conservative force field, conservation for mechanical energy and

their applications

TBHM-604 CO 4.Ability to assess and prepare the critical thinking skills of Chasles’

theorem, general relationship between time derivatives of a vector for different references,

relationship between velocities of a particle for different references

References:

1. Shames, I.H., and Krishna, G.,Rao, M.,Engineering Mechanics: Statics and Dynamics,

Dorling Kindersley (India) Pvt. Ltd. (Pearson Education), Delhi, 2009. (4th Ed.).

2. Hibbeler, R.C. and Ashok Gupta, Engineering Mechanics: Statics and Dynamics,

Dorling Kindersley (India) Pvt.Ltd. (Pearson Education), Delhi,11th Ed.

CO-PO Matrix MechanicsTBHM-604

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

TBHM-

604CO1 3 - 2 - 2 - 1 2 - 3 1 1

TBHM-

604CO2 3 2 2 2 2 - - 2 - 2 2 2

TBHM-

604CO3 3 2 2 - 2 - - 1 - 2 1 2

TBHM-

604CO4 3 2 2 1 1 - - 2 3 - 2 2

Average

CO

(TBHM-

604)

3.0 2.0 2.0 1.5 1.8 - 1.0 1.8 3.0 2.3 1.5 1.8

Mode of Evaluation











Course Name Differential Geometry


1. To analyse the equivalence of the two curves by applying some theorems.

2. To understand and illustrate the Fundamental forms and curvature of surfaces and

applications of the curvature

3. To learn the basic techniques of envelope & developable surface.

4. To understand the important concept of Local non-intrinsic properties of a surface.

UNIT I (Total Topics-10 and Hrs- 9)

Theory of Space Curves: Space curves, Planer curves, Curvature, torsion and Serret-Frenet

formulae. Osculating circles, Osculating circles and spheres. Existence of space curves.

Evolutes and involutes of curves.


Theory of Surfaces: Parametric curves on surfaces. Direction coefficients. First and second

Fundamental forms. Principal and Gaussian curvatures. Lines of curvature.


Euler’s theorem. Rodrigue’s formula, Conjugate and Asymptotic lines. Developables:

Developable associated with space curves and curveson surfaces, Minimal surfaces.


Geodesics: Canonical geodesic equations. Nature of geodesics on a surface of revolution.

Clairaut’s theorem. Normal property of geodesics. Torsion of a geodesic. Geodesic

curvature. Gauss-Bonnet theorem. Surfaces of constant curvature. Conformal mapping.

Geodesic mapping. Tissot’s theorem.


Tensors: Summation convention and indicial notation, Coordinate transformation and

Jacobian, Contra-variant and Covariant vectors, Tensors of different type, Algebra of tensors

and contraction, Metric tensor and 3-index Christoffel symbols, Parallel propagation of

vectors, Covariant and intrinsic derivatives, Curvature tensor and its properties, Curl,

Divergence and Laplacian operators in tensor form, Physical components.


TBHM-604CO 1. Develop the knowledge of differential geometry to other fields such as

tensor and Cosmology

TBHM-604 CO 2. Enhance critical thinking skills by solving problems related to differentia

geometry applicable to various circumstances in mathematical situations

TBHM-604 CO 3. . Analyze the complexity of considerate in mathematical topics in relative

to curves and surfaces.

TBHM-604 CO 1. Acquire the knowledge about possessions connected to curves in space,

osculating plane, developable surface, circle curvature and torsion

References:

1. Willmore, T.J.,An Introduction to Differential Geometry, Dover Publications.

2. O'Neill, B.,Elementary Differential Geometry, Academic Press, 2006,2nd Ed.





3. Weatherburn, C.E.,Differential Geometry of Three Dimensions, Cambridge University

Press 2003.

4. Struik, D.J.,Lectures on Classical Differential Geometry, Dover Publications.

5. Lang, S.,Fundamentals of Differential Geometry, Springer, 1999.

6. Spain, B.,Tensor Calculus: A Concise Course, Dover Publications, 2003.

CO-PO Matrix Differential GeometryTBHM-604

Course Outcome P

O1

P

O2

P

O3

P

O4

P

O5

P

O6

P

O7

P

O8

PS

O1

PS

O2

PS

O3

PS

O4

TBHM-604CO1 3 - 2 - 2 - 1 2 - 3 1 1

TBHM-604CO2 3 2 2 2 2 - - 2 - 2 2 2

TBHM-604CO3 3 2 2 - 2 - - 1 - 2 1 2

TBHM-604CO4 3 2 2 1 1 - - 2 3 - 2 2

Average CO

(TBHM-604) 3.0 2.0 2.0 1.5 1.8 - 1.0 1.8 3.0 2.3 1.5 1.8

Mode of Evaluation








Programme Name B.Sc. (H) Mathematics Programme Code 26



Course Name Dissertation


1. To acquire skills to operate various analytical techniques and their applicability in

research and utilize modern tools, e-resources for literature survey and data compilation

2. To demonstrate technical skills to conduct Software based experiments and ability to

record observation and interpret data to derive a solution/conclusion to complex

problem.

3. To exhibit competent writing (with critical analysis), communication and

presentation skills

Guidelines:

• Students will have to do a project related to any one subject of curriculum in the

college or in industry/Research Organization.

• Each student will submit 3 copies of hard bound in the department.

• Final evaluation will be done on the basis of quality of work, performance and

presentation


TBHM-604 CO1. Acquire skills to operate various analytical techniques and instruments,

identify their applicability in research and utilize modern tools, e-resources for literature

survey and data compilation

TBHM-604 CO2. Demonstrate technical skills to conduct software-based experiments and

ability to record observation and interpret data to derive a solution/conclusion to complex

problem.

TBHM-604 CO3. Exhibit competent writing (with critical analysis), communication and

presentation skills.

CO-PO Matrix Dissertation TBHM-604

Course Outcome PO1

PO2

PO3

PO4

PO5

PO6

PO7

PSO1

PSO2

PSO3

PSO4

TBHM-604 CO1. 2 2 3 - - 1 2 2 2 3 2

TBHM-604 CO2. 1 3 3 - - 2 2 2 3 3 2

TBHM-604 CO3. - - - - 3 - - - - - - Average CO (TBHM-604)

1.5 2.5 3 - 3 1.5 2 2 2.5 3 2

Mode of Evaluation


Component Internal Assessment End Semester Examination

Weightage 40 60





Programme Name B.Sc.(Hons)

Mathematics

Programme Code 26

Course Code ADP-605 Credit 1


Course Name Aptitude & Reasoning Skills


1. Enhance problem solving and analytical skills needed in an organization. Listening,

identifying and proposing solution to the problem.

2. To gamut the skills which facilitate them to enhance their employability quotient and

overall personality development.

3. To enable students to manage the placement challenges more effectively.

UNIT I (Total Topics- 2 and Hrs- 5 )

Direct Letter Coding, Number/Symbol Coding, Matrix Coding, Substitution, Deciphering

Message Word Code\s, Deciphering Number and Symbol Codes for Messages


Blood Relations Relation Puzzles, Coding Relations. Direction Sense Test Problems based

on Distance and Direction, Problems based on Angles, Alphabet Test Letter Word

Problems, Rule Detection.


Alpha Numeric Sequence Puzzles Ranking and Time Sequence Test , Problems Based on

Seating/Standing Positions, Inequalities ,Coded Inequalities.


Seating Linear Arrangement, Rectangular Arrangement, Classification Type Questions,

Comparison Type Question, Family Based Puzzles, Problems based on Numbers, Problems

based on Alphabets ,Data Sufficiency Coding Decoding etc.


ADP-605CO 1.Solve campus placements aptitude papers covering Logical Reasoning

ADP-605CO 2.Formulate the problem quantitatively and use appropriate arithmetical,

and/or statistical methods to solve the problem

ADP-605CO 3.Interpret quantitative information (i.e., formulas, graphs, tables, models,

and schematics) and draw implications from them.

ADP-605CO 4.Thinking critically and applying basic mathematics skills to interpret data,

draw conclusions, and solve problems; Developing proficiency in numerical reasoning

Reference:

1. Aggarwal R.S ,A Modern Approach to Logical Reasoning ,S. Chand Publisher,2017

2. Sharma Arun,Quantitative Aptitude , MHE Publisher,2018,8th Edition





CO-PO Matrix Aptitude Reasoning Skills ADP-605

Course

Outcome

PO

1

PO

2

PO

3

PO

4

PO

5

PO

6

PO

7

PO

8

PSO

1

PSO

2

PSO

3

PSO

4

ADP-605

CO1 3 - 2 - 2 - 1 2 - 3 1 1

ADP-605

CO2 3 2 2 2 2 - - 2 - 2 2 2

ADP-605

CO3 3 2 2 - 2 - - 1 - 2 1 2

ADP-605

CO4 3 2 2 1 1 - - 2 3 - 2 2

Average

CO

(ADP-

605)

3.0 2.0 2.0 1.5 1.8 - 1.0 1.8 3.0 2.3 1.5 1.8

Mode of Evaluation



Weightage 25 25

Date post:	04-Nov-2021
Category:	Documents
Upload:	others
View:	2 times
Download:	0 times

UTTARANCHAL UNIVERSITY

Documents