Programme Outcomes (PO) B.Sc. B.Sc. Maths MATHS.pdfProgramme Outcomes (PO) B.Sc. On successful...

Programme Outcomes (PO)

B.Sc.

On successful completion of Bachelor of Science programme, students will develop a scientific

temper, critical thinking, problem solving skills, and research attitude for the betterment of the

society.

Programme Specific Outcomes (PSO)

B.Sc. Maths

By the end of B.Sc. Maths programme, students will be able to get better understanding of

mathematical concepts and their applications.

Course Outcomes (CO)

B.Sc. Maths

Semester I

S.

No.

Subject Name &

Code Course Outcomes

1 Core Paper I -

Algebra - TAM1A

By the end of the course, students will be able to

● solve a polynomial equation and find real roots which are increased

or decreased

● analyse nature of infinite series and find its sum

● assess Symmetric, Skew Symmetric, Hermition, and Skew Hermition

and perform operations on Matrices

● evaluate the concept of Congruence and derive Fermat’s and

Wilson’s theorems

2 Core Paper II -

Trigonometry -

TAM1B


● derive expansion of powers of 𝑠𝑖𝑛𝜃, 𝑐𝑜𝑠𝜃, and expansions of

sin 𝑛𝜃 , 𝑐𝑜𝑠 𝑛𝜃 and tan 𝑛𝜃.

● find the relation between Circular and Hyperbolic functions

● understand and solve problems in Hyperbolic and Inverse

Hyperbolic Functions

● evaluate complex numbers in algebraic and trigonometric forms

● convert trigonometric series to algebraic series and solve them

3 Allied Paper I -

Calculus of Finite

Differences and

Numerical

Analysis I -

SBAME


● find solution for algebraic and transcendental equations using

iterations

● solve simultaneous linear system of equations using numerical

methods

● find finite differences of polynomials using numerical operators

● solve problems of interpolation with equal and unequal intervals

● derive central difference interpolation formula with equal intervals

Semester II

S. No. Subject Name &


1 Core Paper III -

Differential

Calculus - TAM2A


● find derivatives of functions using Leibnitz’s theorem

● calculate maxima and minima of functions of two variables

● find curvature, radius of curvature, and centre of curvature for

given functions

● determine angle of intersection of two curves and slopes of tangent

in polar coordinates

● find asymptotes parallel to axes and intersection of a curve with an

asymptote

2 Core Paper IV -

Analytical

Geometry -

TAM2B


● understand chord of contact, polar and pole, conjugate points, and

conjugate lines of conics

● describe co-normal points and concyclic points of conic, and derive

polar equations of straight lines and circles

● write equations of chord, tangent and normal of conics, and prove

the equation of asymptotes of hyperbola

● derive systems of planes and orthogonal projections

● represent lines, angle between a line and a plane, co-planar lines,

shortest distance between two skew lines and intersection of three

planes

● derive equation of a sphere and section of a sphere by a plane

● evaluate radical plane, coaxial system of spheres, and orthogonal

spheres

3 Allied Paper II -

Calculus of Finite

Differences and

Numerical

Analysis II


● derive derivative of a function using numerical difference formula

● find integration of a function using special cases of general

quadrature formula

● solve linear homogeneous and non-homogeneous difference

equations using appropriate numerical methods

Semester III



1 Core Paper V -

Integral Calculus -

TAM3A


● obtain reduction formula for various functions

● find area of curved surfaces and volume of solid by applying

integrals

● describe the relationship between beta and gamma functions

● evaluate directional derivative, gradient, divergence curl, and unit

normal

● solve the problems in line, surface, and volume integrals using

Gauss, Stokes, and Green’s theorem

2 Core Paper VI -

Differential

Equations -

TAM3B


● understand linear, non-linear, partial, and ordinary differential

equations

● identify methods to solve homogeneous and non-homogeneous

linear and higher order equations

● form partial differential equations by eliminating arbitrary

constants and arbitrary functions

● solve partial differential equation using various methods

3 Allied II -

Mathematical

Statistics I -

SBAOA


● understand data classification and apply measures of central

tendency and dispersion to grouped and ungrouped data cases

● interpret univariate and bivariate random variables and

mathematical expectations

● analyse standard distributions

● compute univariate and bivariate regression through correlation

analysis

Semester IV



1 Core Paper VII -

Transform

Techniques

TAM4A


● understand concept of Laplace transform, Fourier series, and

Fourier transform

● derive Fourier series of periodic functions by evaluating Fourier

coefficients

● evaluate problems using properties of transform techniques

● apply Laplace and Fourier transform to initial and boundary value

problem

2 Core Paper VIII -

Statics - TAM4B


● understand basic concepts like distance, time, velocity, and

acceleration

● apply these concepts to solve problems related to force

● find centre of mass and evaluate stability of equilibrium

3 Allied II -

Mathematical

Statistics II -

SBAOB


● understand basic principles of statistical inference (estimation and

hypothesis testing) and sampling distributions

● analyse statistical inference procedures (confidence intervals,

hypothesis tests for one population, and hypothesis tests for two

populations)

● construct estimators for given population and derive their

properties

● choose appropriate methods for testing of hypothesis of

large samples and small samples

Semester V



1 Core Paper IX -

Algebraic

Structures -

TAM5A


● understand the properties of group, ring, and field

● derive proofs to various theoretical statements and problems using

group, ring, and field

● apply algebraic structures in solving problems

2 Core Paper X -

Real Analysis I -

TAM5B


● describe fundamental properties of set theory in real analysis

● classify countable and uncountable sets

● understand concept of sequences, limit of a sequence,

convergence, divergence, and bounded sequences

● analyse series using different types of test

● describe concept of metric spaces and find limits in metric spaces

3 Core Paper XI -

Dynamics -

TAM5C


● identify the relationship among distance, time, velocity, and

acceleration

● understand concepts of balancing of rotating mass

● analyse inertia forces in mechanism

● find motion of a particle

● apply vector mechanics to solve kinematic problems

4 Core paper XII -

Discrete

Mathematics -

TAM5D


● understand basic principles of set theory and Boolean Algebra

● construct switching circuits and Boolean gates

● enumerate generating functions

● apply Graph theory to derive mathematical proofs and solve

problems

5 Elective I -

Programming

Language ‘C’ with

Practicals and

Theory - TEM5A


● understand concept of ‘C’ Programming and its different modules

that include conditional and looping expressions, arrays, strings,

functions, pointers, structures, and file programming

● apply programming concepts in writing a program

● create, compile, and debug programs in ‘C’ language

Semester VI



1 Core Paper XIII-

Linear Algebra -

TAM6A


● understand basis, dimension, kernel, rank, and nullity of vector

space

● recollect properties of vector space, dual space, and inner product

space

● construct an orthonormal base for any vector space using Gram-

Schmidt orthogonalisation process

● apply principles of matrix algebra to linear transformation

2 Core Paper XIV -

Real Analysis II -

TAM6B


● understand open and closed sets, connected sets, and bounded

sets

● describe connectedness, compactness in a metric space, and

continuity of a function

● determine Riemann integrability of a bounded function, and study

its existence and properties

● define derivatives and understand the concept through Rolle’s

theorem, Law of Mean, and fundamental theorem of Calculus

● differentiate between pointwise and uniform convergence of

sequence of functions

3 Core Paper XV -

Complex Analysis

- TAM6C


● understand analytic functions and complex differentiable functions

as power series

● compute complex line integrals and real integrals using residue

theorem

● determine whether a given function is differentiable or not, and find

its derivative if it is differentiable

● apply Cauchy theorem to verify and solve line integral

● solve differentiation and line integral problems using standard

theorems

4 Elective II - Graph

Theory - TEM6B


● understand the basic principles of Graph Theory

● construct graphs using theoretical concepts

● derive simple mathematical proofs using graphs

● apply Graph Theory to solve practical problems

5 Elective III -

Operations

Research -

TEM6C


● solve linear programming problems using simplex, Big–M-method

and duality, and find optimum solutions with profit maximisation

● solve balanced and unbalanced assignment problems

● find feasible solutions for transportation problems using NWC, LCM,

and VAM method and calculate its optimality using MODI methods

● evaluate relationship between primal and dual of an LPP

● compute CPM and PERT for a network

Other Department Papers



1 I M.Com

Core Paper –

Quantitative

Techniques for

Business Decision

KDA2B


• calculate mean distribution for samples obtained from normal

population

• apply correlation to identify strength, direction, and linear

relationship between two variables

• evaluate problem on correlation coefficient and regression lines

• perform test of hypothesis and calculate confidence interval for

population parameter for large and small samples

• formulate and solve Linear Programming problems at minimum

cost or maximum profit

• find optimal solution for transportation and assignment problems

2 Allied II Paper I:

II B.Sc Computer

Science

Statistical Methods

and their

Applications I

SBAOC


• present diagrammatic representation of statistical data

• apply measures of central tendency, dispersion and skewness in

grouped and ungrouped data

• understand concept of probability of an event

• solve problems on probability using addition, multiplication, and

Baye’s theorem

• analyse correlation between variables using scatter diagram


3 Allied II Paper I:

II B.Sc Computer

Science

Statistical Methods


● understand concept of random variable and find its expectation,

moments, and moment generating function

● analyse standard distributions

● understand concept of sampling distribution

and their

Applications I

SBAOD

● perform test of hypothesis and calculate confidence interval for

population parameter for large and small samples

● apply non-parametric test such as Wilcoxon signed rank test and

Mann Whitney U test to solve problems

4 Allied I – Paper I

Mathematics I

SBAMM

I B.Sc Computer

Science, I BCA, I B.Sc

Physics, I B.Sc

Chemistry


● compute characteristic equation, Eigen value, and Eigen vector

of a matrix

● find inverse of matrix and higher order of matrix using Cayley

Hamilton Theorem

● evaluate roots of equation using various methods

● find approximate roots using Newton’s and Lagrange’s method

● derive expansion of sin 𝑛𝜃, cos 𝑛𝜃, 𝑠𝑖𝑛𝑛 𝜃 and 𝑐𝑜𝑠𝑛𝜃

● calculate radius of curvature and find maximum and minimum

values of function

5 Allied I – Paper II

Mathematics II

SBAMN

I B.Sc Computer

Science, I BCA, I B.Sc

Physics, I B.Sc

Chemistry


● obtain reduction formula for various functions

● understand linear, non-linear, partial, and ordinary differential

equations

● form partial differential equations by eliminating arbitrary

constants and arbitrary functions

● recognise even and odd functions and use resulting

simplifications in Fourier series

● evaluate directional derivative, gradient, divergence, curl and unit

normal

● solve problems in line, surface, and volume integrals using Gauss,

Stokes, and Green’s theorem

● understand concept of Laplace transform and apply it to solve

second order differential equations

6 II BCA

Core Paper: VII

Numerical and

Statistical Methods

SAZ3C


● solve algebraic or transcendental equations and linear system

equations using numerical methods

● perform error analysis and evaluate numerical differentiation

using numerical methods

● understand Sampling and Frequency Distribution

● analyse measures of location, dispersion, and probability to solve

various problems

● apply Chi-Square Test to calculate Independence and Goodness of

Fit

● calculate problems under Regression and Correlation Analysis and

F-Test

7

II BBA

Allied II:

Operations

Research

MBM4D


● understand concept of linear programming problem and solve by

graphical and simplex method

● apply mathematical tools to solve optimisation problems

● build and solve Transportation Models and Assignment Models

● design simple models like CPM and PERT

● perform error analysis using numerical methods

8 Allied: II BBA

Business

Mathematics and

Statistics

MBM3C



• apply measures of central tendency, dispersion, and skewness in

grouped and ungrouped data


• apply mathematical computation techniques to find solutions to

business related problems

• conduct business forecasting using time series analysis

9 Allied:

I B.Com A&F

Business Statistics -

CDG1A


• apply measures of location and dispersion in grouped and

ungrouped data


• identify and interpret business related problems

• conduct business forecasting using time series analysis

• analyse business statistics problems in context

I B.Com A&F

Operations

Research - CDG2A


• translate real world problems into mathematical models

• apply mathematical tools to solve optimisation problems

• build and solve Transportation Models and Assignment Models

• evaluate problems solving and decision making techniques

• suggest decisions during conflict situations or crisis

10 Non-Major Elective:

Functional

Mathematics I & II

SNM1A, SNM2E


• apply basic formulae of Mathematics to solve aptitude problems

• construct problems quantitatively, and use appropriate

arithmetical and/or statistical methods to solve the problems

(Common for all UG degrees)

பகுதி - 1 தமிழ்

முதலாமாண்டு - முதல் பருவம்

S.N

o.

Subject

Name & Code Course Outcomes

1 பபொதுத்தமிழ்

Paper - I

CLA1L

மொணவியரக்ள் இந்தப் பொடத்ததக் கற்றலின் முடிவில்,

● நொட்டுப்புற இலக்கியங்களின் வதகப்பொடுகள்,

சிறுகதத, உதரநதட, மரபு கவிதத, புதுக்கவிதத

ஆகியவற்றின் ஆசிரியர ் குறிப்புகள்,

அவ்வொசிரியரக்ள் வொழ்ந்த கொலசச்ூழல், அவரக்ள்

எழுதிய நூல்குறிப்புகள் முதலொனவற்தற நிதனவில்

பகொள்கிறொரக்ள்

● பதடப்பிலக்கியங்களின் முக்கியத்துவத்ததயும்

இலக்கியங்களின் பதொன்தமதயயும் புரிந்து


● ஊடகத்தில் பமொழிதயப் பயன்படுத்தும் முதற,

துதறசொரந்்த கதலசப்சொற்கதள அறிந்து

பகொள்ளுதல், பசொற்களின் பபொருள் அறிதல் ஆகிய

பமொழிப்பயிற்சிதயப் பபறுகிறொரக்ள்

● நொட்டுப்புற இலக்கியங்களின் வொயிலொகப்

பபறப்படும் மனித உணரவ்ுகதளயும் தற்கொல

இலக்கியங்களில் பவளிப்படும் சமூக

அவலங்கதளயும் மதிப்பீடு பசய்யும் தன்தமதயப்

பபறுகிறொரக்ள்

● நவீன இலக்கிய உத்திகதள உள்வொங்கி அவற்தறப்

பின்பற்றிக் கவிதத, கட்டுதர எழுதும் திறதனப்

பபறுகிறொரக்ள்

முதலாமாண்டு - இரண்டாம் பருவம்

S.

No

Subject



Paper II-

CLA2H


● சிற்றிலக்கியங்கள், கிறித்துவ இசுலொமிய

இலக்கியங்கள் ஆகியவற்றின் ஆசிரியர ்

குறிப்புக்கதளயும், கொலசச்ூழதலயும் நிதனவில்

தவத்துக் பகொள்கிறொரக்ள்

● சிற்றிலக்கியங்களில் எளிய மக்கள் கததத ்

ததலவன் ததலவிகளொகப் பதடக்கப்பட்டதன்

நநொக்கத்ததப் புரிந்து பகொள்கிறொரக்ள்

● நிலம் சொரந்்த மக்களின் வொழ்க்தக முதறதயயும்

மூநவந்தர ் மரதபயும் கொப்பிய இலக்கியத ்

தன்தமதயயும் புரிந்துபகொள்கிறொரக்ள்

● சிற்றிலக்கியங்கதளப் பிற இலக்கியங்கநளொடு

ஒப்பிட்டு இவ்விலக்கியங்கள் சமூகத்தத எவ்வொறு

பிரதிபலிக்கின்றன என்பதத மதிப்பீடு

பசய்கிறொரக்ள்

● இலக்கண விதிகதளக் பகொண்டு தமிழ் பமொழியில்

தவறின்றிப் நபசவும் எழுதவும் பயிற்சி


இரண்டாமாண்டு - மூன்றாம் பருவம்

S.

No

Subject



Paper III-

CLA3M


● தசவ தவணவ இலக்கியக் குறிப்புகள்,

நொயன்மொரக்ள் மற்றும் ஆழ்வொரக்ளின் பபயரக்ள்,

வள்ளலொர ் பற்றிய குறிப்புகள், சமூக அரசியல்

கொலசச்ூழல்கள் நபொன்றவற்தற நிதனவுப்படுத்திக்


● பக்தி இலக்கியங்களின் இதறபநறிதயயும்

கும்பகரண்னின் அறவுணரத்வயும், கன்தற இழந்த

பசுவிற்கு நீதி வழங்கிய மனுசந்சொழனின் முதற

மொண்தபயும் புரிந்து பகொள்கிறொரக்ள்

● பக்தி இலக்கியங்கள் உணரத்்தும் பமய்பநறிதயக்

கதடப்பிடித்து வொழ்வியல் முதறதய நமம்படுத்திக்


● உலகியல் வொழ்க்தகயிலிருந்து நம்தம நவறுபடுத்தி

நிதலயொன வீடுநபற்தற அதடவதற்கொன

வழிமுதறகதளப் பகுத்துணரக்ிறொரக்ள்

● அறம், பக்தி, நீதி, ஒழுக்கம் ஆகிய தனிமனிதப்

பண்புகதள மதிப்பீடு பசய்கிறொரக்ள்

● அரசு அலுவலகங்கள் மற்றும் தனியொர ்நிறுவனங்கள்

ஆகியவற்றிற்குக் கடிதம் எழுதும் திறதனயும்

இலக்கிய நிகழ்வுகதளக் கொட்சியொக நடித்துக்

கொட்டும் திறதனயும் பபறுகிறொரக்ள்

இரண்டாமாண்டு - நான்காம் பருவம்

S.

No

Subject



Paper IV-

CLA4K


● சங்க இலக்கியங்கள், நீதி இலக்கியங்கள்,

கொப்பியங்கள் ஆகியவற்றின் கொலப் பின்னணி,

சங்கப்புலவரக்ளின் வொழ்க்தகக் குறிப்புகள்

நபொன்றவற்தற நிதனவில் தவத்துக்


● எட்டுத்பதொதக, பத்துப்பொட்டு, சிலப்பதிகொரம்,

மணிநமகதல, திருக்குறள் ஆகியவற்றில் பண்தடத்

தமிழ் மக்களின் அகம் புறம் சொரந்்த வொழ்வியல்

நிதலப்பொட்டிதனப் புரிந்து பகொள்கிறொரக்ள்

● பமொழிப்பபயரப்்பு விதிகதளயும் உத்திகதளயும்

பயன்படுத்தி எழுத்துப் பயிற்சிதயப் பபறுகிறொரக்ள்

● பசவ்வியல் இலக்கியங்கதளக் கற்பதன் மூலம்

திதண, துதற விளக்கங்கதளத ் திறனொய்வு


● பண்தடய மக்களின் வொழ்வியல் பகொள்தககதளத ்

தற்கொல மக்களின் வொழ்நவொடு ஒப்பிட்டு மதிப்பீடு


● பமொழிப்பபயரப்்புப் பயிற்சியின் மூலம் கட்டுதர,

அறிக்கக ஆகியவற்தற பமொழியொக்கம்


Paper 1 - Hindi

I Year - Semester I

S.

No.

Subject Name

& Code Course Outcomes

1. Hindi I - CLE1E By the end of the course, students will be able to

● recollect the interesting words and phrases used in the prescribed texts

● practise writing leave letters, complaint letters, order letters, and

enquiry letters

● analyse the concepts or themes in the prescribed texts

● write error-free official memos, government orders, notices, and

various forms of official correspondence

I Year - Semester II

S.

No.

Subject Name


1. Hindi II - CLE2G By the end of the course, students will be able to

● remember new vocabulary learnt from translation practice (English to

Hindi)

● understand the dramatic elements in one-act plays

● analyse the themes in short stories

● enact scenes from one-act plays

● write critical essays on prescribed texts

II Year - Semester III

S.

No.

Subject Name


1. Hindi III - CLE3H By the end of the course, students will be able to

● describe different literary trends in poetry

● understand the themes in the prescribed poems

● analyse the poetic language used by poets like Surdas, Tulasidas, and

Meera Bai

● use newly learnt vocabulary in speech and writing

● writing critical essays on the prescribed poems

II Year - Semester IV

S.

No.

Subject Name


1. Hindi IV - CLE4J By the end of the course, students will be able to

● understand the characteristics of modern poetry

● apply the vocabulary used by modern poets in speech and writing

● analyse the poetic techniques used by the modern poets

● describe the techniques used in short stories and one-act plays

● write critical essays on modern writers and their works

Paper 1 - French

I Year - Semester I

S.

No.

Subject Name


1 French I-

CLK1S


● remember basic words and phrases related to transportation, fruits,

and vegetables

● understand basic grammar concepts like articles, prepositions, verbs,

and adjectives

● practise pronunciation using listening comprehension activities

● analyse sentence structures in simple texts

● write short essays using simple vocabulary


S.

No.

Subject Name


1 French II-

CLK2L


● recollect new vocabulary learnt from prescribed texts

● understand grammatical rules and sentence structures

● apply grammar rules and write error-free sentences

● develop conversations using simple vocabulary

● write simple essays or stories using new vocabulary


S.

No.

Subject Name


1 French III-

CLK3M


● recollect new vocabulary and grammatical rules

● apply grammatical rules to make meaningful sentences

● understand cultural references in the prescribed texts

● write general essays on favourite film, book, monument, etc.


S.

No.

Subject Name


1 French IV-

CLK4N


● remember new vocabulary and grammatical rules

● apply grammatical rules and make error-free sentences

● understand cultural differences using prescribed texts

● analyse sentence structures in prescribed texts

● write essays and letters in the prescribed formats

Part II - English

I Year - Semester I

S.

No.

Subject Name


1 English I –

CLZ1L (for B.A.,

B.Sc.,

B.Com.CS)

CLZ1K (for

B.Com. Gen.,

A&F, BBA, BCA)


• remember English vowel and consonant sounds and symbols, along

with the rules for word stress, sentence stress, intonation, and voice

modulation

• understand the life and works of renowned writers

• apply grammatical rules of tense, aspect, auxiliaries, ques tion tags,

interrogative / negative statements in writing error-free sentences

• analyse poetic language or story elements in the prescribed texts

• write critical essays and enact scenes from the prescribed stories


S.

No.

Subject Name


1 English II –

CLZ2L (for B.A.,

B.Sc.,

B.Com.CS)

CLZ2K (for

B.Com. Gen.,

A&F, BBA, BCA)


• recollect new vocabulary learnt through word-building activities

• apply grammatical rules of tenses, framing questions, and question

tags in identifying errors in sentences

• analyse figurative language in prescribed poems

• evaluate story elements in short stories

• synthesise information and write critical essays on poems, short

stories, and one-act plays


S.

No.

Subject Name


1 English III –

CLZ3P


• remember complex vocabulary used in literary contexts

• apply grammatical rules and avoid errors in speaking and writing

• analyse poetic elements in prescribed poems

• evaluate various biographies and critique the lives and works of famous

personalities

• develop their interview skills through mock-interviews


S.

No.

Subject Name


1 English IV –

CLZ4R


• remember interesting words and phrases used in one-act plays and

selected scenes from Shakespeare

• analyse the complex themes in one-act plays and short stories

• apply various techniques in letter writing, précise writing,

paraphrasing, and report writing

• evaluate writing techniques used by playwrights and short story writers

• enact scenes from Shakespeare, one-act plays, or short stories

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