· Web viewPigeonhole Principle (b) Principle of Inclusion & Exclusion. Q5 (a) find the no. of...

COURSE PLAN

2013-14

Regulation: R11

FACULTY DETAILS:Name of the Faculty:: Dr. Sumagna Patnaik

Designation: Prof. & Head Department:: MCA

COURSE DETAILS Name Of The Programme:: M.C.A Batch:: 2013

Designation:: Year 2013 Semester First

Department:: MCATitle of The Subject Mathematical

Foundation of Computer Science

Subject Code 09MCC111

No of Students 11

COURSE PLAN

2013-14

Regulation: R11


Designation: Prof. & Head Department:: MCA

1. TARGET

a) Percentage Pass 90%

b) Percentage I class 80%

2. COURSE PLAN

(Please write how you intend to cover the contents: i.e., coverage of Units by lectures, guest lectures, design exercises, solving numerical problems, demonstration of models, model preparation, or by assignments, etc.)

As a faculty my intention is cover the contents of units by lectures, solving numerical problems from inside the book as well as from outside. In order to make the students to attend other problems to improve their problem solving techniques, my plan is to give assignment to students before the first and second internals.

3. METHOD OF EVALUATION

3.1. √ Continuous Assessment Examinations (CAE 1, CAE 2)

3.2. √ Assignments / Seminars

3.3. Mini Projects

3.4. Quiz

3.5. √ Term End Examination

3.6. Others

4. List out any new topic(s) or any innovation you would like to introduce in teaching the subject in this Semester.

Prim’s Algorithm to find minimal spanning tree Kruskal algorithm to find minimal spanning tree

Signature of HOD Signature of FacultyDate: Date:

GUIDELINES TO STUDY THE SUBJECT

2013-14

Regulation: R11


Designation: Professor & Head Department:: M.C.A

Guidelines for Preparing the Course:

Course Description:Master of Computer Application is a course where a student has to acquire knowledge regarding the real world application. Student has to understand the concept

thoroughly so that he/she can apply the related concept based on situation.

Course Objectives:1. Reasoning using mathematical logic develops in every area of knowledge 2. Logic is the science dealing with methods of reasoning can be presented with the help of quantified

statement 3. Set theory & relation concept are presented in the form of recapitulation. 4. Set theoretic properties of functions and their immediate consequences 5. Algebraic structure, semi group, group structure are discussed6. Combinatorics deals with counting technique and related algebra with principles of inclusion and

exclusion is discussed7. Recurrence relation with illustrative examples are discussed8. Introduce and illustrate the concepts of directed graph and graphs in graph theory9. Related concepts of planar graph and trees are discussed10. Graph colouring and spanning tree in graph theory are discussed

Learning Outcomes:Students can improve reasoning skills using mathematical logic which develops in every area of knowledge. Concepts of set theory & its properties, relations and function can be clear so that it can be represented in the form of matrix and pictorial representation.Student can represent some basic material concerned with graphs with the help of related concept of graph theory.

COURSE OBJECTIVES2013-14

Regulation: R11


Designation: Professor & Head Department:: MCA

On completion of this Subject / Course the student shall be able to:

S.No. Objectives Outcomes

1. Understands reasoning with the help of mathematical logic

Ability to develop reasoning skill

2. Concepts of representing quantified statement in the form of logic is clear

Ability to develop logic in every area of knowledge

3. Set theory , its properties, relation concepts must be clear

Ability to represent in the form of matrix and pictorial representation

4.

Ability to apply on real world situation based on this concept

Algebraic structure, semi group, group structure must be clear

5.

Ability to improve the counting technique

counting technique and related algebra with principles of inclusion and exclusion is discussed6.

Recurrence relation with illustrative examples are discussed

Ability to understand the concept of recurrence relation with examples

7.To explain the concept of directed graph and graphs in graph theory

Ability to understand the concepts of graph theory

8. Related concepts of planar graph is discussed in detail

Ability to represent the planar and non planar graph

9. Concepts of trees are discussed in detail Ability to represent in graphical form

of tree

10.

Graph colouring and spanning tree in graph theory are discussed

Ability to represent some basic material concerned with graphs with the help of related concept og graph theory

Signature of FacultyDate:

Note: For each of the OBJECTIVE indicate the appropriate OUTCOMES to be achieved.Kindly refer Page 16, to know the illustrative verbs that can be used to state the objectives.

4

COURSE OUTCOMES2013-14

Regulation: R11



The expected outcomes of the Course / Subject are:

S.No. General Categories of Outcomes Specific Outcomes of the Course

A.An ability to apply knowledge of mathematics, An ability to apply the knowledge of mathematical logicscience, and engineering

B.An ability to design and conduct experiments, as

An ability to analyze and interpret data in the form of set theory and relation

well as to analyze and interpret data

An ability to design a system, component, or An ability to apply specific mathematical technique to meet desired needs C. process to meet desired needs within realistic

Constraints such as economic, environmental,social, political, ethical, health and safety,Manufacturability and sustainability

D. An ability to function on multi-disciplinary teams An ability to solve multi disciplinary problems

E.An ability to identify, formulate, and solve An ability to identify, formulate, and solveengineering problems engineering problems

F.An understanding of professional and ethical An understanding of professional and ethicalresponsibility responsibility

G. An ability to communicate effectively An ability to represent effectively

The broad education necessary to understand the The mathematical education is necessary to understand theH. impact of engineering solutions in a global, impact of engineering solutions in a global,

economic, environmental, and societal context economic, environmental, and societal context

I.A recognition of the need for, and an ability to A recognition of the need for an ability toengage in life-long learning engage in life-long learning

J. A knowledge of contemporary issues A knowledge of contemporary issues

An ability to use the techniques, skills, and An ability to use the mathematical skills necessary to solve the problemsK. modern engineering tools necessary for

engineering practice.

Objectives – Outcome Relationship Matrix (Indicate the relationships by mark). Outcomes

A B C D E F G H I J KObjectives

1. X X X2. X X X3.4.5.6.7.8.9.10.

5



The Schedule for the whole Course / Subject is::

COURSE SCHEDULE2013-14

Regulation: R11

S. No. Description Duration (Date) Total No.From To of Periods

1.

Mathematical logic, statements and notation, connectives Well formed formulas, Truth Tables, tautology, equivalence implication, Normal forms, Quantifiers, universal quantifiers.

Predicates: Predicative logic, Free & Bound variables, Rules of inference, Consistency, proof of contradiction, Automatic Theorem Proving.

2.

Relations: Properties of binary Relations, equivalence, transitive closure, compatibility and partial ordering relations, Lattices, Hasse diagram. Functions: Inverse Function, Composition of functions, recursive Functions, Lattice and its Properties.

Algebraic structures: Algebraic systems, Examples and general properties, Semi groups and monoids, groups, and sub groups, homomorphism, Isomorphism.

3.

Elementary Combinatorics: Basics of counting, Combinations & Permutations, with repetitions, Constrained repetitions, Binomial Coefficients, Binomial and Multinomial theorems, the principles of Inclusion – Exclusion, Pigeon hole principles and its application

4.

Recurrence Relations: Generating Functions, Function of Sequences, Calculating Coefficients of generating functions, Recurrence relations, Solving recurrence relation by substitution and Generating functions, the method of Characteristic roots, solution of Inhomogeneous Recurrence Relations.

5.

Graph Theory: Representation of Graphs, DFS, BFS, Spanning Trees, Planar Graphs.

Graph Theory and Applications, Basic Concepts, Isomorphism and Sub graphs, Multi graphs and Euler circuits, Hamiltonian graphs, Chromatic Numbers.

Total No. of Instructional periods available for the course: Hours / Periods

SCHEDULE OF INSTRUCTIONS2013-14

UNIT - I Regulation: R11


Designation: Professor & Head

Department:: MCA

The Schedule for the whole Course / Subject is:: MFCS

SI. No. of Objectives & ReferencesDate Topics / Sub - Topics Outcome (Text Book, Journal…)No. Periods Nos. Page No___ to ___

1 1 Logical connectives and Truth Tables Rp1 Page No 1 to 14

2 1 Tautology, Contradiction, Normal forms R1 Page No 14 to 40

3 1Examples on Normal forms Principal Normal form, R1 Page No 41 to 45

4 2Open statement quantifier, free & bound variable, logical equivalence R1 Page No 68 to 78

5 1Rule of Inference, Examples based on rule of inference R1 Page No 51to 64

6 1 Logical implication involving quantifier R1 Page No 83 to 90

7 1 Examples , Methods of proof R1 Page No 98 to 101

8 2 Solving problem while clarifying doubts

Signature of FacultyDate

Note: 1. ENSURE THAT ALL TOPICS SPECIFIED IN THE COURSE ARE MENTIONED.2. ADDITIONAL TOPICS COVERED, IF ANY, MAY ALSO BE SPECIFIED BOLDLY. 3.MENTION THE CORRESPONDING COURSE OBJECTIVE AND OUT COME NUMBERS AGAINST EACH TOPIC.


UNIT - II Regulation: R11



Department:: MCA



1 Set Theory and its properties

1 Digraph of relation with examples

1 Composition of relation with examples

2Properties of binary Relations, Reflexive, symmetric, transitive, Antisymmetric relation

1 Equivalence relation, partial order, total order

1 Hasse Diagram with examples, POSET

1 Lattice with examples,Function

1Inverse function, composition of function & recursive function

2 Algebraic structure, Groups, Semi groups


Note: 1. ENSURE THAT ALL TOPICS SPECIFIED IN THE COURSE ARE MENTIONED.2. ADDITIONAL TOPICS COVERED, IF ANY, MAY ALSO BE SPECIFIED BOLDLY.

MENTION THE CORRESPONDING COURSE OBJECTIVE AND OUT COME NUMBERS AGAINST EACH TOPIC.


UNIT - III Regulation: R11



Department:: MCA



1 Rule of sum and product

2 Permutation and examples based on concept

1 Combination and examples based on concept

1 Binomial and multinomial theorem

1 Examples based on concept

2Principle on inclusion and exclusion with examples

1 Pigeonhole principle and its application

1 Repetition of combinatorics


Note: 1. ENSURE THAT ALL TOPICS SPECIFIED IN THE COURSE ARE MENTIONED.

2. ADDITIONAL TOPICS COVERED, IF ANY, MAY ALSO BE SPECIFIED BOLDLY. MENTION THE CORRESPONDING COURSE OBJECTIVE AND OUT COME NUMBERS AGAINST EACH TOPIC.


UNIT - IV Regulation: R11



Department:: MCA



1 Generating Functions with examples

1 Recurrence Relation with examples

1 Method of generating functions

2 Solving Problems based on this concept





UNIT - V Regulation: R11

FACULTY DETAILS:Name of the Faculty:: Dr. Sumagna patnaik


Department:: MCA



1 Directed graph, in-degree, out-degree, graph

1Bipartite graph, complete bipartite graph, vertex degree, hand shaking property

1Isomorphism, isomorphism of a graph, sub graph, vertex disjoint, edge disjoint graph,

2 Walk & classification, Euler circuit and Euler Trail

1 Hamilton cycle and Hamilton path

1 Planar and non-planar graph

1 Graph coloring, tree, spanning tree

2 BFS and DFS algorithm for spanning tree

1 Minimal spanning tree,

1Kruskal and Prim’s algorithm for finding out the minimal spanning tree




COURSE COMPLETION STATUS

2013-14

Regulation: R11

FACULTY DETAILS: Name of the Faculty:: Dr. Sumagna Patnaik

Subject:: MFCS Subject Code

Department:: MCA

Actual Date of Completion & Remarks, if any

Nos. of

Units Remarks Objectives

Achieved Unit 1 Completed

Unit 2 Completed

Unit 3 Completed

Unit 4 Completed

Unit 5 Completed

Signature of Dean of School Signature of FacultyDate: Date:

NOTE: AFTER THE COMPLETION OF EACH UNIT MENTION THE NUMBER OF OBJECTIVES ACHIEVED.

TUTORIAL SHEETS - I

2013-14

Regulation: R11




Date:

This Tutorial corresponds to Unit Nos.1 & 2 Time:

Q1. a) Discuss the rules of inference?b) Explain clearly the proof of contradiction?

Q2. a) Let P, Q,R are the stmts. P: you have the fee Q: You miss the final exam R: You pass the course Write the following properties into stmt form:

i) p->Q ii) 7Q->R iii) Q->7R iv)PVQVR v)(p->7R)V(Q->7R) vi) (p^Q)V(7Q^R) You have to give truth tables also

b) What is the minimal set of connectives required for a well formed formula?

Q3. a)Let f(x)=2x+3 g(x)=2x-4 and h(x) =4x for x ε R where R is the set of real numbers. Find gof , fog,fof, gog,foh,hog,hof and fohog

Note: functions f(x),g(x),h(x) may change in examb) What is Hanediagram in partial ordered set?Draw the diagram for m=25?(atleast 4 elements)

Q4. a) What is connective & Explain EX-OR and NAND? b) Write truth table for (p↓p)↑[(Q↓ Q) V (7P ↑ 7Q)]

Q5. a) What is NF? Describe types?b) What is the diff b/w PCNF & PDNF?

Please write the Questions / Problems / Exercises which you would like to give to the students and also mention the objectives to which these questions / Problems are related.


TUTORIAL SHEETS - II

2013-14

Regulation: R11




Date:

This Tutorial corresponds to Unit Nos.3 & 4 Time:

Q1. .(a) On the set Q of all rational numbers , the operation * is defined by a*b=a+b-ab . Show that under this operation , Q forms commutative Monoid.

(b) For any element a, b in a Group G , we have (i) (a-1)-1 = a (ii) (ab)-1 = b-1a-1

Q2. (a) A woman has 11 close relatives and she wishes to invite 5 of them to dinner. In how many ways can she invite them in the

following situations

(i) There is no restriction in the choice

(ii) Two particular person will not attend separately

(iii) Two particular person will not attend together

(b)Prove that for all integers n, r >= 0 if n+1 > r then

P(n+1,r)= (n+1 / n+1-r) P(n,r)

Q3. (a) find the co-efficient of a2 b3 c2 b5 in the expansion of (a+2b-3c+2d+5)16

(b)Find the co-efficient of x3 y3 z2 in the expansion of (2x-3y+5z)8

Q4 Explain

(a) Pigeonhole Principle (b) Principle of Inclusion & Exclusion

Q5 (a) find the no. of integers solutions of x1+x2+x3+x4+x5=30, Where x1>2, x2 ≥ 3 x3≥ 4 x4≥2 x5≥0 (b) A total amount of 1500 is to be distributed three poor students A, B, C of class in how many ways the distribution can be made in multiples of 100

1. If every one of two must get at least 300 rupees.2. If a must get at least 500 rupees and B and C get at least 400 each.





TUTORIAL SHEETS - III

2013-14

Regulation: R11

Date:

This Tutorial corresponds to Unit Nos.5 Time:

Q1. . Explain BFS algorithm for finding spanning tree with one example

Q2. Explain DFS algorithm for finding the spanning tree with an example

Q3 (a) When two graphs are said to be isomorphic? Explain with an example?(b) The following graphs are isomorphic or not

a b e

d c g f

Q4. Explain(i) Chromatic Number(ii) Hamilton Graph

Q5. Explain prime’s algorithm and Kruskal algorithm with example?



h

ILLUSTRATIVE VERBS

FOR STATINGINSTRUCTIONAL OBJECTIVES

2013-14

Regulation: R11

These verbs can also be used while framing questions for Continuous Assessment Examinations as well as for End – Semester (final) Examinations.

ILLUSTRATIVE VERBS FOR STATING GENERAL OBJECTIVES

Know Understand Analyze Generate

Comprehend Apply Design Evaluate

ILLUSTRATIVE VERBS FOR STATING SPECIFIC OBJECTIVES:

A. Cognitive Domain

1 2 3 4 5 6

Knowledge Comprehension Application Analysis Synthesis EvaluationUnderstandingof knowledge & of whole w.r.t. its combination of judgementcomprehension constituents ideas/constituents

Define Convert Change Breakdown Categorize Appraise

Identify Defend Compute Differentiate Combine Compare

Label Describe (a Demonstrate Discriminate Compile Conclude

List procedure) Deduce Distinguish Compose Contrast

Match Distinguish Manipulate Separate Create Criticize

Reproduce Estimate Modify Subdivide Devise Justify

Select Explain why/how Predict Design Interpret

State Extend Prepare Generate Support

Generalize Relate Organize

Give examples Show Plan

Illustrate Solve Rearrange

Infer Reconstruct

Summarize Reorganize

Revise

B. Affective Domain C. Psychomotor Domain (skill development)Adhere Resolve Bend Dissect Insert Perform Straighten

Assist Select Calibrate Draw Keep Prepare Strengthen

Attend Serve Compress Extend Elongate Remove Time

Change Share Conduct Feed Limit Replace Transfer

Develop Connect File Manipulate Report Type

Help Convert Grow Move preciselyReset Weigh

Influence Decrease Handle Operate Run

Initiate Demonstrate Increase Paint Set

LESSON PLANUnit-1

2013-14

Regulation: R11

Name of the Faculty:

Subject Subject CodeUnit

INSTRUCTIONAL OBJECTIVES:

SessionNo

Topics to be coveredTime Ref

Teaching Method

1Logical connectives and Truth Tables

2Tautology, Contradiction, Normal forms

3Examples on Normal forms Principal Normal form,

4Open statement quantifier, free & bound variable, logical equivalence

5

6

7

8

9

10

On completion of this lesson the student shall be able to(Outcomes)1.

2.

3.

4

ASSIGNMENTUnit-I

2013-14

Regulation: R11

Assignment / Questions

Signature of Faculty

Note: Mention for each question the relevant objectives and outcomes.

LESSON PLANUnit-II

2013-14

Regulation: R11




SessionNo


Teaching Method

On completion of this lesson the student shall be able to1.

2.

3.

4

ASSIGNMENTUnit-II

2013-14

Regulation: R11




LESSON PLANUnit-III

2013-14

Regulation: R11




SessionNo


Teaching Method

On completion of this lesson the student shall be able to(Outcomes)1.

2.

3.

4

ASSIGNMENTUnit-III

2013-14

Regulation: R11




LESSON PLANUnit-IV

2013-14

Regulation: R11




SessionNo


Teaching Method

On completion of this lesson the student shall be able to (Outcomes)1.

2.

3.

4

ASSIGNMENTUnit-IV

2013-14

Regulation: R11




LESSON PLANUnit-V

2013-14

Regulation: R11




SessionNo


Teaching Method

On completion of this lesson the student shall be able to (Outcomes)1.

2.

3.

4

ASSIGNMENTUnit-V

2013-14

Regulation: R11




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