Lesson Plan DiscreteMathematics

8/10/2019 Lesson Plan DiscreteMathematics

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Dept. of Information Technology

VASAVI COLLEGE OF ENGINEERING

1. Course title : Discrete Mathematics

2.

Course code : BIT201

3. Lecture tutorial contact hours : 4 hrs per week

4. Total Semester Marks (Internal & External) : Internal 25 External 75

5. Prerequisites : Basic Mathematics.

6.

Nature of Course (Core/Elective) : core

7. Offering Department : Information Technology

8. Learning Objectives: This course is designed to introduce students to the techniques,

algorithms, and reasoning processes involved in the study of discrete mathematical

structures. Students will be introduced to set theory, inductive reasoning, elementary

and advanced counting techniques, equivalence relations, recurrence relations, graphs,

and trees. Through their study of these topics students will develop a greater

understanding of the breadth of mathematics and will acquire a familiarity with

concepts, structures and algorithms that are essential to the field of computer science

and applied mathematics.

9. Learning/Course Outcomes:

Upon successful completion of this course, students will:

i. Students will construct mathematical arguments using logical connectives and

quantifiers. Verify the correctness of an argument using propositional and predicate

logic and truth tables. Apply algorithms and use definitions to solve problems to

prove statements in elementary number theory.

ii.

Students will be able construct proofs using direct proof, proof by contraposition,proof by contradiction, Proof by cases, and mathematical induction. Calculate and

generate Permutation and Combination for the given scenario.

iii. Students will demonstrate the ability to solve problems using counting techniques in

the context of discrete probability. Solve problems involving recurrence relations and

generating functions.

iv. Analyze a relation and the properties and represent those using different properties

and diagrams. Define a graph and construct different paths and representing them.


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v. Define a tree and apply different traversal techniques to find the best solution.

Designing a circuit using different Logic gates and minimize them.

Topic Layout

10.

Lesson Plan11.Evaluation Scheme & Tools: Tests, quiz & assignments.

12.Teaching methodology & Supporting Tools: Blackboard, video lectures, OHP,PPTs

13.

Text Books & Reference Books:

i.

Kenneth H.RosenDiscrete Mathematics and its application5thedition, Mc

GrawHill, 2003.

ii.

J.P.Trembly, R.Manohar, Discrete Mathematical Structure with Application to

Computer Science, Mc Graw- Hill1997

14.Mapping of Course Objective & Program Objective

15.

Matrix of Course Outcome and Demonstration of Course Outcome

Distribution of each hour of course:

Topics to be covered

Tutorials to be done

Any activity related to the course (presentations/quiz/projects etc.)

8. Learning Outcomes

Unit I: (1.5weeks)

The student will be able to

1.

Prove propositional equivalence

2. Differentiate the types of Functions and their behavior

3. Analyze Quantifiers and Nested Quantifiers

4. Analyze the complexity of an algorithm

Unit II: (3 weeks)

1.

Construct proofs using direct proof, proof by contraposition, proof by

Contradiction, proof by cases, and mathematical induction.

2. Solve counting problems involving the multiplication rule, permutations, and

combinations (with and without replacement). Use standard notation.

3. Apply the Addition Rule and the Principle of Inclusion and Exclusion


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Unit III (3 weeks)

1. Solve Recurrence relations

2. Find the probability of random variable

3. calculate probabilities and discrete distributions for simple combinatorial

processes; calculate expectations

4. solve the problem using Divide & Conquer Method

5. apply inclusionexclusion principle

Unit IV (3 weeks)

1. Explain different types of relations and their properties.

2. Find shortest path

3. Explain graph coloring

Unit V (3 weeks)

1. Apply DFS and BFS for tree traversals

2. Find shortest path by using spanning tree

3. Find minimum spanning tree for a given graph

4. Design combinational logical circuits

Tutorials

For every two weeks one Tutorial based on the previous topics covered

Quizzes

Two Quizzes for every unit (5 Quizzes)

ASSIGNMENTS

One Assignment per unit (5 assignments)

Classroom Activities:

1. Polling

2.

Think pair share


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Graduate Attributes

PROGRAM

OUTCOMES

GRADUATE ATTRIBUTES

i ii iii Iv v vi vii viii ix x xi

a x x x

b x x X x

c X x x x

d X x x x x

e x x X x x x x

f x x x x x

g x x x x x

h x x x x x x x

i x x x x

j x x x x

K x X x x x

1. Program Outcomes

At the end of the program, the graduates will demonstrate


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a. Knowledge of required Mathematical, Electronic and Information Technology

Skills required in analyzing and solving real life problems.

b. Active participation in attempting and succeeding in competitive exams like

GATE, GRE, CAT etc.

c. An ability to identify, analyze and solve problems in the area of Information

Technology and Computer Science.d. An ability to develop software programs using various programming languages to

solve problems.

e. An ability to develop software applications for different real time problems.

f. Skills in handling the different Engineering tools, software tools and Equipment in

analyzing and solving problems.

g. Good written and oral communication skills

h.

An ability to work in laboratories and in a multi disciplinary environment.

i. An aptitude for continuous self education and ability for lifelong learning.

j.

Good professional and Ethical responsibilities.

k. An understanding of the impact of Engineering solutions on the society at large

and will be aware of the contemporary issues.

Graduate Attributes (based on OBE)

i. Engineering knowledge

ii. Problem analysis

iii. Design and development of solutions

iv. Investigation of complex problem

v. Modern tool usage

vi.

Engineer and societyvii. Environment and sustainability

viii. Ethics

ix. Individual and team work

x. Communication

xi. Lifelong learning + project management and finance


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Unit-1

week Lecture tutorial practical

1

Logic - Basic Compound Propositions,

Truth tables, Problems on TranslatingEnglish sentences into symbolic form

and vice versa, Propositional

Equivalences , Tautologies,

-

2

Predicates and quantifiers - Nested

quantifiers ,Set Operations- Functions,

Algorithms- Complexity of Algorithms,

Integers and division- Theorems

Propositional

Equivalence,

Tautology,

contradiction,

Quantifiers

-

3

Integers and division- some more

Theorems & Problems, Integers and

Algorithms, Applications to Number

Theory- Matrices

-

Unit - 2


4

Proof Strategy - Sequence and

Summation, Proof Strategy -

Sequence and Summation-examples,

Mathematical Induction, Recursive

Definitions and Structural Induction -

Recursive Algorithms

5

Basics of countingproblems,

Pigeonhole principlePermutation

and Combinations,

Mathematical

Induction

6

Permutation and Combinations

some more problems, Identities on

permutations and combinations,

Generalized Permutations and

combinations

Pigeonhole problems-

7

Binomial CoefficientsIdentities -

Generating permutations and

combinations,

Permutations &

Combinations-


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Unit-3


8

An introduction to Discrete

Probability - Probability Theory

Theorems and problems, Solving

recurrence Relations, Divide and

conquer relationsproblems.

Binomial theorem

9

Problems on Non- Homogeneous

Linear Recurrence Relations,

Generating functions Problems,

InclusionExclusionApplicationsof InclusionExclusion

Discrete probability,

Divide & Conquer-

Unit-4


10

Relations & their Properties, n-ary

relations and applications,

Representing relations Closures-

Equivalence relations - Partial

orderings, Problems on Equivalence

relations and partial orderings

Recurrencerelations, Inclusion-

Exclusion

-

11

Representing Graphs and Graph

Isomorphism, Connectivity

theorems, Euler and Hamiltonian

paths, Shortest path problems

-

12

Planar Graphs- Definitions

Theorems, Eulers Theorem Proof,

Coloring of Graphs Definitions -

Theorems

Graph, Hamilton

path, shortest path

problem

-

Unit-5

week lecture Tutorial practical

13 Introduction to Trees- Theorems, Graph coloring -


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G x x x x x

H x x x x x x x

I x x x x

J x x x x

K x x x x x

2. Program Outcomes

At the end of the program, the graduates will demonstrate

l. Knowledge of required Mathematical, Electronic and Information Technology

Skills required in analyzing and solving real life problems.

m. Active participation in attempting and succeeding in competitive exams like

GATE, GRE, CAT etc.

n. An ability to identify, analyze and solve problems in the area of Information

Technology and Computer Science.

o.

An ability to develop software programs using various programming languages to

solve problems.

p.

An ability to develop software applications for different real time problems.

q. Skills in handling the different Engineering tools, software tools and Equipment in

analyzing and solving problems.

r.

Good written and oral communication skillss. An ability to work in laboratories and in a multi disciplinary environment.

t. An aptitude for continuous self education and ability for lifelong learning.

u. Good professional and Ethical responsibilities.

v.

An understanding of the impact of Engineering solutions on the society at large

and will be aware of the contemporary issues.

Graduate Attributes (based on OBE)

i. Engineering knowledge

ii.

Problem analysisiii. Design and development of solutions

iv. Investigation of complex problem

v. Modern tool usage

vi.

Engineer and society

vii.

Environment and sustainability

viii.

Ethics

ix. Individual and team work

x. Communication

xi. Lifelong learning + project management and finance


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Unit-1

The Student will be able to

1.

Prove the given logical equivalence using/without using truth table

2.

Find the time complexity of an algorithm3.

List different types of functions

Unit-2

1.

Lesson Plan DiscreteMathematics

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