Discrete Mathematics

Discrete Mathematics (CSC 13103)

III Sem B.Tech. CSE & Dual Degree CSE

(3-0-0)

Attendance: Students having attendance below 75% will not be allowed to appear in End Sem exam.

Class Timing:

Tuesday: 10:00 - 10:55 AM

Wednesday: 10:00 - 10:55 AM

Thursday: 08:00 - 08:55 AM

Marks Distribution:

Mid Sem Exam

30

End Sem Exam

60

Class Test &

Assignment

10

Exam Schedule:

Mid Sem Exam

19th Sep 2018

Time: 8:30-10:30 AM

End Sem Exam

24th Nov 2018

Time: 9:00-12:00 PM

Course Content:

Mathematical Logic: Propositional logic; Conjunction, Disjunction, Negation, Conditional statements; Tautology; De Morgan’s Laws; Predicates and Quantifiers; Rule of Inferences; Methods of Proofs; Conjunctive and Disjunctive Normal Forms.

Sets: Types of Set; Set Operations; Partitions of Sets; Set Identities; Addition Principle; Computer Representation of Sets.

Functions: Injective, Surjective, Bijective Functions; Inverse of a Function; Composition of Functions; Theorems related to Function.

Relation: Relations; Representation of Relation; Properties of Relation; Equivalence Relations; Partial Orderings; Lattices; Maximal Properties of Relation.

Congruence Arithmetic: Elementary properties; Linear Congruence equation.

Induction and Recurrence: Mathematical Induction; Linear Recurrence Relations; Divide-and-Conquer Recurrence Relations.

Combinatorics: Basic Counting Principles; The Inclusion-Exclusion Principle; Pigeonhole Principle; Permutations and Combinations.

Graph Theory: Basic Terminologies; Degree; Connectivity; Trees.

Boolean Algebra: Basic Theorems on Boolean Algebra; Duality Principle.

Group: Properties; Types of Group; Lagrange’s Theorem.

Ring: Properties; Types of Ring; Integral Domain; Field.

Text and Reference Books:

    1. Discrete Mathematics and its applications, K. H. Rosen, McGraw-Hill Education (India) Pvt. Ltd.

    2. Discrete Mathematics for Computer Scientist & Mathematicians, J. L. Mott, A. Kandel, and T. P. Baker, Prentice-Hall.

    3. Discrete Mathematical Structures, B. Kolman, R. C. Busby, and S. C. Ross, PHI.

    4. Discrete Mathematical Structures with Applications to Computer Science, J. P. Tremblay and R. Manohar, Tata McGraw-Hill Education (India) Pvt. Ltd.

    5. Discrete Mathematics, S. Lipschutz, M. L. Lipson, and V. H. Patil, McGraw-Hill Education (India) Pvt. Ltd.

Resource Material:

  1. Discrete Mathematics and its applications, K. H. Rosen

  2. Mid Semester Question Paper, Monsoon, 2017-18