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:
Discrete Mathematics and its applications, K. H. Rosen, McGraw-Hill Education (India) Pvt. Ltd.
Discrete Mathematics for Computer Scientist & Mathematicians, J. L. Mott, A. Kandel, and T. P. Baker, Prentice-Hall.
Discrete Mathematical Structures, B. Kolman, R. C. Busby, and S. C. Ross, PHI.
Discrete Mathematical Structures with Applications to Computer Science, J. P. Tremblay and R. Manohar, Tata McGraw-Hill Education (India) Pvt. Ltd.
Discrete Mathematics, S. Lipschutz, M. L. Lipson, and V. H. Patil, McGraw-Hill Education (India) Pvt. Ltd.
Resource Material:
Discrete Mathematics and its applications, K. H. Rosen
Mid Semester Question Paper, Monsoon, 2017-18