Utkal University, Odisha, Mathematics Semester 1, Discrete Mathematics Syllabus

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Unit - 1 Sets

Unit 1

Sets

1.1 Sets

1.2 Relations Equivalence relations partial ordering well ordering axiom of choice Zorn’s lemma

1.3 Functions cardinals and ordinals countable and uncountable sets statements compound statements

1.4 Proofs in Mathematics Truth tables Algebra of propositions logical arguments

1.5 Wellordering property of positive integers Division algorithm Divisibility and Euclidean algorithm

1.6 Congruence relation between integers modular arithmetic

1.6 Chinese remainder theorem Fermat’s little theorem

Unit - 2 Principles Of Mathematical Induction

Unit 2

Principles of Mathematical Induction

2.1 Principles of Mathematical Induction

2.2 Pigeonhole principle

2.3 Principle of inclusion and exclusion

2.4 Fundamental Theorem of Arithmetic

2.5 Permutation combination circular permutations binomial and multinomial theorem

2.6 Recurrence relations generating functions generating function from recurrence relations

Unit - 3 Matrices

Unit 3

Matrices

3.1 Matrices algebra of matrices

3.2 Determinants fundamental properties minors and cofactors product of determinantLook at the following procedure in order to understand the concept of determinants

3.3 Adjoint and inverse of a matrix Rank and nullity of a matrix

3.4 Systems of linear equations row reduction and echelon forms solution sets of linear systems applications of linear systems

3.5 Eigen values Eigen vectors of a matrix

Unit - 4 Graphs

Unit 4

Graph terminology

4.1 Graph terminology types of graphs subgraphs isomorphic graphs

4.2 Adjacency and incidence matrices

4.3 Paths Cycles and connectivity

4.4 Eulerian and Hamiltonian paths

4.5 Planar graphs

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