Below is the syllabus for Discrete Structures:-
Set Theory & Logic
Fundamentals – Sets and subsets, Venn Diagrams, Operations on sets, Laws of Set Theory, Power Sets and Products, Partition of sets, The Principle of Inclusion-Exclusion.
Logic: Propositions and Logical operations, Truth tables, Equivalence, Implications, Laws of Logic, Normal forms, Predicates and quantifiers, Mathematical Induction.
Relations, diagraphs, and lattices
Product sets and partitions, relations and diagraphs, paths in relations and digraphs, properties of relations, equivalence and partially ordered relations, a computer representation of relations and diagraphs, manipulation of relations, Transitive closure, and Warshall’s algorithm, Posets and Hasse Diagrams, Lattice.
Functions and Combinatorics
Definitions and types of functions: injective, subjective and bijective, Composition, identity and inverse, Review of Permutation and combination-Mathematical Induction, Pigeon hole principle, Principle of inclusion and exclusion, Generating function-Recurrence relations.
Algebraic structures with one binary operation – semigroups, monoids and groups, Product and quotient of algebraic structures, Isomorphism, homomorphism, automorphism, Cyclic groups, Normal sub-group, codes and group codes, Ring homomorphism, and Isomorphism.
- Elements of Discrete Mathematics C.L Liu, 1985, Reprinted 2000, McGraw Hill
- Discrete mathematical structures by B Kolman RC Busby, S Ross PHI Pvt.
- Discrete Mathematics by Bisht & Dhami, Oxford University Press,2015
- Discrete Mathematical Structures with Applications to Computer Science, by Tremblay P, and Manohar R., McGraw Hill Book Company, 1975, International Edition, 1987.
- Discrete and Combinatorial mathematics “, Ralph, Grimaldi, Addison-Wesley Publishing Company, Reprinted in 1985.
- Discrete Mathematics and its Applications “, Kenneth H.Rosen, McGraw Hill Book Company, 1999. Sections: 7.1 to 7.5.
- Discrete Mathematics for computer scientists and Mathematicians, Joe L. Mott, Abraham
Below is the link to download Discrete Structures notes.