Fundamental approach to discrete mathematics

Salient Features Mathematical logic, fundamental concepts, proofs and mathematical induction (Chapter 1) Set theory, fundamental concepts, theorems, proofs, Venn diagrams, product of sets, application of set theory and fundamental products (Chapter 2) An introduction to binary relations and concepts, graphs, arrow diagrams, relation matrix, composition of relations, types of relation, partial order relations, total order relation, closure of relations, poset, equivalence classes and partitions. (Chapter 3) An introduction to functions and basic concepts, graphs, composition of functions, floor and ceiling function, characteristic function, remainder function, signum function and introduction to hash function. (Chapter 4) The algebraic structure includes group theory and ring theory. Group theory includes group, subgroups, cyclic group, cosets, homomorphism, introduction to codes and group codes and error correction for block code. The ring theory includes general definition, fundamental concepts, integral domain, division ring, subring, homomorphism, an isomorphism and pigeonhole principle (chapters 5, 6 and 7)