Discrete Mathematics
The complete BCA syllabus for Discrete Mathematics (CASC-01), the first-semester Discipline-Specific Course of the Bachelor in Computer Application programme at Chhattisgarh state universities (NEP four-year UG, 2024-28) — sets, relations, POSETs and lattices; mathematical logic, Boolean algebra and switching circuits; group theory; and graph theory.
Discrete Mathematics · English
by Dr. H.K. Pathak · ₹480 — covers this full syllabus.
Course contents — unit by unit
Unit 1 · Sets & Relations, POSET & Lattices
Definitions and types of sets, operations on sets, inclusion-exclusion principle, Cartesian product and its properties; relations and their types, equivalence relation, partial-order relation; functions — injective, surjective and bijective mappings; properties of partially ordered sets (POSET), Hasse diagrams, maximal and minimal elements, join and meet semilattices, sub-lattices, distributive and complemented lattices.
Unit 2 · Mathematical Logic, Boolean Algebra & Switching Circuits
Propositional logic and logical connectors; Boolean algebras and their properties, conjunctive and disjunctive normal forms, Boole's expansion theorem, Boolean polynomials and their minimal forms, Quine-McCluskey method, Karnaugh diagrams, switching circuits and their applications.
Unit 3 · Group Theory
Semigroup, monoid, group, subgroup, abelian group, finite and infinite groups, product and quotient of algebraic structures, Lagrange's theorem, rings, integral domain, field, and applications of group theory.
Unit 4 · Graphs
Definition, examples and basic properties of graphs, Königsberg seven-bridge problem, subgraphs, pseudographs, complete graphs, planarity, cyclic and chromatic number, handshaking theorem, bipartite graphs, isomorphism of graphs, paths and circuits, Eulerian circuits, Hamiltonian cycles, adjacency matrix, weighted graphs, travelling-salesman problem, shortest path and Dijkstra's algorithm.