MTH-401 DISCRETE MATHEMATICS

Sets: Definition, subsets and powersets, complement, union, intersection, Basic Laws of set operation

Relations: Cartesian product relations, domain and range, composition of relations, equivalence relations, partial ordering relations, lattices

Functions: Function as a relation, injection, surjection & bijection, composition of functions, identity and inverse functions, cardinality, characteristic function

Peano postulates & Finite induction: Example of proof by induction, recursive definitions, binary operations on a set

Groupoids: Commutative and associative, binary operations, binary operations with identity

Semi-groups : Monoid, boolean algebra, axiom of properties, atomic structure of a finite boolean algebra, homomorphism and isomorphism, disjunctive and conjunctive normal forms, algebra of propositions

Theory of group: axioms, properties, subgroups, cyclic groups, cosets, Lagrange’s theorem, normal subgroup, factor subgroup, homomorphism and isomorphism, fundamental theorem on homomorphism, permutations.

Finite Field: Definition, field of order ‘p’ (p is prime), polynomial over a field, Euclidean domain

TEXTBOOKS

1. Modern Algebra - by S. Nanda

2. Discrete Mathematics – by J.P Trumbley & R. Manalia

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