SCHEME/SYLLABUS
: MCA(SE)
(First Semester)
Code
No. : BA 607
Paper : Discrete Mathematics
Sets , Relations & Functions: Property of binary relations, equivalence, compatibility, partial ordering relations, hasse diagram, functions, inverse functions, composition of functions, recursive functions.
Mathematical Logic: Logic operators, Truth tables, Theory of inference and deduction, mathematical calculus , predicate calculus, predicates and quantifiers.
Groups & Subgroups: Group axioms, permutation groups, subgroups, cosets, normal subgroups, semi - groups , free semi – groups, monoids, sequential machines, error correcting codes, modular arithmetic, grammers.
Lattices & Boolean Algebra: Axiomatic definition of boolean algebra as algebraic structures with two operations basic results truth values and truth tables, the algebra of propositional functions, boolean algebra of truth values.
Finite Fields: Definition, representation, structure, minimal polynomials, primitive elements, polynomial roots.
Combinatorics & Recurrence Relations: Disjunctive and sequential counting, combinations and permutations, enumeration without repetition, recurrence relation, fibonacci relation, solving recurrence relation by substitution, solving non – recurrence relation by conversion to linear recurrence relation.
References: