B.Sc. CSIT - Second Semester
Sets: Sets and subsets, power set, Cartesian product, set operations, Venn diagram, inclusion-exclusion principle, computer representation of sets. Functions: basic concepts, one-to-one, onto, composition, inverse functions.
Integers and division; primes and GCD; Extended Euclidean Algorithm; integers and algorithms; applications of number theory such as linear congruences. Matrices: matrix operations, inverses, applications.
Propositional logic; propositional equivalences; predicates and quantifiers; negation of quantified statements; proofs of quantified statements; nested quantifiers; rules of inference; proof techniques including direct, indirect, and contradiction.
Mathematical induction; strong induction and well-ordering principle; generalized induction; recursive definitions; structural induction; recursive algorithms; program correctness.
Basics of counting; pigeonhole principle; permutations and combinations; two-element subsets; counting subsets; binomial coefficients; generalized permutations; discrete probability concepts.
Relations and their properties; n-ary relations with applications; representing relations; closure of relations; equivalence relations; partial orders. Graphs: basic definitions, types of graphs, applications in computer science.