CertifiedCourse Overview:
This university-level course introduces key discrete structures used in computer science and engineering. Students explore propositional and predicate logic, proof techniques, sets, relations, functions, combinatorics, recurrence relations, graphs, and algebraic structures like groups and lattices. Designed for BTech or BCA students, it emphasizes practical applications in algorithm design and program correctness.
Learning Objectives:
Master logic and proof methods for rigorous problem-solving.Apply counting principles, permutations, and inclusion-exclusion to combinatorial problems.Analyze graphs, trees, and relations for modeling computational problems.Solve recurrence relations and understand algebraic structures for advanced CS topics.
Syllabus OutlineUnit 1:
Logic and Proofs – Propositional equivalences, quantifiers, rules of inference, direct/contradiction proofs, mathematical induction.
Unit 2:
Sets, Relations, Functions – Operations, properties, equivalence relations, injections/surjections, composition.
Unit 3:
Combinatorics – Pigeonhole principle, permutations/combinations, binomial theorems, generating functions.
Unit 4:
Number Theory and Recurrences – Modular arithmetic, GCD, solving linear recurrences via substitution or characteristic equations.
Unit 5:
Graphs and Algebraic Structures – Paths/circuits, Euler/Hamilton, groups, lattices, Boolean algebra.
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