Master the mathematical foundations of computer science with rigorous proofs, detailed explanations, and comprehensive examples from logic to graph theory
Courses
DM-01
Propositional Logic
Propositions, logical connectives, truth tables, logical equivalences, and normal forms (DNF/CNF)
DM-02
Predicate Logic and Proofs
Predicates, quantifiers, inference rules, and proof methods including direct, contraposition, and induction
DM-03
Sets and Set Operations
Set theory fundamentals, operations, identities, power sets, Cartesian products, and Venn diagrams
DM-04
Functions
Function definitions, injections, surjections, bijections, inverse functions, and composition
DM-05
Sequences and Cardinality
Sequences, summations, countable and uncountable sets, Cantor's diagonalization, and cardinality theory
DM-06
Algorithm Complexity
Algorithm analysis, Big-O/Ω/Θ notation, growth of functions, and complexity classes
DM-07
Number Theory
Divisibility, modular arithmetic, primes, GCD, Euclidean algorithm, and Chinese Remainder Theorem
DM-08
Induction and Recursion
Mathematical induction, strong induction, recursive definitions, and structural induction
DM-09
Counting Principles
Product and sum rules, permutations, combinations, binomial theorem, and pigeonhole principle
DM-10
Advanced Counting
Recurrence relations, generating functions, inclusion-exclusion principle, and derangements
DM-11
Relations
Binary relations, equivalence relations, partial orders, closures, and Hasse diagrams
DM-12
Graph Theory and Trees
Graph fundamentals, connectivity, Euler and Hamilton paths, trees, spanning trees, and planar graphs
Ready to Master Discrete Mathematics?
Begin your journey with propositional logic and build a solid foundation in discrete structures and mathematical reasoning