This course is an advanced (honors) version of "COMP 2711: Discrete Mathematical Tools for Computer Science" which provides a much more in-depth treatment of a wide variety of important mathematical concepts that form the theoretical basis of modern computer science.

Discrete mathematics needed for the study of computer science: sets, functions, propositional logic, predicate logic, rules of inference, proof techniques, pigeonhole principle, basic and generalized permutations and combinations, binomial coefficients, inclusion-exclusion principle, probability theory, Bayes theorem, expectation, variance, random variables, hashing, cryptography and modular arithmetic, Euclid’s division theorem, multiplicative inverse, divisibility, RSA cryptosystem, Chinese remainder theorem, mathematical induction, strong induction and well-ordering property, recursion, recurrence relations, graph representation, isomorphism, connectivity, Eulerian paths, Hamiltonian paths, planarity, graph coloring. Gentle introduction to many discrete mathematical concepts that will appear later in more advanced computer science courses.

• Proofs and Reasoning: Propositional Logic, First-order (Predicate) Logic, Quantifiers, Proof by contradiction, Mathematical Induction, the Pigeonhole Principle, the Invariant Principle, the Extremal Principle, ...
• Set Theory: ZMC, Peano's Axioms, Dedekind Cuts, Relations, Functions, Ordinals and Cardinals, Russel's Paradox, ...
• Enumerative Combinatorics: Rules of Sum and Product, Permutations and Combinations, Inclusion-Exclusion, Catalan and Stirling Numbers, Generating Functions, Recurrence Relations, Double Counting, ...
• Probability Theory: Discrete and Countable Probability Spaces, Axiomatic Probability Theory, Measure Functions, Lebesgue Integrals, Conditional Probability, Independence, Random Variables, Bayesian Reasoning, Expectation, Stochastic Processes, Markov Chains, Markov Decision Processes, ...
• Number Theory: Divisibility, GCD, LCM, Primes, Congruence, Chinese Remainder Theorem, Theorems of Fermat, Euler and Wilson, Quadratic Reciprocity Law, the RSA and El-Gamal Cryptosystems, ...
• Graph Theory: Adjacency, Walks, Paths, Cycles, (Strong) Connectivity, Distance, Trees, Spanning Trees, Bipartite Graphs, Matchings, Shortest Paths, ...
• Game Theory: Combinatorial Games, Sprague-Grundy Theorem, Normal Form (Nash) Games, Nash Equilibria, Correlated Equilibria, Infinite Games on Graphs, ...