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Mathematical logic and proof, mathematical induction, counting methods, recurrence relations, algorithms and complexity, graph theory and graph algorithms.
Discrete Mathematics with Graph Theory, Goodaire and Parmenter, 3rd edition
Logic and proofs: Compound statements, proofs, truth tables, sets, relations, functions.
|0.1-0.2, 2.1-2.4, 3.1-3.2||11|
Algorithms and recursion. Division algorithm, Euclidean algorithm, congruence, mathematical induction, recursively defined sequences, recurrence relations and the characteristic polynomial, algorithms, complexity, searching and sorting.
|4.1-4.2, 4.4-4.5, 5.1-5.3, 8.1-8.3||11|
Combinatorics: Inclusion/exclusion principle, addition and multiplication rules, pigeonhole principle, permutations, combinations, repetitions, probability, binomial theorem.
|6.1-6.3, 7.1-7.5, 7.7||11|
Graph Theory: Isomorphism, Eulerian paths, Hamiltonian paths, Dijkstra's algorithm, trees, Kruskal's algorithm, planar graphs, chromatic number.
|9.1-9.3, 10.1-10.2, 10.4, 12.1-12.3, 13.1-13.2||11|