Topics: Discrete mathematics, logic, sets, functions, sequences, matrices, algorithms, Number theory, cryptography, induction, recursion, counting, discrete probability, advanced counting techniques, counting techniques, Linear Recurrence Relations, modelling computation, Finite-State Machines, relations, graphs, trees, boolean algebra, modelling computation, Boolean Functions, Logic Gates, Minimization of Circuits.Tree Traversal, Spanning Trees, Minimum Spanning Trees, Graph Models, Graph Terminology, Graph Isomorphism, Connectivity, Euler path, Hamilton Path, Shortest-Path Problems, Planar Graphs, Graph Coloring, Representing Relations, Equivalence Relations, Probability Theory, Bayes Theorem, variance, Pigeonhole Principle, permutation combination, binomial coefficient, Recursive Algorithms, Program Correctness, Divisibility, Modular Arithmetic, Integer Representations, Set Operations, Cardinality of Sets

Topics: Abstract Algebra, intergers, functions, groups, polynomials, commutative rings, fields, Congruences, intergers modulo, equivalence relations, permutations, subgroups, isomorphisms, cyclic groups, permutation groups, homomorphism, cosets, factor groups, Ring Homomorphism, quotient fields, Algebraic Elements, geometric constructions

Topics: Abstract Algebra, Binary Operations, groups, Symmetric Groups, subgroups, Isomorphism, Cosets, Lagrange's Theorem, Ring Theory, Quaternions, Circle Group, logic, Elementary Number Theory, partitions, Equivalence Relations, functions, Elementary Number Theory, Partitions, Equivalence Relations

Topics: relations, set, set operation, integer, modular arithmetic, groups, factor groups, homomorphism, direct products, finite abelian groups, automorphism, morphism, symmetric group, alternating group, sylow theorem, rings, factor rings, isomorphism, domains, Irreducible Polynomials, vector spaces, field extensions, public key cryptography, straightedge, compass constructions

Topics: Group, function, permutation, isomorphism, group element, subgroup, function, cyclic group, partition, equivalence relation, counting coset, homomorphism, quotient group, homomorphism theorem, ring, quotient ring, integral domain, polynomial, factoring polynomial, extension of fields, vector space, field extension, ruler, compass, Galois theory, set theory