Math101 · Independent Ontario learning library
12 · Subject library
Discrete Mathematics
Logic, proof, counting, graphs, recurrences, and the mathematics of finite structures.
Start with Algorithms →19 complete · 19 total lessons
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Every topic below opens as a full lesson with interactive practice and a printable cheat sheet.
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01AlgorithmsA rigorous introduction to algorithms: specifications, correctness, termination, efficiency, and traceable examples.Full lesson + sheet02Big O NotationA precise guide to asymptotic upper bounds, comparison rules, proofs, and the limits of Big O claims.Full lesson + sheet03CountingA proof-oriented treatment of sum, product, bijection, complement, and inclusion–exclusion counting strategies.Full lesson + sheet04Direct ProofA rigorous guide to direct proofs built from definitions, hypotheses, and valid forward implications.Full lesson + sheet05Functions in Discrete MathematicsA precise treatment of functions on finite and countable sets, including injectivity, surjectivity, composition, and inverses.Full lesson + sheet06Graphs and NetworksAn exact introduction to graph models, degrees, paths, connectivity, and network reasoning.Full lesson + sheet07Logic and StatementsA careful foundation in propositions, connectives, implication, and the difference between syntax and truth.Full lesson + sheet08Logical EquivalenceA rigorous guide to equivalent propositions, laws of logic, and proof-preserving rewrites.Full lesson + sheet09Mathematical InductionA complete guide to weak induction, its logical structure, variants, and common proof gaps.Full lesson + sheet10Methods of ProofA decision guide to direct, contrapositive, contradiction, induction, cases, and counterexample arguments.Full lesson + sheet11Pigeonhole PrincipleA rigorous treatment of ordinary and generalized pigeonhole arguments, with sharp bounds and applications.Full lesson + sheet12Proof by ContradictionA precise guide to contradiction proofs, correct negation, and identifying the impossible conclusion.Full lesson + sheet13QuantifiersA precise introduction to universal and existential quantifiers, domains, scope, order, and negation.Full lesson + sheet14Recurrence RelationsA rigorous introduction to recursively defined sequences, initial conditions, iteration, and closed-form verification.Full lesson + sheet15RelationsA precise treatment of binary relations and the reflexive, symmetric, antisymmetric, transitive, equivalence, and order properties.Full lesson + sheet16Set OperationsA precise guide to union, intersection, difference, complement, Cartesian product, and set identities.Full lesson + sheet17SetsA rigorous foundation in sets, membership, subsets, equality, cardinality, and power sets.Full lesson + sheet18TreesA precise introduction to trees, unique paths, edge counts, rooted structure, and spanning trees.Full lesson + sheet19Truth TablesA systematic guide to constructing truth tables, evaluating compound statements, and recognizing tautologies and equivalence.Full lesson + sheet
