This page collects together all of the “readings” associated with individual modules.
In this site, readings represent “passive” learning opportunities, as opposed to experiences, which represent “active” learning opportunities. In many courses, readings and experiences together constitute the “assignments”.
Propositional logic, applications of propositional logic, propositional equivalences
Textbook 35 pages
Formal logic, assertions and propositions, logical connectives, translating English into propositional logic.
Application of propositional logic to logic design, tautologies, contradictions, contingencies, implications, equivalences.
Predicates and quantifiers, nested quantifiers, rules of inference, introduction to proofs
Textbook 55 pages
Translation between English and predicate logic, classification of assertions, implications and equivalences, inference rules.
Functions, operations on functions, classification of total functions, cardinality, set membership.
Systems of linear equations, Gaussian elimination with back-substitution, Gauss-Jordan elimination, Cramer’s Rule.
Divisibility, modular arithmetic, primes, greatest common divisors
Textbook 30 pages
Number theory, LCM and GCD, primes and factorization, congruences and modular arithmetic, applications to computer science.
Mathematical induction, strong induction and well ordering, recursive definitions, structural induction, recursive algorithms
Textbook 61 pages
Inductive definitions, strings and languages, recurrence systems.
Proof by induction, first and second principles of mathematical induction.
Basics of counting, pigeonhole principle, permutations and combinations, binomial coefficients and identities, generalized permutations and combinations
Textbook 50 pages
Introduction to combinatorics, choosing elements from a set, permutations, samples.
Combinations, selections pigeonhole principle, another view of inclusion-exclusion.
Screencast on factorials and permutations (Trevor)
Screencast 17 minutes TrevTutor
Screencast on solving permutation problems (Trevor)
Screencast 15 minutes TrevTutor
Discrete probability, probability theory, Bayes’ theorem, expected value and variance
Textbook 49 pages
Introduction to probability theory, terminology, computing discrete probabilities, applications of combinatorics to discrete probability.
Random variables, discrete distribution functions, probabilistic algorithms, Bayes’ Theorem.