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This course does not yet exist. This site is a repository for materials that could become part of the course when it is offered.

Approximate timetable

• Week 1: Introduction; syntax and proof theory of the propositional calculus.
• Week 2: Syntax and proof theory of the predicate calculus; introduction to set theory.
• Week 3: Naive set theory; relations.
• Week 4: Functions; model theory of the propositional and predicate calculi.
• Week 5: Mathematical induction; course-of-values induction; structural induction; first hour exam.
• Week 6: Permutations, combinations, selections, and partitions.
• Weeks 7 and 8: Counting, generating, ranking, and unranking combinatorial objects; binomial coefficients; sigma-notation.
• Week 9: Finite sequences; strings; binary trees.
• Week 10: Divide-and-conquer algorithms; recurrence relations; second hour exam.
• Weeks 11 and 12: Graphs.
• Week 13: Inclusion and exclusion; the pigeonhole principle; optional topics.
• Week 14: Numeration systems; numeration to different bases; modular arithmetic; review for final exam.

There may be enough room in this timetable for one or more of the optional topics, such as the halting problem, λ calculus, monoids and homomorphisms, lattices, Gray codes, median algebras, Gray codes, binary decision diagrams, and symmetry and Burnside's lemma.

List of readings (with exercises)

Main topics

• Classes and membership
• Cardinality
• Union and intersection

Sidebars

• Russell's paradox

Sample programming exercises ... R6RS support libraries ... LaTeX sources for readings

To be written

• Syntax of the propositional calculus
• Proof theory for the propositional calculus
• Syntax of the predicate calculus
• Proof theory for the predicate calculus
• Mathematical induction
• Course-of-values induction
• Structural induction
• Denumerability of the rational numbers
• Non-denumerability of the real numbers
• Non-denumerability of {S | S ⊆ ℕ}
• Class difference and sundering
• Relations
• Relation attributes, relations, and operations
• Partial and total orderings
• Equivalence relations
• Partitions
• Functions
• Injections, surjections, and bijections
• Finite sequences
• Strings
• Model theory for the propositional calculus
• Model theory for the predicate calculus
• Permutations
• Combinations
• Selections
• Counting techniques
• Binomial coefficients
• Undirected graphs
• Paths and circuits
• Trees
• Planarity
• Graph isomorphism
• Directed graphs
• Monoids
• Homomorphisms of algebras
• Free monoids
• Lattices
• Boolean algebras
• Groups
• Lexicographic ordering
• Ranking
• Unranking
• Generating functions
• Recurrence relations
• The principle of inclusion and exclusion
• The pigeonhole principle
• Symmetry
• Burnside's lemma
• Diagonalization
• Boolean functions
• Conjunctive normal form
• Median algebras
• Bitwise and wordwise operations
• Binary decision diagrams
• Gray codes
• Bases of numeration
• Modular arithmetic
• The halting problem
• The λ calculus