CSE 260 Fall 2005
Mathematical Foundations of Computer Science
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CSE 260 Course Topics:
Mathematical reasoning and proof principles, Logic
Set Theory
Relations, Functions, Partial Functions
Induction on N
Composition of relations and functions
Recursion on N
Injection, surjections, bijections
Inverses of functions and relations
Direct and Inverse Images
Equinumerosity, Cantor's Theorem,
Pigeonhole Principle, SchroederBernstein's Theorem
Strings, Multisets, Indexed Families
An amazing surjection: Hilbert's squarefilling curve
Some counting problems
Binomial coefficients, the binomial formula
Partial Orders, Lattices
WellFounded Orderings and complete Induction
Equivalence Relations and Partitions. Closures.
Distributive Lattices, Boolean algebras, Heyting algebras
Trees, Multiset Ordering, String and Tree Embedding
Graphs (directed and undirected; unlabeled and labeled); Graph homomorphisms and isomorphisms
Simple CombinatoricsCounting
Baby Number Theory: divisibility, modular arithmetic
Related Material: Some Talks, Slides and Links
Intuitionistic logic for dummies
(pdf)
Intuitionistic logic (Part 2/2)
(pdf)
Introduction to proof theory
(pdf)
Proofs are programs
(ppt)
Intuitionistic Logic (from Stanford Encyclopedia of Philosophy)
(html)
Intuitionistic Logic (From Wikipedia)
(html)
Intuitionistic Logic (From Mathworld)
(html)
Intuitionistic Logic (From Absolute Astronomy)
(html)
Axioms of ZermeloFraenkel Set Theory (from Wikipedia)
(html)
ZermeloFraenkel Axioms (from MathWorld)
(html)
ZermeloFraenkel Set Theory (from Stanford Encyclopedia of Philosophy)
(html)
Set Theory (from Stanford Encyclopedia of Philosophy)
(html)
The Axiom of Choice (by Eric Schechter)
(html)
Eric Schechter's home page
(html)
Axiom of choice (from Wikipedia)
(html)
Axiom of choice (from MathWorld)
(html)
CantorSchroederBernstein Theorem (from Wikipedia)
(html)
CantorSchroederBernstein Theorem (from PlanetMath)
(html)
Tarski's Fixed Point Theorem (from MathWorld)
(html)
KnasterTarski Theorem (from Wikipedia)
(html)
PlaneFilling Function (from MathWorld)
(html)
Hilbert Curve (from MathWorld)
(html)
Plane Filling Curves (from Alexander Bogomolny)
(html)
SpaceFilling Curves (from Wikipedia)
(html)
Using SpaceFilling Curves for multidimensional indexing
(html)
Stirling's Formula (from Wikipedia)
(html)
Wellfounded relation (from Wikipedia)
(html)
Wellfounded induction (from PlanetMath)
(html)
Lattice (from Wikipedia)
(html)
Distributive Lattice (from Wikipedia)
(html)
Complete Lattice (from Wikipedia)
(html)
Boolean algebra (from Wikipedia)
(html)
Boolean algebra (from Stanford Encyclopedia of Philosophy)
(html)
Graph theory (from Wikipedia)
(html)
Some Course Notes and Slides
Discrete math. basics, induction, inductive definitions
(Chapter from ``Logic for Computer Science'', by J. Gallier)
(ps)

(pdf)
Macro prooftree.tex
(tex)
Macro mac.tex
(tex)
Macro mathmac.tex
(tex)
Discrete Mathematics for Computer Science (book manuscript)
(html)