Math 239 01, Introduction to Mathematical Proof

(Image adapted from https://commons.wikimedia.org/wiki/File:8106-1ByrneTP.png, the title page to Oliver Byrne's 1847 edition of Euclid's Elements, public domain.)

Welcome to Professor Baldwin’s proofs course (or more formally, SUNY Geneseo’s spring 2018 Math 239 01, Introduction to Mathematical Proof). The links below will take you to the main components of the course.

• Introduction
  • Syllabus
  • Sample Grade Breakdown
  • 01/17 - Introduction
  • 01/19 - Syllabus Review
• Propositional Logic
  • 01/22 - Statements
  • Problem Set 1 - Propositions
  • 01/24 - Introduction to Proof
  • 01/26 - LaTeX
  • 01/29 - Compound Statements
  • Problem Set 2 - Propositional Logic
  • 01/31 - Logical Equivalence
• Predicate Logic
  • 02/02 - Sets
  • 02/05 - Set Builder Notation
  • Problem Set 3 - Sets
  • 02/07 - Quantifiers
  • 02/09 - More Quantifiers
• Proof of Conditionals/Biconditionals
  • 02/12 - Direct Proofs
  • Problem Set 4 - Proofs about Conditionals
  • 02/14 - Proofs about Conditionals
• Proof by Contradiction
  • 02/19 - Proof by Contradiction
  • Problem Set 5 - Proofs by Contradiction and Cases
• Proof by Cases
  • 02/26-28 - Proof by Cases
  • 03/05 - The Division Algorithm
• Proof by Induction
  • 03/07 - Introduction to Induction
  • 03/09 - Induction
  • 03/19 - Variations on Induction
  • Problem Set 6 - Proof by Induction
  • 03/21 - Strong Induction
  • 03/23-26 - Strong Induction and Expressions
  • Sample Exam 2 Questions
• Sets
  • 03/30 - Set Operations
  • Problem Set 7 - Introduction to Set Theory
  • 04/02 - Set Relationships
  • 04/04 - Set Algebra
  • 04/06 - The Cartesian Product
  • Problem Set 8 - Proofs about Sets
  • 04/09 - Indexed Families of Sets
• Functions
  • 04/11 - Introduction to Functions
  • 04/13 - Injections, Surjections, Bijections
  • Problem Set 9 - Sets and Functions
  • 04/16 - Composition
  • 04/18 - Inverse Functions
• Equivalence Relations
  • 04/20 - Relations
  • Problem Set 10 - Relations and Countability
  • 04/23 - Equivalence Relations
• Infinite Sets
  • 04/25 - Finite Sets
  • 04/27 - Countably Infinite Sets
  • 04/30 - Uncountable Sets
• Review
  • Sample Final
  • 05/02 - Review