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 Prof. Baldwin’s proofs class (more formally, SUNY Geneseo’s spring 2019 Math 239 01, Introduction to Mathematical Proof). Use the links below to explore the course.

• Introduction
  • Textbook
  • Representative Past Grade Distribution
  • 01/23 - Introduction
• Propositional Logic
  • 01/25 - Statements
  • Problem Set 1 - Propositions
  • 01/28 - Conditional Statements
  • 01/30 - Creating Proofs
  • 02/01 - Writing Proofs with LaTeX
  • Problem Set 2 - Direct Proofs
  • 02/04 - Compound Statements
  • 02/06 - Logical Equivalence
• Predicate Logic
  • 02/08 - Sets
  • 02/11 - Predicates
  • 02/13 - Set Builder Notation
  • Problem Set 3 - Propositional Logic
  • 02/15 - More about Quantifiers
  • Sample Exam 1
• Proof of Conditionals/Biconditionals
  • 02/18 - Divisibility and Direct Proof
  • 02/20 - Proof Via the Contrapositive
  • Problem Set 4 - Methods of Proof
  • 02/25 - Biconditionals
• Proof by Contradiction
  • 02/27 - Introduction to Proof by Contradiction
  • Problem Set 5 - Proofs by Contradiction and Cases
• Proof by Cases
  • 03/04 - Proof in Cases
  • 03/06 - The Division Algorithm
• Proof by Induction
  • 03/08 - Inductive Sets
  • 03/11 - Weak Induction
  • 03/13 - More Induction
  • Problem Set 6 - Induction
  • 03/15 - Extending Induction
• Sets
  • 03/25 - Set Operations
  • 03/27 - Proofs about Set Relationships
  • Problem Set 7 - Sets
  • 03/29 - Set Algebra
  • Sample Questions for Exam 2
  • 04/01 - Induction Review
  • 04/05 - Cartesian Products
  • 04/08 - Indexed Families of Sets
  • Problem Set 8 - Sets
• Functions
  • 04/10 - Introduction to Functions
  • 04/12 - Injection, Surjection, Bijection
  • 04/15 - Functions’ Inverses
  • Problem Set 9 - Functions
• Equivalence Relations
  • 04/19 - Introduction to Relations
  • 04/22 - Equivalence Relations
  • 04/24 - Equivalence Classes
• Infinite Sets
  • Problem Set 10 - Infinite Sets
  • 04/26 - Finite Sets
  • 04/29 - Countably Infinite Sets
  • 05/01 - More about Countably Infinite Sets
  • 05/03 - Uncountable Sets
  • 05/06 - Countable and Uncountable
  • 05/08 - Cantor’s Theorem
  • 05/09 - Review
  • Sample Final Exam Questions