Math 239 03, 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 (or, more formally, SUNY Geneseo’s spring 2021 Math 239 03, “Introduction to Mathematical Proof”). The links below will take you to the main materials for this course….

• Introduction
  • Syllabus
  • Cohorts
  • 02/01 - Introduction
  • Policies and Practices Discussion
  • 02/03 - Policies and Practices
• Logic and Logical Statements
  • Topic: Statements
    • Statements Discussion
    • 02/05 - Statements
    • Problem Set 1 - Statements
    • Conditionals Discussion
    • 02/08 - Conditional Statements
  • Topic: Direct Proof
    • Direct Proofs Discussion
    • 02/10 - Introduction to Direct Proof
    • “A Minimalist Introduction to LaTeX” Reading
    • Writing Proofs Discussion
    • 02/12 - Writing Proofs
    • Problem Set 2 - Direct Proofs
  • Topic: Connectives
    • Compound Statements Discussion
    • 02/15 - Compound Statements
    • Logical Equivalence Discussion
    • 02/17 - Logical Equivalence
    • 02/19 - Logical Equivalence
    • Problem Set 3 - Propositional Logic
  • Topic: Sets
    • Elementary Sets Discussion
    • 02/22 - Elementary Sets
    • Set Builder Notation Discussion
    • 02/24 - Set Builder Notation
  • Topic: Quantifiers
    • Introductory Quantifiers Discussion
    • 02/26 - Introduction to Quantifiers
    • Advanced Quantifiers Discussion
    • 03/01 - More About Quantifiers
    • 03/03 - Proofs about Quantifiers
    • Problem Set 4 - Sets and Quantifiers
• Proof Techniques
  • Topic: Divisibility
    • Divisibility and Congruence Discussion
    • 03/05 - Divisibility and Congruence
  • Topic: Proof Via the Contrapositive
    • Proofs Via the Contrapositive
    • Problem Set 5 - Proofs Involving the Contrapositive or Biconditionals
  • Topic: Biconditionals
    • 03/10 - Review
    • Proving Biconditionals Discussion
    • 03/12 - Biconditionals
  • Topic: Proof by Contradiction
    • Proof by Contradiction Discussion
    • 03/15 - Proof by Contradiction
    • Irrational Square Roots Discussion
    • 03/17 - Irrational Square Roots
    • Problem Set 6 - Proof by Contradiction
  • Topic: Proof by Cases
    • Proof by Cases Discussion
    • 03/19 - Proof by Cases
    • Division Algorithm Discussion
    • 03/22 - More Modular Congruence
  • Topic: Proof by Induction
    • Inductive Sets Discussion
    • 03/26 - Inductive Sets
    • Induction Proofs Discussion
    • 03/29 - Proof by Induction
    • Problem Set 7 - Proofs by Cases and Induction
    • 03/31 - Proof by Induction 2
    • Problem Set 8 - Proof Technique Review
• Sets
  • Topic: Set Operations
    • Set Operations Discussion
    • 04/02 - Set Operations
    • Cardinality of a Power Set Discussion
    • 04/05 - Cardinality of a Power Set
    • Element-Chasing Proofs Discussion
    • 04/07 - Element Chasing Proofs
    • Set Algebra Discussion
    • 04/09 - Set Algebra
    • Problem Set 9 - Set Theory
  • Topic: The Cartesian Product
    • Cartesian Product Discussion
    • 04/12 - Cartesian Products
  • Topic: Indexed Families of Sets
    • Indexed Families of Sets Discussion
    • 04/14 - Indexed Families of Sets
• Functions
  • Topic: Introduction
    • Functions Discussion
    • 04/16 - Introduction to Functions
    • Problem Set 10 - Sets and Functions
  • Topic: Types of Function
    • Injections, Etc. Discussion
    • 04/19 - Injections, Surjections, and Bijections
    • 04/21 - Function Types Example
  • Topic: Inverse Functions
    • Inverse Functions Discussion
    • 04/23- Inverses of Functions
• Relations
  • Topic: General Relations
    • Relations Discussion
    • 04/26 - Introduction to Relations
    • Problem Set 11 - Relations and Functions
  • Topic: Equivalence Relations
    • Equivalence Relations Discussion
    • 04/28 - Equivalence Relations
    • Equivalence Classes Discussion
    • 04/30 - Equivalence Classes
• Finite and Infinite Sets
  • Topic: Cardinality
    • Equivalent (Cardinality) Sets Discussion
    • 05/03 - Equivalent Cardinalities
  • Topic: Countable Sets
    • Countable Sets Discussion
    • 05/05 - Countable Sets Part 1
    • Cartesian Products of Countable Sets Discussion
    • 05/07 - Cartesian Products and Countability
  • Topic: Uncountable Sets
    • “Dodge Ball” Discussion
    • 05/11 - Uncountable Sets