SUNY Geneseo Department of Mathematics

Lecture List

Math 239 03
Fall 2016
Prof. Doug Baldwin

Last modified December 13, 2016

Caveat

These are electronic records of class discussion from Math 239 03 (Introduction to Mathematical Proof). They are generally captured as a class unfolds, and slightly cleaned up afterwards. They are not clean, carefully-planned lecture notes in the usual sense. They are more an electronic equivalent of notes on the blackboard: they record some of what the instructor said, some of what students said, the things that really happened in the class—including the misunderstandings, false starts, and similar things that happen in real classes. The goal of these notes is as much to help students remember how they learned as it is to help them remember what they learned (because the “how” of learning is at least as important as the “what”).

Please make WWW or other electronic links to this page only—I want people reading these notes to see the “caveat” above.

Send comments, questions, etc. related to these notes to Doug Baldwin.

  1. Aug. 29—Introduction
  2. Aug. 31—Statements
  3. Sep. 2—Introduction to Direct Proofs
  4. Sep. 7—Writing Proofs
  5. Sep. 9—Professional Proofs
  6. Sep. 12—Compound Statements and Connectives
  7. Sep. 14—Equivalent Statements
  8. Sep. 16—Equivalence via Boolean Algebra
  9. Sep. 19—Introduction to Sets
  10. Sep. 21—Predicates and Sets
  11. Sep. 23—Introduction to Quantifiers
  12. Sep. 26—Quantifiers, Part 2
  13. Sep. 28—Direct Proof
  14. Sep. 30—Exam 1 — no lecture notes
  15. Oct. 3—Proof via the Contrapositive
  16. Oct. 5—Proving Biconditionals
  17. Oct. 7—Proof by Contradiction
  18. Oct. 12—Proof by Cases
  19. Oct. 14—Congruence and the Division Algorithm
  20. Oct. 17—Introduction to Induction
  21. Oct. 19—Induction Part 2
  22. Oct. 21—Extending Induction
  23. Oct. 24—The 2nd Principle of Induction
  24. Oct. 26—Exam 2 — no lecture notes
  25. Oct. 28—Basic Operations on Sets
  26. Oct. 31—Proofs of Set Relations
  27. Nov. 2—Proving Sets Disjoint
  28. Nov. 4—The Algebra of Sets
  29. Nov. 7—The Cartesian Product
  30. Nov. 9—Families of Sets
  31. Nov. 11—Introduction to Functions
  32. Nov. 14—Equality of Functions
  33. Nov. 16—Injections, Surjections, Bijections
  34. Nov. 18—Function Composition
  35. Nov. 21—Inverses of Functions
  36. Nov. 28—Functions on Sets
  37. Nov. 30—Introduction to Relations
  38. Dec. 2—Equivalence Relations
  39. Dec. 5—Equivalence Classes
  40. Dec. 7—Finite and Infinite Sets
  41. Dec. 9—Countably Infinite Sets
  42. Dec. 12—Uncountable Sets
  43. Dec. 13—Review Session