| Date | Lecture | Reading | Notes | Additional Topics |
|---|---|---|---|---|
| Week 1 | ||||
| 8/24 | Course Introduction; Theorems, Definitions, and Proofs | Chapter 1 | §1 | Proof Writing Tips; Spotlight: George Pólya; Tips on Doing Homework |
| 8/26 | Logical Statements: connectives, truth tables, implication | Chapter 2 | §2 | |
| Week 2 | ||||
| 8/31 | The Contrapositive and the Converse | Chapter 3 | §2 | |
| 9/2 | Set Notation; Variables and Quantifiers; negating quantified statements | Chapter 4 | §2.1-2.2 | Tips on Quantification |
| Week 3 | ||||
| 9/7 | No Class - Labor Day (University Closed) | |||
| 9/9 | The Simplest Proofs: direct proof and the contrapositive | Chapter 5 | §3 | Tips on Definitions |
| Week 4 | ||||
| 9/14 | Proof Techniques: contradiction, proof by cases, counterexamples | Chapter 5 | §3 | |
| 9/16 | Sets: subsets, set equality, proving containment | Chapter 6 | §9.1 | Spotlight: Paradoxes |
| Week 5 | ||||
| 9/21 | Operations on Sets; families of sets, indexed unions and intersections | Chapters 7-8 | §9.2-9.3, 14.1 | De Morgan's laws |
| 9/23 | The Power Set and the Cartesian Product | Chapter 9 | §9.3 | Tips on Writing Mathematics |
| Week 6 | ||||
| 9/28 | Relations; Equivalence Relations | Chapter 10 | §12.1 | Tips on Reading Mathematics |
| 9/30 | Partitions and equivalence classes; order relations | Chapter 11 | §12.1-12.2 | Tips on Putting It All Together |
| Week 7 | ||||
| 10/5 | Review for Midterm Exam 1 | Chapters 1-11 | ||
| 10/7 | Midterm Exam 1 (Chapters 1-11) | |||
| Week 8 | ||||
| 10/12 | Order in the Reals: inequalities, upper bounds, suprema | Chapter 12 | §5 | The Archimedean property (from Chapter 13); Tips: You Solved It. Now What? |
| 10/14 | Catch-Up / Flexible Day | Reserved for material carried over from earlier in the term | ||
| Week 9 | ||||
| 10/19 | Functions, Domain, and Range | Chapter 14 | §10.1 | Spotlight: The Definition of Function |
| 10/21 | Injective, Surjective and Bijective Functions; Inverses and composition | Chapters 15-16 | §10.2 | |
| Week 10 | ||||
| 10/26 | Images and Inverse Images | Chapter 17 | §15.1 | Spotlight: Minimum or Infimum?; continuous functions (§15.2) |
| 10/28 | Catch-Up / Flexible Day | Reserved for material carried over from earlier in the term | ||
| Week 11 | ||||
| 11/2 | Mathematical Induction | Chapter 18 | §4.1 | |
| 11/4 | Complete Induction; Recursion; the Well Ordering Principle | Chapter 18 | §4.2-4.3 | |
| Week 12 | ||||
| 11/9 | Sequences | Chapter 19 | §6 | |
| 11/11 | Convergence of Sequences of Real Numbers | Chapter 20 | §7 | |
| Week 13 | ||||
| 11/16 | Cauchy Sequences and Completeness; Review for Midterm Exam 2 | Chapter 20 | §8.1 | |
| 11/18 | Midterm Exam 2 (Chapters 12, 14-20) | |||
| Week 14 | ||||
| 11/23 | Equivalent Sets | Chapter 21 | §11.1 | |
| 11/25 | No Class - Thanksgiving Holiday (University Closed) | |||
| Week 15 | ||||
| 11/30 | Cardinality: finite sets, countable and uncountable sets; the Cantor-Schröder-Bernstein theorem | Chapters 22-24 | §11.2 | Cantor's diagonal argument; Spotlight: The Continuum Hypothesis |
| 12/2 | Congruence Modulo m; Modular Arithmetic | Chapter 27 | §13.1-13.3 | |
| Week 16 | ||||
| 12/7 | The GCD, the Euclidean algorithm, and Modular Inverses; Review for the Final Exam | Chapter 27 | §13.4 | Open and closed subsets of R (§14.2), time permitting |
| 12/11 | Final Exam - Friday, December 11, 12:30-2:30 p.m. (cumulative) | |||