| Date | Lecture | Reading | Notes | Handouts |
|---|---|---|---|---|
| Week 1 | ||||
| 8/24 | Course Introduction; Theorems, Definitions, and Proofs | Chapter 1 (read after class) |
Notes Erum Hussain |
|
| 8/26 | Logical Statements: connectives, truth tables, implication | Chapter 2 | Notes Erum Hussain |
|
| Week 2 | ||||
| 8/31 | The Contrapositive and the Converse | Chapter 3 | Notes Jenna Klein |
|
| 9/2 | Set Notation; Variables and Quantifiers; negating quantified statements | Chapter 4 | Notes Zoë Barnes |
|
| Week 3 | ||||
| 9/7 | No Class - Labor Day (University Closed) | |||
| 9/9 | The Simplest Proofs: direct proof and the contrapositive | Chapter 5 | ||
| Week 4 | ||||
| 9/14 | Proof Techniques: contradiction, proof by cases, counterexamples | Chapter 5 | ||
| 9/16 | Sets: subsets, set equality, proving containment | Chapter 6 | ||
| Week 5 | ||||
| 9/21 | Operations on Sets: union, intersection, complement, difference; De Morgan's laws | Chapter 7 | ||
| 9/23 | More on Operations on Sets: families of sets, index sets, indexed unions and intersections | Chapter 8 | ||
| Week 6 | ||||
| 9/28 | The Power Set and the Cartesian Product | Chapter 9 | ||
| 9/30 | Relations; Equivalence Relations | Chapter 10 | ||
| Week 7 | ||||
| 10/5 | Review for Midterm Exam 1 (~50 min); Partitions and equivalence classes (begin) | Chapters 1-10 review; Chapter 11 | ||
| 10/7 | Midterm Exam 1 (Chapters 1-10, 75 minutes), then Partitions and equivalence classes continued (Chapter 11) | |||
| Week 8 | ||||
| 10/12 | Order in the Reals: inequalities, upper bounds, suprema; the Archimedean property (Chapter 13) | Chapter 12 | ||
| 10/14 | Catch-Up / Flexible Day — material carried over from earlier in the term | |||
| Week 9 | ||||
| 10/19 | Functions, Domain, and Range | Chapter 14 | ||
| 10/21 | Injective, Surjective and Bijective Functions; Inverses and composition | Chapters 15-16 | ||
| Week 10 | ||||
| 10/26 | Images and Inverse Images; continuous functions | Chapter 17 | ||
| 10/28 | Catch-Up / Flexible Day — material carried over from earlier in the term | |||
| Week 11 | ||||
| 11/2 | Mathematical Induction | Chapter 18 | ||
| 11/4 | Complete Induction; Recursion; the Well Ordering Principle | Chapter 18 | ||
| Week 12 | ||||
| 11/9 | Sequences | Chapter 19 | ||
| 11/11 | Convergence of Sequences of Real Numbers | Chapter 20 | ||
| Week 13 | ||||
| 11/16 | Cauchy Sequences and Completeness; Review for Midterm Exam 2 | Chapter 20 | ||
| 11/18 | Midterm Exam 2 (Chapters 12, 14-20) | |||
| Week 14 | ||||
| 11/23 | Equivalent Sets | Chapter 21 | ||
| 11/25 | No Class - Thanksgiving Holiday (University Closed) | |||
| Week 15 | ||||
| 11/30 | Cardinality: finite sets, countable and uncountable sets; Cantor's diagonal argument; the Cantor-Schröder-Bernstein theorem | Chapters 22-24 | ||
| 12/2 | Congruence Modulo m; Modular Arithmetic | Chapter 27 | ||
| Week 16 | ||||
| 12/7 | The GCD, the Euclidean algorithm, and Modular Inverses; open and closed subsets of R (time permitting); Review for the Final Exam | Chapter 27 | ||
| 12/11 | Final Exam - Friday, December 11, 12:30-2:30 p.m. (cumulative) | |||