| Week | Monday | Wednesday | Reading and Assignments |
|---|---|---|---|
| 1/23 | Administrivia 1.1 Discussion: the irrationality of √2 1.2 Preliminaries Discussion of natural numbers, rationals, and reals. |
Discussion of rationals-- why is every rational an (eventually) repeating decimal and vice versa? 8.6 Ordered fields 1.3 the Axiom of Completeness |
Read all of chapter 1 in Abbott. Background: Alcock, ch.1-4 Suggested: Alcock, ch.10 |
| 1/30 | 1.4 Consequences of Completeness 1.5, 1.6, 1.7 Cardinality and Cantor's theorem |
2.1 Intro: Rearranging series 2.2 Limits of sequences |
Start reading Chapter 2 of Abbott HW 1 Due Wed, 2/8 |
| 2/6 | 2.3 Limit theorems 2.4 monotone convergence theorem |
2.4 continued : the Harmonic series, Cauchy condensation, p-series 2.5 Subsequences, Bolzano-Weierstrauss |
Read the rest of Abbott ch.2 Suggested: Alcock, ch.5 HW 2 Due Wed, 2/15 |
| 2/13 | 2.6 Cauchy sequences 2.7 Properties of infinite series |
2.8 Double summation, Products of series 2.9 Epilogue 3.1 The Cantor set |
Start reading Abbot ch.3 Suggested: Alcock, 6.1-6.8 HW 3 Due Wed, 2/22 |
| 2/20 | Proof party 3.2 Open and Closed sets |
3.3 Compactness | Finish reading Abbot ch.3 HW 4 Due Wed, 3/1 |
| 2/27 | 3.3 Heine-Borel Theorem | 4.1, 4.2 Limits of functions 4.3 Continuity |
Start reading Abbot Ch.4 Suggested: Alcock, ch.7 |
| 3/6 | review for midterm. | Midterm 1 covers chapters 1-3 Here is a copy of the midterm, and here are the solutions. |
HW 5 Due Wed, 3/22(after break) |
| 3/13 | Spring Break (probably not like this) |
Spring Break | |
| 3/20 | 4.3 A bit more on continuity 4.4 Continuous functions on compact sets |
4.4 Extreme Value Theorem 4.5 Intermediate Value Theorem 4.6 Discontinuities |
HW 6 Due Wed, 3/29 Finish reading Abbot Ch.4 |
| 3/27 | 5.1 Continuity of Derivatives 5.2 Derivatives and Intermediate Value Property |
5.3 Mean Value Theorem 5.4 A continuous, nowhere differentiable function |
HW 7 Due Wed, 4/3 read Abbot Ch.5 |
| 4/3 | 6.1, 6.2 Uniform Convergence of a sequence of functions 6.3 Uniform convergence and differentiation |
6.4 Series of functions 6.5 Power series |
HW 8 Due Wed, 4/10 read Abbot Ch.6 Suggested: Alcock, ch.8 |
| 4/10 | 6.6 Taylor series | 6.7 Weierstrauss approximation theorem | HW 9 Due Wed, 4/26(1 week after midterm) start reading Abbot Ch.7 Suggested: Alcock, ch.9 |
| 4/17 | review for midterm. | Midterm 2 covers chapters 4, 5, 6.1-6.3 Here is a copy of the midterm, and here are the solutions. |
|
| 4/24 | 7.1, 7.2 The Riemann integral 7.3 discontinuities |
7.4 Properties of integrals 7.5 Fundamental theorem of Calculus |
HW 10 Due Wed, 5/3 finish Abbot Ch.7 |
| 5/1 | 7.6 a non-integrable derivative | review? | Paper due on Friday, May 5 |
| 5/8 | Final Cumulative Thursday, May 11, 5:30pm, Physics P-128. |
If you want to relive the magic, here is the exam, and here are the solutions. |