Real Analysis (honors)
Winter 2018
General Info | Day-to-day
Syllabus and homework assignments
wk | date | reading | topic | homework | |
1 | 1/3 | Ch I | Introduction | Ch I: 3b, 4b, 5a, 7d, 10a | |
1/5 | Ch II.1-2 | Ordered fields | Ch II: 2a, 3, 6 | ||
2 | 1/8 | Ch II.3-4 | Least upper bound | Ch II: 11, 13 | |
1/10 | Ch III.1 | Metric spaces | Ch III: 1ab | ||
1/12 | Ch III.2 | Open sets | Ch III: 3, 4, 5 | ||
3 | 1/15 | Ch III.2 | (continued) | - | |
1/17 | Ch III.3 | Convergence | Ch III: 8, 10, 11, 18 | ||
1/19 | Ch III.4 | Complete spaces | Ch III: 24 | ||
4 | 1/22 | Ch III.5 | Compact sets | Ch III: 35, 36, 37 | |
1/24 | Ch III.5 | Heine-Borel | - | ||
1/26 | Ch III.6 | Connected sets | - | ||
5 | 1/29 | Ch IV.1 | Continuous functions | Ch IV: 1ad, 3, 4, 5, 9a | |
1/31 | Ch IV.2 | Functions and limits | - | ||
2/2 | Ch IV.3 | Rational functions | Ch IV: 10a | ||
6 | 2/5 | Ch IV.4/5 | Functions on compact and connected sets | - | |
2/7 | Ch IV.6 | Sequences of functions | Ch IV: 41 | ||
2/9 | - | The Hilbert curve | - | ||
7 | 2/12 | Ch V.1,2 | Derivatives | - | |
2/14 | Ch V.3 | Mean Value Theorem | Ch V: 8, 9a, 12 | ||
2/16 | Ch V.4 | Taylor's Theorem | Ch V: 14 | ||
8 | 2/19 | Ch VI.1 | Riemann intergral | Ch VI: 1, 2 | |
2/21 | Ch IV.2, 3 | Properties of integral | Ch VI: 11, 20 | ||
2/23 | - | Integrable functions | Ch VI: 3 (prove it is 0) | ||
9 | 2/26 | Ch VI.4, 5 | Fundamental theorem | - | |
2/28 | Ch VII.1 | Interchange of limit operations | - | ||
2/23 | Ch VII.2,3 | Power series | - |