Real Analysis (honors)
Winter 2019
General Info | Day-to-day
Syllabus and homework assignments
wk | date | reading | topic | homework | |
1 | 1/4 | Introduction | |||
2 | 1/7 | Ch I | Sets and functions | Ch I: 3a, 5b, 7d, 10a | |
1/9 | Ch II.1-2 | Ordered fields | Ch II: 2a, 3, 6 | ||
1/11 | Ch II.3-4 | Least upper bound | Ch II: 11 (hint: you don't have to use the hint), 13 | 3 | 1/14 | Ch III.1 | Metric spaces | - |
1/16 | Ch III.2 | Open and closed sets | Ch III: 3, 4, 5 | ||
1/18 | Ch III.3 | Limits of sequences | Ch III: 8, 11, 18 | 4 | 1/22 | - | - | - |
1/23 | Ch III.4 | Completeness | Ch III: 24, 29 | ||
1/25 | Ch III.5 | Compactness | Ch III: 28, 31, 32, 33 | 5 | 1/28 | Ch III.5 | Heine-Borel theorem | Ch III: 35, 36, 37 |
1/30 | - | - | - | ||
2/1 | Ch III.6 | Connectedness | - | 6 | 2/4 | Ch IV.1 | Continuous functions | Ch IV 1d, 3, 4 |
2/6 | Ch IV.2 | Functions and sequences | - | ||
2/8 | Ch IV.3 | Rational functions | - | 7 | 2/11 | Ch IV.4 | Cont fns and compact sets | Ch IV: 14 |
2/13 | Ch IV.5 | Cont fns and connected sets | Ch IV: 29 | ||
2/15 | Ch IV.6 | Sequences of functions | Ch IV: 33 | 8 | 2/18 | Ch IV.6 | Uniform convergence | Homework: The Hilbert curve |
2/20 | Ch V.1-3 | Derivatives | Ch V: 4, 6, 12 | ||
2/22 | Ch V.4 | Taylor's Theorem | - | 9 | 2/25 | Ch VI.1 | Riemann Intergral | Ch VI: 11, 20 |
2/27 | Ch VI.3 | Integrability | - | ||
3/1 | Ch VI.3 | (continued) | Ch IV: 5 (from chapter 4!) | 10 | 3/4 | Ch VI.4 | Fund Thm of Calculus | - |
3/6 | Ch VI.5 | Elementary Functions | - |