Real Analysis (honors)
Winter 2015
General Info | Day-to-day
Syllabus and homework assignments
wk | date | reading | topic | homework | |
1 | 1/5 | Ch I.1-4 | Sets | Ch I: 3b, 4b, 7bd, 10a | |
1/7 | Ch II.1-2 | Ordered fields | Ch II: 2ab, 3, 6 | ||
1/9 | Ch II.3-4 | Least upper bound | Ch II: 10a, 11, 13 | ||
Homework #1 is due Wed Jan 14 | |||||
2 | 1/12 | Ch III.1 | Metric spaces | Ch III: 1abc | |
1/14 | Ch III.2 | Open sets | Ch III: 4, 5, 6 | ||
1/16 | Ch III.2 | (continued) | |||
3 | 1/19 | MLK | No class | ||
1/21 | Ch III.3 | Convergence | Ch III: 8, 10, 11, 18 | ||
Homework #2 is due Wed Jan 28 | |||||
1/23 | Ch III.4 | Complete spaces | Ch III: 24 | ||
4 | 1/26 | Ch III.5 | Compact spaces | Ch III: 31, 32, 33 | |
1/27(x) | Ch III.5 | (continued) | Ch III: 27, 29 | ||
1/28 | Ch III.6 | Connectedness | |||
1/30 | Ch IV.1 | Continuity | Ch IV: 1acd, 3, 4 | ||
Homework #3 is due Wed Feb 11 | |||||
5 | 2/2 | Ch IV.2 | Continuity and sequences | ||
2/4 | Ch IV.3 | Rational fns | |||
6 | 2/9 | Ch IV.4 | Cont fns and compact sets | Ch IV: 14, 21 | |
2/11 | Ch IV.5 | Cont fns and connected sets | Ch IV: 29b | ||
2/13 | Ch IV.6 | Sequences of fns | Ch IV: 33, 42 | ||
7 | 2/16 | Ch IV.6 | Spaces of functions | Homework: The Hilbert curve | |
2/18 | Ch V.1-3 | Derivatives | |||
2/20 | Ch V.4 | Taylor's Thm | Ch V: 11 | ||
Homework #4 is due Wed Feb 25 | |||||
8 | 2/23 | Ch VI.1-2 | Riemann integral | Ch VI: 2, 11, 8 | |
2/25 | Ch VI.3 | Integrability | |||
2/27 | Ch VI.3 | Integrability | Lecture notes: Riemann integrability | ||
9 | 3/2 | Ch VI.4-5 | Calculus | ||
3/4 | Ch VII.1 | Derivative of a limit | |||
3/6 | Ch VII.2-3 | Power series | |||
10 | 3/9 | Ch VII.3-4 | Analytic functions |