Math 63
Real Analysis (honors)
Winter 2018


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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)