Math 63
Real Analysis (honors)
Winter 2019


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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 -