Math 63
Real Analysis (honors)
Winter 2015

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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