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MATH 630 , Fall 2017: Notes and Summary

Lecture Date What was covered Notes Textbook Section
1 Aug. 29 Numbers (N,Z,Q,R,C). Relations (equivalence, order) get assignment 1 1.1, 1.3, 1.4
2 Aug. 31 Metric spaces. Completion of rationals. - 1.2, 1.5
3 Sep. 5 (Axiom of Choice and Zorn's Lemma. Countability.) Metric Spaces. Topology. Topological Spaces return assignment 1; get assignment 2 1.2 (1.5, 1.6) 2.1
4 Sep. 7 Completion of Metric Spaces
5 Sept.12 Norms, Banach Spaces, Separability, Scalar products, Hilbert Spaces (I) return assignment 2; get assignment 3 3.1
6 Sept.14 Hilbert Spaces (II): orthonormality, Pythagora, Bessel, Cauchy-Schwarz, non-separability of l^inf 3.2
7 Sept.19 completion of l^p return assignment 3; get assignment 4
8 Sept.21 Duality in Hilbert Spaces. Riesz Representation theorem 3.2, 3.3
9 Sept.26 Riemeann-Stieltjes Integral (1) return assignment 4; get assignment 5 4.1
10 Sept.28 Functions in BV space. Jordan decomposition. Pure point part of a BV function 4.15
11 Oct. 3 Riemann-Stieltjes integral (2) return assignment 5; get assignment 6 4.1
12 Oct. 5 Cantor sets. Cantor function. 4.2
13 Oct.10 Cantor Function (2) get assignment 7 4.2 , MATH 3206
14 Oct.12 Measurable spaces and functions. Borel and Baire Sigma algebras. return assignment 6 4.3 (and Chapter 2 for Gdelta, Fsigma sets), MATH 3206
15 Oct.17 return assignment 7
- Oct.18 REVIEW SESSION 3:15pm-4:50pm CSIC 4122
16 Oct.19 MID TERM EXAM
17 Oct.24
18 Oct.26
19 Oct.31
20 Nov. 2
21 Nov. 7
22 Nov. 9
23 Nov.14
24 Nov. 16
25 Nov.21
- Nov.23 THANKSGIVING BREAK NO CLASS
26 Nov.28
27 Nov.30
28 Dec. 5
29 Dec. 7 LAST CLASS
- Thurs., Dec.14 REVIEW SESSION 12:30pm-2:30pm CSIC 4122
- Mon, Dec. 18 FINAL EXAM CSIC 4122 1:30pm-3:30pm