Math 5307     Mathematical Analysis I   Course schedule

 Tuesday Thursday 8/26     The real numbers        § 1.1-1.10   HW: Problems # 1.9, 1.11 8/28 The real numbers (cont'd) § 1.11-1.20 HW: Problems # 1.18, 1.20, 1.21 9/2    Basic Set Theory     § 2.1-2.11 HW: Prove Theorems A, B, and C (see class notes)             Problems : 2.2, 2.3, 2.4, 2.10, 2.11, 2.12,  2.13, 2.16, 2.17, 2.18, 2.21 9/4 Basic Set Theory (cont'd) § 2.12-2.15 HW: Problems 2.5 a, e, f, g; 2.6, 2.7, 2.8, 2.9 HW Due Tuesday 9/9 #1.11, 1.21, 2.9, 2.13, 2.17 9/9  Point Set Topology  § 3.1-3.5 HW: Problems # 3.1, 3.2 a-d, 3.4, 3.8, 3.9 HW # 1 Due 9/11 Point Set Topology (Cont'd) § 3.6-3.8 9/16 Point Set Topology (Cont'd) § 3.9-3.11 HW: Problems # 12, 15, 17, 18, 19 9/18 Point Set Topology (Cont'd) § 3.12-3.14 HW: Problems # 20 9/23 Point Set Topology (Cont'd) § 3.15-3.16 HW: Problems # 26, 29, 30 HW Due Tuesday 10/7  # 3.17, 3.30 9/25 Review Examination I Examination I Friday September 26, 1:00-3:30 p.m. 9/30 Sequences and convergence § 4.1-4.3 10/2 Cauchy sequences, completeness  § 4.4-4.7 HW: Prove Theorems D, E , and F         Study Theorems 4.13 and 4.14 10/7 Continuity § 4.8-4.12       HW: Prove Theorem 4.16; Study Theorems 4.18-4.20; Prove Theorem 4.22 (modified); Do problems # 4.8, 4.9 HW # 2 Due 10/9   Intermediate Value Theorem, Connectedness  § 4.13-4.16 HW: Prove Theorem G; Do problems # 4.13, 4.21, 4.34, 4.38 10/14 Uniform continuity, discontinuities § 4.19-4.22 HW: Prove Theorem H; do problem on square root of x given in class; Problems # 4.50, 4.51, 4.52, 4.54 (also do 4.33) 10/16 Monotone functions § 4.23; Derivatives § 5.1-5.3 HW: Problems # 4.62, 4.64, 4.69 10/21 Chain rule, local extrema § 5.5-5.8 HW: Problems  # 5.5, 5.14 10/23 Rolle's Theorem, Mean Value Theorem, Darboux's Theorem § 5.9-5.11 HW: # 5.17, 5.23, 1-11 Handout 10/28 Review for Test #2 10/30 Test # 2 Examination II Thursday October 30 11/4 No class 11/6 Functions of bounded variation: Chapter 6 HW Due Tuesday 11/18  Problems # 6.11, 6.12 11/11 The Riemann-Stieltjes Integral with increasing integrators 11/13 Riemann-Stieltjes integral: Properties 11/18 HW # 3 Due Riemann-Stieltjes integral reduction to a Riemann integral 11/20 Riemann Stieltjes Integral with integrators of bounded variation HW: Handout 11/25 Integrators of bounded variation (cont'd); Sets of measure zero HW: Problem 7.32; Handout on Cantor Set # 2, 4 11/27 Thanksgiving Holidays 12/2 Lebesgue's Theorem 12/4 Review Final Examination