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