Time: | Tue & Thur 11 a.m. - 12:15 p.m. | Room: | SMLC 352 |
Instructor Info: | Anna Skripka, skripka [at] math [dot] unm [dot] edu |
Office hours: | Tue and Thur 3:30 - 4:45 p.m., and by appointment, SMLC 212 |
Week |
Important Dates |
Chapters |
Topics |
Homework |
1 |
Aug 19 (Pretest), 21 |
Chapter 1 |
Review of Advanced Calculus. |
2 |
Aug 26, 28 (HW1) |
Chapter 2 |
Countable and uncountable sets. Cantor set. Monotone functions. |
3 |
Sep 2, 4 (HW 2); Drop with no grade: Sep 5 |
Chapter 3 |
Metric and normed spaces. ℓp spaces. |
|
4 |
Sep 9, 11 (HW 3) |
Chapter 4 |
Open and closed sets. Relative metric. |
|
5 |
Sep 16, 18 (HW 4) |
Chapters 5, 6 |
Continuous functions. Connected sets. |
|
6 |
Sep 23, 25 (Exam 1) |
Chapter 6 |
Connectedness. |
|
7 |
Sep 30, Oct 2 |
Chapter 7 |
Complete metric spaces. Fixed points. |
|
8 |
Oct 7 (HW 5) |
Chapter 8 |
Compactness. Continuous functions on compact spaces. |
|
9 |
Oct 14, 16 (HW 6) |
Chapters 8, 10 |
Uniform continuity. Pointwise and uniform convergence. Interchanging limits. |
|
10 |
Oct 21, 23 (HW 7) |
Chapter 10 |
Interchanging limits. Series of functions. Space B(X). The Weierstrass M-test. Power series. Nowhere differentiable function. |
|
11 |
Oct 28 (Exam 2), 30
| Chapter 11 |
The Weierstrass approximation theorem. |
|
12 |
Nov 4, 6 (HW 8); Withdrawal deadline: Nov 7 |
Chapter 11 |
Approximations in C(R). Equicontinuity. Compact subsets of C(X). |
|
13 |
Nov 11, 13 (HW 9) |
Chapter 13 |
Functions of bounded variation. |
|
14 |
Nov 18, 20 (HW 10) |
Chapter 14 |
Riemann-Stieltjes integral with an increasing integrator. |
|
15 |
Nov 25 |
Chapter 14 |
Properties of Riemann-Stieltjes integrable functions. |
|
16 |
Dec 2, 4 |
Chapter 14 |
Riemann-Stieltjes integral with a general integrator. Properties of the Riemann integral. Review. |
|
17 |
Final Exam Dec 9 (Tuesday), 12:30 - 2:30 p.m. |
Office hour: Dec 8, 2:30 - 4 pm |