Readings are noted on the day when they should be completed. Daily homework problems are noted on the day when they are assigned; they will be discussed on the following day. Weekly (graded) homework assignments are noted on the day when they are assigned, and the due date is provided.
| Week | Date | Reading | Daily Homework | Weekly Homework |
|---|---|---|---|---|
| 8/21 - 8/25 | 8/21 | No class | 8/23 | No reading (first day of class) | 1.9, 1.10 | 8/25 | Chapter 2 | 2.2, 2.9 | HW 1 (due Tue 8/29 by 5:00 pm): 1.7, 1.8 |
| 8/28 - 9/1 | 8/28 | Chapter 2 | HW 2 (due Fri 9/8): 2.10,2.11,2.13,2.14 | 8/30 | No class | 9/1 | No class |
| 9/4 - 9/8 | 9/4 | No class (Labor Day) | 9/6 | 3.1 | 3.2 (part 1) | 9/8 | 3.2 | 3.2 (part 2) | HW 3 (due Fri 9/15): 3.1(c)(b),3.4,3.5 |
| 9/11 - 9/15 | 9/11 | 3.2 | 9/13 | 3.3 | 9/15 | 3.3,3.4 | 3.10 | HW 4 (due Fri 9/22): 3.18,3.24 |
| 9/18 - 9/22 | 9/18 | 3.4 | Show that the space of continuous functions on [0,1] with the metric d(f,g) = integral of |f(x)-g(x)| from x=0 to x=1 is not complete. | 9/20 | 3.4 | Handout (Martin Gardner problem) | 9/22 | 3.5 | Let (X,d) be a discrete metric space. When is (X,d) sequentially compact? |
HW 5 (due Fri 9/29): 3.32,3.33,3.36 |
| 9/25 - 9/29 | 9/25 | 3.5 | Show that the set of sequences of real numbers which are bounded by one, equipped with the supremum metric, is bounded but not totally bounded. |
9/27 | 3.5 | 9/29 | 3.6 | No HW (Exam 1 next week) |
| 10/2 - 10/6 | 10/2 | 3.6, Review problems for Exam 1 | 10/4 | 4.1 | 4.1 | NOTE: Exam 1 this evening! 7:00 - 8:15 347 Altgeld Hall |
10/6 | 4.1, 4.3 | 4.1 (continued) | HW 6 (due Fri 10/13): 4.2, 4.3, extra problem |
| 10/9 - 10/13 | 10/9 | 4.1,4.2 | 4.10 | 10/11 | 4.4 | 4.17 | 10/13 | 4.4, 4.5 | 4.15 | HW 7 (due Fri 10/20): 4.14, 4.16, 4.27, extra problem |
| 10/16 - 10/20 | 10/16 | equivalences between metric spaces (handout) | 10/18 | 4.6 | 4.32 | 10/20 | 4.6 | 4.42 | HW 8 (due Fri 10/27): 4.34, 4.39, 4.41, 4.43 |
| 10/23 - 10/27 | 10/23 | completion of a metric space (X,d) as a subset of C_b(X) | 10/25 | 5.1 | 5.2 | 10/27 | 5.2 | No HW (Exam 2 next week) |
| 10/30 - 11/3 | 10/30 | 5.3 | 11/1 | 5.3,5.4 | NOTE: Exam 2 this evening! 7:00 - 8:15 345 Altgeld Hall |
11/3 | Riemann integration (reference: Chapter 17 in D'Angelo and West) |
HW 9 (due Fri 11/10): 5.5, 5.8, two extra problems |
| 11/6 - 11/10 | 11/6 | Riemann integration: integrability of monotone, continuous functions | 11/8 | Riemannian integration: Fundamental Theorem of Calculus | 11/10 | Riemann integration: applications, elementary functions | HW 10 (due Thu 11/16 by 5 pm NOTE NEW DATE AND TIME!): 6.10, 6.11, two extra problems |
| 11/13 - 11/17 | 11/13 | Riemann integration: elementary and special functions | 11/15 | Riemannian integration: sets of measure zero and characterization of the points of discontinuity of an integrable function | 11/17 | No class | No HW (Exam 3 next week) |
| 11/27 - 12/1 | 11/27 | 7.1 | 7.3 | HW 11 (due Wed 12/6): 7.5,7.11,7.18,7.20(a,c,d,e),7.35 In problem 7.20, you may use the result of 7.19 without proof | 11/29 | 7.5,7.2 | NOTE: Exam 3 this evening! 7:00 - 8:15 141 Altgeld Hall |
12/1 | 7.2 |
| 12/4 - 12/8 | 12/4 | 7.2,7.3 | 12/6 | 7.3 | 12/8 | 7.3,existence of a continuous nowhere differentiable function |