| Tentative schedule |
|---|
Readings should be completed by the start of class on the dates listed below.
Similarly, homework is due at the start of class on the assigned dates.
| Week beginning | Assigned reading | Assigned homework | Description |
|---|---|---|---|
| August 25, 2008 | Chapter 1 (by Wed, Aug. 27) Chapter 2 (by Fri, Aug. 29) |
1.7, 1.13, 1.14, 1.15, 1.16, 1.21, 1.22, 1.50
due Wed, Sept. 3 |
The real numbers |
| September 1, 2008 | none | 2.2, 2.4, 2.9, 2.16, 2.21, 2.31, 2.32, 2.37, 2.40(a) and
these supplementary problems (this list is now final). Note that there is a typo in the hint for Exercise 2.31; it refers you to Remark 2.88, which is not very kind since as far as I can tell it doesn't exist. Please see Remark 2.34 instead. due Wed, Sept. 10 Note on the supplementary problems: These problems assume knowledge of the axioms for a field as well as the order axioms (the definition of a positive set). For the field axioms, please use the list given here. This list is updated from the handout I gave you in class. (It includes as axioms properties that would have required proof if we used the previous list -- in other words, this new list should make your life easier!) The order axioms are the same as those given in class; if you didn't take notes, these axioms constitute Definition 1.40 on p.16 of our book. |
Real numbers, ctd., and mathematical statements |
| September 8, 2008 | Chapter 3 (by Mon, Sept. 8) | 3.1, 3.11, 3.15, 3.22, 3.25, 3.29, 3.35, 3.44
Extra credit problem (to be turned in to me, not the grader; it must be written/typed on a separate sheet of paper): | Induction |
| September 15, 2008 | Chapter 4 (by Mon, Sept. 15) Chapter 5 (by Fri, Sep. 19) |
the HW assignment (due Wed, Sept. 24) is now posted here | Bijections and cardinality |
| September 22, 2008 | No assigned reading for this week | A list of practice problems for Exam 1 is now posted here Solutions to HW number 4 are now posted here (note that for ease of typesetting, to indicate a difference of two sets I use the symbol "\" where the book would have "–" in other words, I write "A\B" and not "A–B") |
First exam (=celebration of learning) |
| September 29, 2008 | No assigned reading for this week | 5.18, 5.23, 5.27, 5.28, 5.30, 5.31, 5.37, 5.41, 5.42
(due Friday, Oct. 10) |
Intro to combinatorics |
| October 6, 2008 | Chapter 6 (by Friday, Oct. 10) | the HW assignment (due Fri, Oct. 17) is now posted here | Intro to number theory (divisibility) |
| October 13, 2008 | no new assigned reading | Divisibility ctd. | |
| October 20, 2008 | Chapter 7 (by Friday, October 24) | A list of practice problems for Exam 2 is now posted here Solutions to HW 6 are posted here |
Modular arithmetic |
| October 27, 2008 | no new assigned reading | HW 7 (due Wednesday, November 5) is now posted here | Modular arithmetic ctd. |
| November 3, 2008 | Chapter 13 (by Wednesday, November 5) | Introduction to real analysis | |
| November 10, 2008 | no new reading assigned | HW 8 (due TBA) is now posted here | Introduction to real analysis, ctd. |
| November 17, 2008 | no new reading assigned | Chapter 14 is not assigned reading, but it would be helpful as a written reference for our discussion of infinite series. A list of practice problems for Exam 3 is now posted here HW #8 solutions are now posted here |
Introduction to real analysis, ctd. |
| December 1, 2008 | Chapter 10 | Exercises 10.1, 10.2, 10.8, 10.12, 10.15, 10.28, 10.29, 10.36, 10.37 | The pigeonhole principle and the principle of inclusion-exclusion |