Math 347 (Rezk, Section X1 12:00 MWF).

Math 347 (Rezk, 12:00 MWF, Section X1, 152 Henry).

Office hours

See my homepage.

Syllabus

Here is the syllabus.

Errata for textbook

Our text is Mathematical Thinking (MT) by D'Angelo and West. This page has a list of errors in the text.

Reading

Wednesday, August 24. MT pp. 2-15.
Friday, August 26. MT pp. 31-39.
Monday, August 29. MT pp. 27-31.
Wednesday, August 31. MT pp. 39-44.
Friday, September 2. MT pp. 15-20.
Wednesday, September 7. MT pp. 4-6.
Friday, September 9. no reading.
Monday, September 12. MT pp. 50-54
Wednesday, September 14. MT pp. 54-62.
Friday, September 16. MT pp. 63-71.
Monday, September 19. no reading.
Wednesday, September 21. no reading.
Friday, September 23. MT pp. 76-85.
Monday, September 26. no reading.
Wednesday, September 28. First midterm.
Friday, September 30. MT pp. 85-90.
Monday, October 3. MT pp. 100-104.
Wednesday, October 5. no reading.
Friday, October 7. MT pp. 104-110.
Monday, October 10. no reading.
Wednesday, October 12. no reading.
Friday, October 14. MT pp. 111-118.
Monday, October 17. no reading.
Wednesday, October 19. no reading
Friday, October 21. no reading
Monday, October 24. MT pp. 122-126.
Wednesday, October 26. MT pp. 126-129.
Friday, October 28. no reading
Monday, October 31. MT pp. 129-131.
Wednesday, November 2. Second midterm.
Friday, November 4. no reading.
Monday, November 7. MT pp. 139-145.
Wednesday, November 9. no reading.
Friday, November 11. MT pp. 145-147.
Monday, November 14. no reading.
Wednesday, November 16. MT pp. 147-149.
Friday, November 18. MT pp. 256-258.
Monday, November 28. no reading.
Wednesday, November 30. MT pp. 259-263.
Friday, December 2. no reading.
Monday, December 5. MT pp. 271-275.
Wednesday, December 7. no reading
Friday, December 9. no reading.

Tests

Wednesday, September 28. First midterm. Here is the practice test, with solutions. Here are solutions to the midterm itself.
Wednesday, November 2. Second midterm. Here is the practice test, with solutions. Here are solutions to the midterm itself.
Monday, December 12. Final (7pm in the usual room.) Here is a study guide. Here is the practice test, with solutions.

Homework

Note: When a problem asks to "prove" or "show" something, I expect to see a formal proof from you (unless I say otherwise.)

Due Friday, August 26. Here are solutions.
1. Let n be an odd integer.
  1. Prove that n²+1 is an even integer.
  2. Prove that (n²+1)/2 is an odd integer.
2. Let n be an odd integer.
  1. Prove that (n²-1)/2 is an even integer.
  2. What can you say about the evenness/oddness of (n²-1)/4?
Due Friday, September 2. Here are solutions.
1. MT 1.13.
2. MT 1.50. (Note: some printings of the book have a typo; in part (a), there should be two intersection symbols, not two union symbols.)
3. MT 2.4.
4. MT 2.11. (Give an explanation of your reasoning, but formal proof is not necessary. Note: Dollars count as coins.)
5. MT 2.24. (Proofs not required here.)
6. MT 2.52.
Due Friday, September 9. Here are solutions. (For the first three problems, you can assume without proof all consequences of the basic field axioms (which just amount to basic algebra); however, you must explicitly state how you use the Ordered field axioms P1, P2, P3.) I have put off the last three problems to next week.
1. Using only the Ordered Field axioms, show that x≤y and u≤v imply x+u≤y+v. (There was an error in the original statement, now fixed. 9/5/05 CR.)
2. Using only the Ordered Field axioms, show that 0<x implies 0<x^-1.
3. Using only the Ordered Field axioms, show that 0<x<y implies 0<y^-1< x^-1.
Due Friday, September 16. Here are solutions.
1. MT 1.29.
2. MT 1.32.
3. MT 1.35.
4. MT 1.47. (Note: you are allowed to use the fact that integers are either even or odd. Part b does not ask for proof.)
5. MT 3.5.
6. MT 3.15.
Due Friday, September 23. Here are solutions.
1. MT 3.16.
2. MT 3.23.
3. MT 3.24.
4. MT 3.26.
5. MT 3.31.
6. MT 3.47.
Due Friday, September 30. Here are solutions.
1. MT 3.38.
2. MT 3.56.
3. MT 3.62.
4. MT 4.6.
5. MT 4.11.
6. MT 4.25 (no proofs here).
Due Friday, October 7. Here are solutions.
1. MT 4.22.
2. MT 4.29.
3. MT 4.34.
4. MT 4.47.
Due Friday, October 14. Here are solutions.
1. MT 5.2.
2. MT 5.5.
3. MT 5.9.
4. MT 5.13.
5. MT 5.14.
6. MT 5.18.
Due Friday, October 21. Here are solutions.
1. MT 5.28.
2. MT 5.31.
3. MT 5.36.
4. MT 5.39.
5. MT 5.50.
6. MT 5.57.
Due Friday, October 28. Here are solutions.
1. MT 5.49
2. MT 5.52.
3. MT 5.55.
4. MT 5.58.
5. MT 6.2.
6. MT 6.22.
Due Friday, November 4. Here are solutions.
1. MT 6.5.
2. MT 6.17.
3. MT 6.23.
4. MT 6.29.
Due Friday, November 11. Here are solutions.
1. MT 6.40.
2. MT 6.48.
3. MT 7.11.
4. MT 7.13.
5. MT 7.15.
6. MT 7.25.
Due Friday, November 18. Here are solutions.
1. MT 7.5.
2. MT 7.8.
3. MT 7.18.
4. MT 7.19.
5. MT 7.35.
6. MT 7.42.
Due Monday, December 5. (Note change in due date.) Here are solutions.
1. MT 7.48.
2. MT 13.8.
3. MT 13.19.
4. MT 13.25.
5. MT 13.26.
6. MT 13.28.
Due Friday, December 9. Here are solutions.
1. MT 13.29.
2. MT 14.3.
3. MT 14.4.
4. MT 14.10(a). (You don't need to prove part (b): it requires the Cauchy convergence criterion, which we haven't proved yet.)

Contact info.

email:
office: Illini Hall 242
office hours: Check here.

Last modified 9 December 2005 by Charles Rezk.