| Homework #1 due Fri. Sept. 6
You should give a proof of your answer for each problem. 1.15 set operations. For what conditions on sets A and B does A-B=B-A hold? Note: we will discuss set operations on Wed. 1.19 quadratic equation. What are the dimensions of a rectangular carpet with perimeter 48 feet and area 108 square feet? Given positive numbers p and a, under what conditons does there exist a rectangular carpet with perimeter p and area a? 1.22 mixing problem. We have two identical glasses. Glass 1 contains x ounces of wine; glass 2 contains x ounces of water (x>=1). We remove 1 ounce of wine from glass 1 and add it to glass 2. The wine and water in glass 2 mix uniformly. We now remove 1 ounce of liquid from glass 2 and add it to glass 1. Prove that the amount of water in glass 1 is now the same as the amount of wine in glass 2. (*) Use the triangle inequality to prove that for all a and b, |a|-|b| <= |a-b|. |
Writing Assignment #1 due Fri. Sept.
6
Use LaTeX to type up a proof that for all real numbers x, x<=|x|. |
| Homework #2 due Wed. Sept. 11
1.13, 1.49, 1.50 (in part (a) of 1.50 change both union symbols to intersection symbols - this is an error in the book) |
Writing
Assignment #2
First draft due Mon. Sept. 9 Peer Feedback forms due Tues. Sept. 10 Final draft due Friday Sept. 13 |
| Homework #3 due Wed. Sept. 18
Read Chapter 2. Do Problems 2.1, 2.10, 2.22, 2.28, 2.30. Problem 2.28(b) requires a proof. |
Writing
Assignment #3
First draft due Mon. Sept. 16 Peer Feedback forms due Tues. Sept. 17 Final draft due Friday Sept. 20 |
| Homework #4 due Wed. Sept 25
Read Chapter 3 Do Problems 3.5, 3.11, 3.14b, 3.16 and (*) (i) Prove that if n=ab, where n, a, b are
natural numbers, then either a <= square root of n or b<= square
root of n
|
Writing Assignment #4
Do the worksheets on understanding definitions and on understanding theorems understanding theorems . This was done in class on Tues., Sept. 24. If you didn't turn it in that day, then turn it in by Friday, Sept. 27. |
| Homework #5 due Wed. Oct. 2
Read Chapter 4 Do Problems 4.9, 4.11, 4.12, 4.49, 4.51 |
Writing Assignment #5 |
| Homework #6 due Fri. Oct. 11
Read Chapter 5 Do Problems 5.2, 5.4, 5.7, 5.14, 5.30, 5.38 |
no writing assignment this week - Test #1 on Tues. Oct. 8 |
| Homework #7 due Fri. Oct. 18
Read Chapter 6. Do Problems 6.2, 6.4, 6.8, 6.17, 6.24, 6.30 |
Writing
Assignment #6
This writing assignment will be done in class on Tues. Oct. 15. Please turn in by Fri. Oct. 18. |
| Homework - none due the week of Oct. 21 | Writing Assignment #8
Choose some specific mathematical topic and write a paper about it for a general audience. Include history, background, any references that you use. Rough draft due Mon. Oct. 21, Final draft due Fri. Oct. 25. |
| Homework #9 due Fri. Nov. 1
Read Chapter 7. Do Problems 6.9, 7.1, 7.5, 7.6, 7.11, 7.15, 7.33, 7.34 |
Writing Assignment #9 |
| Homework #10 due Wed. Nov. 6 | Writing Assignment #10 |
| Homework #11 due Wed. Nov. 13
Read Chapters 8 and 13. Do Problems 8.1, 8.5, 8.7 (find r,s, factor), 8.17 (we've done this one in class), 8.25, 13.1, 13.8, 13.9 |
Writing Assignment #11
|
| Homework #12 due Wed. Nov. 20
Finish reading Chapter 13. Do Problems 13.3, 13.5, 13.6, 13.10, 13.11, 13.23, 13.25, 13.29, 13.37 |
Writing Assignment #12
Problem 13.26. Bring 3 copies of your rough draft on Tues. Nov. 19. |
| Homework #13 due Wed. Dec. 4
Read Chapter 14. Do Problems 14.1, 14.3, 14.9, 14.14, 14.15 |
Writing Assignment #13 |
| Homework #14 due Fri. Dec. 13
Read the first part of Chapter 15 Do Problems 14.5, 14.12, 14.33, 14.43, 14.45 (a) Use the epsilon-delta definition to prove that the limit of x^2 as x approaches 2 is 4 (b) Prove that if the limit of f(x) as x approaches a is L and if the limit of g(x) as x approaches a is M, then the limit of f(x)+g(x) as x approaches a is L+M. |
no writing assignment - Test #3 on Tues. Dec. 10 |