Math 248 - Fall 2002 - Assignments

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
(ii) Prove that if n is composite, then it has a prime factor p such that p <= square root of n.  From this, conclude that if n>=2 and n has no prime factor <= square root of n, then n is prime.

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
Choose either 8.26 or 13.21. Write up a rough draft, including introduction and conclusion, and bring three copies to class on Tues. Nov. 12. Final draft (typed) will be due on Fri. Nov. 15. 
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