Homework Assignments

The date refers to the date of the lecture when the assignment is made. Unless otherwise indicated the reading and problems are to be completed by the next class period.

 

Date Reading Exercises/Notes
9/1 pp 1-7 Ex 1.2.1, 1.2.2; order copy of Fermat's Enigma, by Simon Singh
9/3 pp 8-17 Try Exercise 1.2.3, 1.2.12; Hand in exercise distributed in class H1
9/5 pp 18-22 Try exercises 1.2.9, 1.3.9; Hand in 1.2.7 H2
9/8 pp 22-27
chapter 1 of Fermat's Enigma

Try exercises 1.3.6, 1.4.4, 1.4.5 Hand in 1.3.4 and 1.3.7 H3
Due Monday 9/13: one page response to "How would you describe the contribution of Pythagoras to mathematics?"

9/10 pp 29-32 Try 1.3.5a, 1.4.9 Hand in 1.3.8 H4
9/12 Finish ch 1 and pp 35-38 Try 1.4.10, 1.5.3; Your response is due on Monday; in describing his contributions be sure to address whether these were positive or negative, lasting or temporary, important or unimportant, etc. H5 = ch 1
9/15 Start reading Ch 2 of FE;
pp 38-43
Hand in 1.5.4, 1.4.8 a,b -- you may assume the sets are all disjoint;
There will be an assignment on FE due 9/26 H6
9/17 pp 44-53 Try: 2.2.1, 2.2.3, 2.2.4, 2.2.6, 2.3.1, 2.3.2. On Friday 9/26, hand in a list of 10 interesting things you learned in chapter 2 of Fermat's Enigma. Each should be written as a complete sentence and should convince me that you read and thought about the contents of the chapter.
9/19 pp 53-55 Try 2.2.7, Hand in 2.3.4, 2.3.5 H7
9/22 pp 55-58 Try 2.4.2, 2.4.3 Hand in 2.3.10; Test next Monday through section 2.5 I will post a copy of last year's exam on webCT. H8
9/24 pp 58-62 Try 2.5.3 Hand in 2.3.7a,b. List from reading chapter 2 of Fermat's Enigma due on Friday H9
9/26   Prepare for test
9/29   Try 2.6.1, 2.6.5a; Hand in 2.4.4 H10
10/1 pp 62-69 Try 2.7.4, Hand in 2.5.4, 2.6.5b (prove using only the def of Cauchy sequence) H11
10/3 pp 75-84 Try 2.7.9 Hand in 2.7.6 .On Friday 10/10 hand in a list of ten sentences summarizing the highlights of Chapter 3 in Fermat's Enigma H12
10/6 pp 84-89 Try 3.2.1, 3.2.2, 3.2.3; Hand in 2.7.10. H13 Read and study pp 78-82. Send email by 10 am on Wed. Answer the following questions:

1. On p. 79 in the proof of Theorem 3.2.3, can we adjust the proof to show that the intersection of an infinite number of open sets is open? Why/why not?

2. What parts of this section do we need to spend more time on? What ideas are not clear? Doing the try problems should test you understanding of these ideas.
10/8   Try 3.3.3, 3.3.5 Hand in: 3.2.7, 3.2.9ab Finish your list of 10 interesting items from ch 3 of Fermat. H14
10/10 pp 99-108

Try 3.2.9c, 4.2.1ac, 4.2.2; Hand in 3.3.2, 3.3.1 Start reading ch 4 of Fermat H15

By 10:00 am on Monday, send me an email identifying any problems you had with the reading -- pp103-108. Answer the following:

In Theorem 4.2.3 we prove that i) is equivalent to ii). In your own words, explain what is the difference between the two statements.

10/13 pp 109-19 Try 4.3.4, 4.3.7 Hand in 4.2.6, 4.2.9 H16
10/15 pp 120-24 Omit connected Try 4.3.5; Hand in 4.3.9 Hint: Calculuate |y 3 - y 2 | , |y 4 - y 3 | etc. and look for a pattern. Have chapter 4 of Fermat read by Fri Oct. 24. Hand in a list of 10 mathematically significant things you learned -- or at least were reminded about -- as you read this chapter. H17
10/20 pp 125-8 Try 4.4.4, 4.4.6 Hand in 4.4.2, 4.4.7 H18
10/22 pp 129-36 Omit Df Try 4.5.2 Hand in 4.6.4 Fermat due on Friday. Test next Wed sections 2.6 - 5.2. See example test that has been posted. H19
10/24 pp 137-140 Try 5.2.4 Hand in 5.2.1 Start Ch 5 of Fermat H20
10/27   Prepare for test
10/29 p 141-2  
10/31 pp 144-9 Try 5.3.1, 5.3.3 Hand in 5.3.2 On Wed, hand in a brief outline of the major steps described in Ch 5 leading to the ultimate solution of the Fermat Theorem. H21
 11/3  pp 151-157  Hand in 5.3.5 and 5.3.6 H22
11/5 pp 154-160 Try 5.2.5; Start reading Ch 6 of Fermat's enigma
11/7   Try 6.2.1, 6.2.2
11/10 pp 164-7 Try 6.2.3 Hand in 6.2.4, 6.2.7 H23
11/12 pp 167-8 Try 6.3.2, 6.3.3 On Monday I'd like a couple summaries/reflections based on your readings from ch 6 of Fermat. First, most of you have or will study group theory in MAT 330. Write a few thoughts about what you learned about Galois. Secondly, reflect on what you have learned about the way that mathematics is done -- especially in regard to the proof of Fermat's theorem.
11/14 pp 169-73 Try 6.4.1, 6.4.2; Hand in 6.3.4 a,b H24
11/17 pp 183-94 Try 6.4.7, 6.5.1, 6.5.4; Hand in 6.4.6 H25 Test on Monday; Darboux's theorem p. 134 through Ch 6 *** Note change ***
11/19   Try 6.6.3, 6.6.4, 6.6.5 Start reading ch 7 of Fermat.
11/21   Prepare for test
11/24 pp 194-8 Finish Ch 7 and Epilogue -- Write a few paragraphs about what you think about the end of the story. Due Wed Dec 3.
Try 7.2.2, 7.2.3
12/1   Try 7.3.1, 7.3.2; Hand in 7.2.5, 7.2.6; I will not do Theorem 7.4.2 in class but you should be able to do it. I will gladly answer and questions. H26
12/3 pp 199-205 Try 7.5.1, 7.5.2