Math 398 - History of Math -- Chapter 4 Reading Assignments
February 23 - April 4

(Last modified: Tuesday, April 10, 2001, 12:07 PM )

Unless otherwise indicated, all reading are from Mathematical Expeditions by Laubenbacher and Pengelley.

For Friday February 23

Email Subject Line : Math 398 2/23 Your Name
To read: Pp 156 - 160

Reading Question:

    Why is Euclid's Proposition 36 from Book IX equivalent to the statement "If 2n+1 is prime for some n >=1, then 2n(2n+1-1) is perfect" ?

For Monday February 26

Email Subject Line : Math 398 2/26 Your Name
To read: Pp 160-161, and Section 4.2

Reading Questions:

  1. Use Proposition II-8 of Diophantus's Arithmetica to write 36 as the sum of two squares. Use a=2.
  2. Give an example of similar plane numbers with proportionality factor 3/5.

For Wednesday February 28

To read: Reread Section 4.2

No reading questions since the Takehome Exam is due today.

For Friday March 2

Email Subject Line : Math 398 3/2 Your Name
To read: Pp 161-166, 179-181

Reading Questions:

  1. If n= 382,725 = 3*7*52*93, how many ways can n2 be written as the sum of two squares?
  2. What result does Euler prove to show that Fermat's Last Theorem holds for n=4?

For MWF, March 5, 7, 9

No Reading Assignments because of In-class Presentations

For Monday March 19

To read: Finish Section 4.3. There is some tough going here.
No Reading Questions since this is the first day after break.

For Wednesday March 21

Email Subject Line : Math 398 3/21 Your Name
To read: Pp 166-168, Section 4.6

Reading Questions:

  1. Which arithmetic operations 'make sense' modulo n? Which don't?
  2. If gcd(x,y)=1 and xy=an, what can you say about x and y?

For Friday March 23

Email Subject Line : Math 398 3/23 Your Name
To read: Pp 185-190

Reading Questions:

  1. Verify that the first condition of Sophie Germain's Theorem holds for p=3 and theta=7.
  2. Verify that the second condition does not hold for p=3, theta=7, and r=1.

For Monday March 26

Email Subject Line : Math 398 3/26 Your Name
To read: Pp 190-192

Reading Question:

    What is the difference between Case I and Case II solutions for Fermat's Last Theorem?

For Wednesday March 28

Email Subject Line : Math 398 3/28 Your Name
To read: Section 4.5

Reading Questions:

  1. What is the fundamental flaw in Lame's approach to Fermat's Last Theorem?
  2. What do numbers in Z[sqrt(-5)] look like?

For Friday March 30

Email Subject Line : Math 398 3/30 Your Name
To read: Reread Section 4.5

Reading Questions:

  1. How many elements are in the ideal number A defined on page 198?
  2. For what values of n was Kummer able to prove Fermat's Last Theorem?

For Monday April 2

Email Subject Line : Math 398 4/2 Your Name
To read: 168-170

Reading Questions:

  1. What is an elliptic curve?
  2. What result did Wiles prove that implied Fermat's Last Theorem?

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Last modified: Tuesday, April 10, 2001, 12:07 PM