Honors Interdisciplinary Seminar (175)

 Fermat's Last Theorem


Assignment following Week #8 (Due 11/9 in class)
(Section 004 - Due 9/28 in class)

  1. Spend at least 30 minutes on the "Constructions" worksheet from class.  Review the constructions we did, and try to finish those that we did not get to.
  2. Read the excerpt from Maor on the Pythagorean Theorem (See "Pythagorean theorem, p. 1-31" on ereserve).   As you read, think about the issue of truth.  Do the Pythagoreans remind you of Flatland at all?
  3. Carefully read the background material on Fermat’s Last Theorem.  You can find most of the material on ereserve in the subfolder entitled "Fermat readings."  The packet of material contains four articles from the New York Times.  There is a separate article from the MAA Focus, a mathematician’s newsletter that you can get here or from D2L.  Pay very close attention to the dates on the articles, but don't worry about the section entitled "The Technical Details."  I recommend printing the articles for easier reading and note taking.
  4. Complete the Study Questions below.
  5. With your group, prepare your proof of the Pythagorean Theorem that you will present at our next class meeting.  You can find a copy of all the proofs of the Pythagorean Theorem here or on D2L.
  6. Read any emails I send you, and respond if requested.
  7. There may be a brief quiz at the start of our next class meeting.

Study Questions 

Please carefully write out your answers to these questions.  Make a copy of your answers and be prepared to hand that copy in at the start of class.  Look at the Study Questions Main Page for general guidelines on study questions in Steve's section.

Follow-up on Euclidean Constructions:  

  1. Given the following triangle:

Construct a copy of this triangle (with a straightedge and compass) onto your homework sheet.  Carefully list your steps (leave your construction marks), and argue that your construction is correct.  

From the Fermat readings:  

  1. Write definitions for each of the following terms: conjecture, theorem, proof, corollary, and counterexample.
  2. Carefully state Fermat’s Last Theorem.
  3. To what “familiar” Theorem is it related and how?  Name and state this Theorem.
  4. Who was Fermat and what prompted his conjecture?  Why is it really his conjecture and not his theorem?
  5. Make a brief timeline of the story of Fermat’s Last Theorem.  Include both Fermat and Wiles, and for Wiles, include the relevant aspects of his journey.  (Your timeline doesn’t have to be to scale!)
  6. Does the story of Fermat’s Last Theorem change or confirm your view of mathematics and mathematicians?  Why or why not?
  7. What does the story of Fermat’s Last Theorem have to do with truth?

Thinking ahead:

  1. Come up with one potential topic for your Final Project debate (see the Final Project Page for details).  Your topic should be an issue related to our class discussion that can reasonably be debated.  Give a brief (just a few sentences) description your potential topic, including a description of both sides of the issue.  You are not committed to this topic. 

 


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