Day 16, Mat305/594, History of Mathematics

Last time: Section 4.2

Next time: Section 4.4

Today:

• Announcements

  • Please hand in your exams

  • Let's make the rest of the problems from Chapter 3 due next week (Wednesday).

  • Maybe it's a good time to remind you that you'll be expected to write a "paper on a mathematician or an idea that we will not cover (from chapter 8 or later). These will be presented during the time slot reserved for our final exam (4:30, 12/16)" (from the syllabus). Your report will satisfy the following:
    • Double-spaced, 12pt type (no funky fonts -- best to use Times New Roman), 1 inch margins.
    • No more than 8 pages of text (not including references, appendices); no fewer than four.
    • No fewer than five references, at least one a print resource (other than our text)
    Your presentation will be at most 10 minutes. Refreshments will be served!;) Your peers will also grade your presentation.

    See the syllabus for more on your paper/presentation.

  • I've rearranged our schedule to bring it back into line. We've lost our "make-up days" from the end of the semester! Rats. But not too surprising.

  • Worksheet for sections 4.4

• Today:
  • Lessons from 4.3
  • Commercial (Paul); can I get a volunteer for the Monday following?
  • Lessons from 4.3

• Mathematical Elements, lessons and problems from section 4.3: Euclid's Number Theory
  • "Euclid was particularly interested in questions pertaining to divisibility." (p. 172)
  • Euclid's division algorithm (p. 180: VII.1, VII.2)
  • If a prime divides a product, then it divides one of the factors (p. 180: VII.30)
  • The result above extends to the Fundamental Theorem of Arithmetic (p. 181: IX.14)
  • The infinitude of primes (p. 183: IX.20)
  • The sum of a geometric series (IX.35) (remember this one from the Rhind papyrus?)