Syllabus

Calendar:

There is a proposed calendar on the syllabus, but here I will record what we actually get through in class.

  • 8-30-2021: Today we talked about Euclid’s Elements, a lot about his geometry and a little about his number theory. We focussed much of the discussion on how new propositions are built on previous propositions as well as on definitions, common notions, and postulates. We also looked at his proof for the infinitude of primes and for searching for perfect numbers. Write up your reflection/summary of what we did in class today to hand in at the start of our next class on 9-13-2021, in two weeks, because of labor day.
  • 9-13-2021: Tonight we looked at the Fundamental Theorem of Arithmetic which states that each positive integer \(n\) can be factored into a product of prime integers in a unique way up to order. Here is a link to the slides we used tonight (Link). We looked at the definitions, axiom, and lemmas leading up to the theorem, particularly Bezout’s Lemma when we played with the jugs. We also talked about some strategies for factoring. Finally we compared how long it takes to factor numbers versus multiply them so that we could understand that even though the F.T.A. tells us the prime factors must exist, factoring is much harder than multiplying. Please make sure you are reading and journaling Sophie’s Diary and your reflection on last night’s activities are due next class; these should only be 2 or 3 paragraphs.
  • 9-20-2021: Today we talked briefly about Sophie’s Diary, your journaling will be checked next week while we watch the movie. We then spent time looking at number systems from different cultures. The discussion included number bases, positional vs. additive systems, and the number zero. Here is a link to the slide show LINK. We then spent time focussed on ancient Egyptian arithmetic focussed on trying to recreate the experience of deciphering the Rosetta stone. Here is the link for that activity, LINK.

Assignments:

  • Automathography (three or four paragraphs) (10%) Due 9/20
  • “Reading” Journal (10%) Checked on 9/27, 10/25, 11/8, 12/6
  • Class Work Write Ups (60%) Hand in at each subsequent class
  • Biography (three or four pages tops, include a bibliography) (10%) Due 11/22
  • Final Project (10%) Presentations on 11/29 and 12/6

Misc. Links and Handouts:

Number Theory (8/30-9/27)

Logic and Reasoning (10/4-10/25)

Cryptology (11/1 & 11/8)

Topology (11/15 & 11/22)

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