Final Exam Week Office Hours:
- Tuesday 12-7-2021: 2:30-4:30pm
- Thursday 12-9-2021: 1:00-3:00pm
- Monday 12-13-2021: 12:00-2:00pm
- Tuesday 12-14-2021: 3:00-5:00pm
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.
- 9-27-2021: Tonight we watched the movie Agora which centers around the life of the mathematician Hypatia. The movie is available on https://media.wcsu.edu/ which you can log onto with your WCSU ID, then search for the movie. You should also take time to read Hypatia’s biography which can be found HERE on the MacTutor History of Mathematics Site. For your write up on last nights class reflect on the movie and the biography; try to see if there are any parallels with Sophie Germain or comparisons with the social upheavals in each time period. You should also start reading Logicomix.
- 10-4-2021: Tonight we started the unit on logic. Class began with a discussion of the start of Logicomix, if you haven’t started reading the novel please do so. We then discussed propositional logic and compared it to wired circuits (circuit handout). Finally we looked at propositional logic and quantifiers, we practiced this with a two lies and a truth exercise with Tarski’s World (Tarski handout).
- 10-11-2021: Tonight we used material form Truth, Reasoning, Certainty, and Proof to help us understand abductive, inductive, and deductive reasoning. We will continue to work with material from this text in order to try and understand a little bit of Godel’s Incompleteness Theorem.
- 10-18-2021: Tonight we continued our work in Truth, Reasoning, Certainty, and Proof. We discussed Cantor’s Continuum Hypothesis and then looked at the material on pp. 109-116 on Gödel’s Incompleteness Theorem. Next week we will be watching “The Man Who Knew Infinity.” Your reading journals for Logicomix are due next week, so you should have finished the novel by then.
- 10-25-2021: Tonight we watched “The Man Who Knew Infinity” about Srinivasa Aiyangar Ramanujan. For next week you should write up any thoughts you have on Ramanujan or Hardy or the Movie. Here is also a podcast about them that you can listen to for supplementary information: Podcast on Hardy and Ramanujan. Next week we start the next unit so you should start reading Breaking the Code.
- 11-1-2021: The main purpose of tonights talk was to discuss the Enigma Cipher Machine and the number of different ways it could be set up. We started class looking at a couple of slide shows in Cyrptology in general: Basics and Definitions & Polyalphabetic Ciphers. Then we looked at the Enigma Machine Emulator in order to familiarize our selves with the basic idea of the machine. We then looked at some rather intense calculations for the number of ways the machine could be set up; a number greater than the number of atoms in the observable universe. We also discussed the number of settings in a more practical perspective and briefly how the cipher was broken. (This link http://dx.doi.org/10.1080/0161-119591883773 should allow you to download a copy of the article on the mathematics of the enigma as long as you are on campus.)
- 11-8-2021: Class Postponed/Cancelled. We will read passages from Breaking the Code and watch Code Breaker: The Alan Turing Story next week.
- 11-15-21: We read passages from Breaking the Code and watched Code Breaker: The Alan Turing Story
- 11-22-21: We watched the videos Wind and Mr. Ug and Seven Bridges of Konigsberg. And in relation to these we looked at properties of the Möbius Strip and discussed Graph Theory.
- 11-29-21: We watched Flatland and then played around with finite differences and the idea of an expanding universe. Next Monday we will be discussing your final projects. They don’t need to be done but they should be well on their way and you should be prepared to describe them. We will be presenting the final projects on Monday the 13th at the usual class time.
- 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)
- Codebreaker: The Story of Alan Turing
Topology (11/15 & 11/22)