Syllabus

Assignments:

  • Automathography (three or four paragraphs) (10%) Due Monday 9/23
  • “Reading” Journal (10%) Checked on 9/30, 10/21, 11/11, 11/25, and 12/9
  • Group Work Write Ups (60%) Hand in at each subsequent class
  • Biography (three or four pages tops, include a bibliography) (10%) Due Thursday 11/25
  • Final Project (10%) Due Monday 12/9

Links and Handouts:

Calendar:

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

  1. 9/9/2019 – We discussed Euclid’s Elements and the way that mathematical ideas build on one another. You spent time mapping out dependencies between propositions and definitions to see precisely how the ideas build. Be sure to submit your group write up, for now you can email me the document or turn it in next week on paper.
  2. 9/16/2019 – We discussed the Fundamental Theorem of Arithmetic. Then we looked at prime factorization and at multiplication. We saw that while multiplication is relatively easy, even by hand, factoring is really very hard; this is an important point relevant to modern information security. Finally, we talked about quadratic and cubic equations, in particular how they may be viewed graphically.
  3. 9/23/2019 – We looked at handouts on Archimedes approximation of \(\pi\) and on Numerals from different cultures. In our discussion of Sophie’s Diary we also highlighted the turbulent and changing philosophies of this time period in France. In year two of the text this could be highlighted by contracting views of women’s rights/responsibilities represented by Jean-Jacques Rousseau (p.77) and Marquis de Condorcet (p.94).
  4. 9/30/2019 – We watch Measuring the World, a fictionalized bio-pic about Gauss and Humboldt. Next week we will start discussing symbolic logic, you should begin reading Logicomix.
  5. 10/7/2019 – Here are the Circuit and Tarski handouts. We worked through these tonight. Next week, and the week after, we will work through some of the text Truth, Reasoning, Certainty, and Proof, you should bring a device so that you can view it.
  6. 10/14/2019 – This week we discussed abductive, inductive, and deductive reasoning. Next week we will discuss Godel’s incompleteness theorem. We will again be using the text Truth, Reasoning, Certainty, and Proof, but you would also benefit from reading The Unsolvable Problem.
  7. 10/21/2019 – We continued our work in Truth, Reasoning, Certainty, and Proof, in particular we discussed conditional statements and Godel’s Incompleteness theorem. Next week we will be watching “The Man Who Knew Infinity,” you may want to read the biographies for Rumanujan and Hardy at MacTutor History of Mathematics Archive or listen to this Podcast on Hardy and Ramanujan so that you have better context for the film.
  8. 10/28/2019 – We watched “The Man Who Knew Infinity”, next week we start cryptology. You should begin reading “Breaking the Code”.
  9. 11/4/2019 – We discussed combinatorics and counted the number of possible settings on the Enigma machine.
  10. 11/11/2019 – We read Act I Scene 5 of Breaking the Code. In reference to this scene we discussed properties of logical systems, recognizing cultural differences, the idea that sometimes war may be considered a necessary evil (see also Tolkien and Lewis), and the potential moral responsibility of scientists for their creations. We then watch Codebreaker a docudrama about Alan Turing’s life. Please turn in a written reflection for this class.
  11. 11/18/2019 – We discussed the field of Topology where we want to find properties that persist even if we stretch or deform a space. In particular we looked at Mobius Strips and Graph Theory.
  12. 11/25/2019 – We watched Flatland and then talked about dimensions from points to hypercubes. For the last part of class we looked at a mini-lesson on calculus set in line land. For the next couple of classes you will be presenting your final projects. I have a couple of volunteers already, the rest of you should volunteer, you you may get voluntold. You should shoot for 15 to 20 minutes
  13. 12/2/2019 Presentations: Cancelled Due to Snow
  14. 12/9/2019 Presentations:
    1. Anthony
    2. Morgan
    3. Dat, Gabriel, Jacqueline
    4. Elijah
    5. Nicole, Joe, Chris
    6. Bhadrangi, Eliot, Matheus
    7. Nikole, Will, Mackensie

Hypercube

Number Theory

Logic an Reasoning

Cryptology

  • Readings from 10/29 to 11/11:
  • Movie: Codebreaker: The Story of Alan Turing

Topology