There is a proposed calendar on the syllabus, but here I will record what we actually get through in class.
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.
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.
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).
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.
10/28/2019 – We watched “The Man Who Knew Infinity”, next week we start cryptology. You should begin reading “Breaking the Code”.
11/4/2019 – We discussed combinatorics and counted the number of possible settings on the Enigma machine.
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 Codebreakera docudrama about Alan Turing’s life. Please turn in a written reflection for this class.
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.
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