Journey through Genius, by William Dunham: Nick. Read most of this... explores a handful of the most important theorems and proofs from math history. If you're reading this, the book won't be that bad. If you're trying the proofs, it can be very difficult, and I wouldn't recommend it. Dunham claims that Archimedes is the greatest of the Greek mathematicians, the crown story. Personal stories of the mathematicians, too; for example, Cardano's tortured life. Not a lot of fun reading, but some really good explanation of why they use the methodology.
Love and Math, Edward Frenkel: Rebecca, Kourtney, Erin. "It's hard work being a teacher..." Great about the hard work being a mathematician, and the difficulties in being Jewish in an anti-semitic world. He had to literally scale the walls to get his math education. He was also moving in discussing how important collaboration is, and how important making mistakes is. The math is really high level - we could see some familiar things from abstract algebra, but there were good analogies for a lot of the ideas. "Where does love come in?" Love of math. Started in physics, but was convinced to go deeper, mentor by mentor.
The Math Book, Clifford Pickover: Anthony. Each page is like a wikipedia article about an idea, but nothing in depth. References are given so if you want to go deeper you can. "The integers came from God, and all else are hand made." - Kronecker. It covers big ideas, inventions and famous mathematicians. Lots of fun ideas, like the birthday paradox or the infinite monkey theorem. The Johnson Theorem, riddles like the barber paradox. History of zero... I'd recommend this for teachers for the history.
Joy of X, Steven Strogatz: Jordan Drake, Nick. Easy read, a narrative. He explained negatives, but noted how we as a society avoid them (building floors, bank statements, temperatures). Strategies for finding your soulmate. What made it so easy to read was taking complicated ideas, like sine and cosine, but then gives real life examples and good visual images to support it. I went through math doing it because I could, but this gets at why these things work or are true. He gives a lot of practical applications. He gives the reasons for "why are we using this?" Really fun to read with a lot of 'aha!' moments.
e: The Story of a Number, Eli Maor: Marty. I thought the whole book would be leading up to e, but we see it already in the third chapter. It starts with Napier, goes through logarithms, explores finance, and then calculus (Newton and Leibniz), ... It was at times interesting and boring. The most beautiful formula which makes a connection with imaginary numbers. Lots of appendices of intense proofs.
The Number Mysteries, Marcus du Sautoy: Heather, Brianna
5 different math mysteries, got into the history of the ideas,
- primes; the building blocks of all numbers.
- geometry; nature is as efficient as possible.
- tricks for games; confusing but interesting, Monopoly and more.
- codes; Everything is a code, languages, DNA, ISBN, modular/clock arithmetic.
- prediction; patterns are detectable, which make things predictable. Seasons lead to the calendar, etc.
Mathematician’s Lament, Paul Lockhart: Hannah. K-12 math needs to be scrapped. Math is an art, it's about playing and imagination. Instead, teachers give facts and formulas for memorizing. Takes away the creativity and engagement of solving. Teachers try to relate it to life when it doesn't. It can be fun because it doesn't relate to your life. A good problem is anyone you don't know how to solve. You want students to struggle and be frustrated. Geometry is the most destructive because it destroys proofs. Instead of being charming, it's a boring list. Write a paragraph of a proof, tell the story of your thinking. Why can't 1 + 1 = 0? Even/odd + even/odd, sum of odd numbers, ... so many ways to reveal the nature of math. "As a future teacher did you find yourself agreeing or disagreeing?" The get rid of the curriculum and let every student figure out what they're working on - I disagree. But the emphasis on memorization needs to go. "Math can be fun when not related? That's really clever. Counter to the message we get."
The Calculus of Friendship, Steven Strogatz: David. Less of a math book, and ever increasing life lessons. The teacher retired and became a famous white water rafter, which is connected with limits and infinity. Irrationality, chaos theory, etc. The monk and the mountain. Will a monk who walks up the mountain and down in irregular patterns ever be at the same point at the same time. Inspiring about going into being a teacher and the effect you can have. Readable even if you don't know calculus.
Mathematical Mindsets, Jo Boaler: Michelle, Tabatha Lathrop. Growth mindset = you can get better at how well you learn things, fixed mindset = you can learn things, but you can't change your intelligence in an area. This really affected me. The brain research is interesting; when you're making mistakes is when you're learning. Feedback makes a big difference. Then she connects with math mindset. Most effective teaching is when learners explore the question, and then get explanations of how and why. Using what the kids came up with is helpful, with engagement to start. Students will say they don't like math because it's too much answer time than learning time. The faster they can do math the better, kids think, when the reality is almost the opposite. Kids don't ask 'when are we going to use this?' in other subjects. I am literally a different person because I read this book. (Others connected to Carol Dweck's Mindset in response.) It's interesting as an adult learner, trying to think about where you're fixed or growth.
The Magic of Math, Arthur Benjamin: Andrew Meeuwsen. Topics align well with the course, but not a lot of the fun history. Lots of worse than dad jokes: mathematician dad jokes. Lots of tricks for doing specific problems. Many connections to his mathemagic show. FOIL, squares, magic of 9, magi of counting, magic of proofs... a lot of good math, but a lot of filler, too. The book has a steep slope, from arithmetic to calculus. My favorite was about infinity. It covers a lot of the subjects from undergrad mathematics.
Jerry missed the discussion, but has a review of The Calculus Gallery.
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