Tuesday, February 25, 2014

Capstone Book Club

One of the courses I'm teaching this semester is a capstone course for our majors. Rather than me picking the book, I let them choose from a list that the Math-Twitter-Blog-o-Sphere helped me put together. Last summer, The Mαth Book and Joy of X were the big hits, this semester, they made some very different choices. (Here's the list and their choices.) Having them choose makes me feel a little less like this:

My notes of the discussion, with links to some of their blogposts. Since they're notes of a discussion, pretty terse. Also, not my point of view, this is the students'. The people who got the most new students interested in their book were those reading The Mathematician's Lament and e: the Story of a Number.

Euler: Master of Us All. History at HS level, proofs at graduate school. Felt outclassed reading it. Simplify or explaining the proofs would have helped. Averaged a paper per week. Very dense.
Review: Alex

Visions of Infinity. Each chapter is a different idea, then has history and the author explains the important proofs about the idea. How mathematicians think vs what they thought about. Eg. squaring the circle, explained why you couldn't do it. Was advanced, but not frustrating. Recommend it to someone who knows about math. Last two chapters… where math is going. Strongly the author's point of view.
Review: Kristine, Emily

The Math Book: one discovery per page. Good if you like quick little synopsis of many topics. Different big discoveries. Learned a lot of little things, but so rudimentary in some places. There were some over your head, too. I would recommend it. Gives sources to dig deeper. Easy to make connections. Biased towards white Christian males.
Pro reviews: Kenton, Erin. Con review: Brittney
Journey through Genius: history, picks important results and proves them. No non-western mathematics. Tries to justify why no islamic mathematicians but comes across as a cop out. The Greeks asked why, but the Egyptians were satisfied with just working. Did give a personal view of the mathematicians. Recommended to people who want to get to know the mathematicians well.
Review: Biz looks at it from a multicultural perspective.

Accessible Mathematics: 10 instructional shifts. Works with field experience, works with math ed classes, what happens when you don't use these. Multiple representations, number sense. Good to examples and non-examples. Recommended to anyone going in to teaching or to teachers who need to change.
Review: Danielle, Becky, Keegan

Concepts of Modern Mathematics: overview of the math classes you have to take here. Like 310, statistics, history on those areas. People who have made significant work in that area. Some new to us, like topology. Pretty dry and boring. First chapter was the peak, then funniness ran out. Long lines of equations. Not a bad book for someone in 210, to know what's coming, but then it would be hard to understand. Examples are pretty simple - maybe even dumbed down. Pretty dull read. Good at explaining ideas like 1 to 1 and onto. Large scale review.
Review: Bryce. Killer line: "Mr. Stewart slowly became less of my friend who I wanted to hang with and more of a dreaded professor whose class you have to sit through every week."

Godel Escher Bach. It's about cognitive science, psychology, computer science, math. The Godel part is the most on math. You think because you are, but you have to be to think. Need a lot of time to dig in. Hurts to read, in a good way. Challenges the way you think. Connections with taoism and Buddhism. Isomorphisms and symbols… uses all these metaphors. Kind of like A Brief History of Time by Hawking or The Elegant Universe by Brian Green.
The Joy of X. Goes from things people have been told is true to why they're true. Negative times a negative, infinity… goes further at the end.
Short review but long notes: Jennifer
Sensible Mathematics, sister to Accessible Mathematics. Written more to administrators than to math teachers. Why it's good to have students explore more. Convinces teachers and parents to go with modern views of learning and teaching mathematics.
Review: Kerry
Love and Math. Hard to understand because it's so into physics. His life story is interesting, discrimination against Jews in Russia as a backdrop.
Kate's review says that you should like physics and math to pick up this book.
The Mathematician's Lament. Talked about how math is an art. It's about discovery, and we need a big do over in education. We're just handed formulas, not told where they're from or who made them. Can't teach teaching. Recommend to any future teacher.We take away the art of math.
Powerful review from Sara.
e: the Story of a Number. I didn't know where e came from. That's why… the math amazes me more. Everything I learn unites math more. This book did that and combined it with physics, through the number e. Pascal's triangle, derivative of e^x is itself. My optics class is about that. The challenging thing the author had to face. Pi could fit in a few pages, but e, there's no place where it came from. Napier and his tables, and how logarithms require e; when you extend to continuous cases… Book does a good job of balancing history, different contributions. His jumps are really strange and don't make sense until you finish reading. Balances history with math, saves all the proofs for the appendix. Bernoulli's conversation with Bach about the space between notes, a logarithmic increase... that was amazing.
Review: Duncan
There wasn't a whole lot of discussion in the whole class setting, but the individual discussions among students who read the same books were deep and intense. Even the group of people who all had read unique (in our class) books.

What do you think of their reactions? Any disagreements? Is there a new book in which you're interested?

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