Tuesday, November 21, 2017

Review of Barron's AP Calculus

Barron's AP Calculus, David Bock, Dennis Donovan, Shirley Hockett, 2015. Glossy's rating: 6/10.

I learned calculus in school in the USSR, and then again in America, where I got a 4 on the AP Calculus BC exam in 1993. But like most people I forgot most of it as an adult.

A guy who doesn't know all of the material covered here shouldn't call himself a nerd. Plus math is fun. So a few months ago I decided to read this book, doing every exercise at the end of every chapter, 599 of them in all.

I quickly fell in with my old habits. When the argument is unambiguous I write sin x simply as sin. To find the sine or cosine of 0, π/2, π, 3π/2, etc. I draw a right triangle inside a little circle, then think. But I've always remembered the sines and cosines of 30, 45 and 60 degrees by heart.

Like many multilingual people I silently "pronounce" numbers in my first language when reading. "In tysyacha chetyresta devyanosto vtorom Columbus sailed the ocean blue". I count, subtract, multiply, etc. in Russian too - I wouldn't be as sure of the result otherwise.

I "pronounce" sin, cos, tan, etc. in the "Russian" (really Latin) way as SEEnoos, CAWseenoos, TUNgens (with the g of "get"). And of course + is ploos with the soft Russian l and - is MEEnoos. But 25 years in America made me think of x and y in the English way instead of the "Russian" eeks and EEgreck.

As I went through this volume I made dozens of electronic flashcards in Anki, mostly using Latex. I hope this will allow me to retain the material better than I did last time.

It was a bother to look up the answers in a different part of the book, shielding future answers with fingers so that I wouldn't see them accidentally. In a perfect electronic textbook there'd be a button next to each exercise which you'd tap to see the answer. You'd also instantly see the percentage of questions you got right so far and the percentage of readers who answered that particular question correctly.

I'm the kind of person who, as soon as he puts on a pair of rollerblades for the first time, instantly wants to read about the equipment, training and habits of rollerblading champions. So it was interesting for me to learn that professional mathematicians never read linearly through any math books. And that in spite of all the math applications out there they still do a lot of their work on paper.

When I play piano every day, I get faster and more accurate at multi-key combinations on the office PC, "chords" like Alt-F4 or Ctrl-X. And I do more of them, avoiding the mouse. Did solving the exercises in this book make me more likely to consciously think through real-life situations? I don't think so, but it did make me acutely aware of how little I really think, consciously think in daily life. It's such an unusual activity after college.

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