What is Calculus About? by W.W. Sawyer.

3/5 rating. 112 pages.

Book #24 of 2022. Read May 8, 2022.

If there were any questions left on whether I’m a complete nerd, those have all been put to bed by my reading this book in my spare time…

“The mathematician has the instincts of the explorer; at all costs, go forward, if things are different, so much the better; that will make it more interesting.”

I absolutely loved this quote! Because it’s true, and behind the drive for new knowledge that is fostered in engineering. And because it just cracked me up having mathematicians call themselves explorers and adventurers.

This book is an inquiry-based introduction to calculus. I think it does a great job of basing all calculus in the exploration of finding speeds. Using this basic idea, Sawyer very plainly goes through how you can use a known position at different times in order to calculate velocities. Between the discussed math, his pointed questions, and the exercises, I think this is a great guide to understanding what calculus can do.

This being said, this is a textbook. I don’t expect anyone to pick this up for some light reading. But, if you are taking a calc class (or any engineering, physics, or related higher-level math class), this could be a really helpful grounding in the topic. So often, students just memorize formulas and don’t actually understand the basis behind them. I think this book could really help fix that.

Quotes:

“Indeed throughout mathematics, this is what formulas should mean to you – not a recipe to be carried out blindly, but to remind you that here is another example of something that you have already studied and understood.”

“It is wise at first to work slowly….There are plenty of students who can write down the wrong answer quickly! Their work has no value at all.”

“The aim of mathematics is to find out the truth for yourself and to know the truth as it really is.”

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