I was a voracious reader as a kid and came across this book when I was 12, and the prologue sounded particularly amusing to me:
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"Considering how many fools can calculate, it is surprising that it should be thought either a difficult or a tedious task for any other fool to learn how to master the same tricks.
Some calculus-tricks are quite easy. Some are enormously difficult. The fools who write the textbooks of advanced mathematics — and they are mostly clever fools — seldom take the trouble to show you how easy the easy calculations are. On the contrary, they seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way.
Being myself a remarkably stupid fellow, I have had to unteach myself the difficulties, and now beg to present to my fellow fools the parts that are not hard. Master these thoroughly, and the rest will follow. What one fool can do, another can."
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It made me believe I could really learn calculus by myself at age 12. After reading the first few chapters, nope. Turns out calculus is built on a foundation of algebra and geometry which I did not have until I was 16. Once I did have the foundation though, calculus became easy and mostly mechanical. But to a 12 year old, this book overpromised and underdelivered.
I also found the exposition a little wordy and tedious, like it was written to explain calculus to an English major. It's the sort of book that one appreciates in retrospect after knowing the subject, but not while learning it. I discovered the most effective way for learning math is actually not by reading but to mechanically work through problems to cultivate intuitions and to develop a pattern matching schema. In doing so, one gains confidence that one can actually solve problems. Once this confidence is achieved, going back and delving into the underlying principles becomes so much more contextualized and rewarding.
Learning math by reading books like this is like learning to ride a bike by reading about it. You try to understand all the principles, but when you need to deploy them, you find yourself unable to execute. Much better to do it the other way around.
EDIT: but I want to soften that by saying that I appreciate not everyone learns this way. It's just I've seen too many struggle with math even though they've read the textbook countless times... when a simple change in stategy would yield much better results.
--
"Considering how many fools can calculate, it is surprising that it should be thought either a difficult or a tedious task for any other fool to learn how to master the same tricks.
Some calculus-tricks are quite easy. Some are enormously difficult. The fools who write the textbooks of advanced mathematics — and they are mostly clever fools — seldom take the trouble to show you how easy the easy calculations are. On the contrary, they seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way.
Being myself a remarkably stupid fellow, I have had to unteach myself the difficulties, and now beg to present to my fellow fools the parts that are not hard. Master these thoroughly, and the rest will follow. What one fool can do, another can."
--
It made me believe I could really learn calculus by myself at age 12. After reading the first few chapters, nope. Turns out calculus is built on a foundation of algebra and geometry which I did not have until I was 16. Once I did have the foundation though, calculus became easy and mostly mechanical. But to a 12 year old, this book overpromised and underdelivered.
I also found the exposition a little wordy and tedious, like it was written to explain calculus to an English major. It's the sort of book that one appreciates in retrospect after knowing the subject, but not while learning it. I discovered the most effective way for learning math is actually not by reading but to mechanically work through problems to cultivate intuitions and to develop a pattern matching schema. In doing so, one gains confidence that one can actually solve problems. Once this confidence is achieved, going back and delving into the underlying principles becomes so much more contextualized and rewarding.
Learning math by reading books like this is like learning to ride a bike by reading about it. You try to understand all the principles, but when you need to deploy them, you find yourself unable to execute. Much better to do it the other way around.
EDIT: but I want to soften that by saying that I appreciate not everyone learns this way. It's just I've seen too many struggle with math even though they've read the textbook countless times... when a simple change in stategy would yield much better results.