ΒΙΒΛΙΟ: An Infinite Descent into Pure Mathematics (pdf)

About the book 

A student in a typical calculus class will learn the chain rule and then use it to solve some prescribed ‘chain rule problems’ such as computing the derivative of $sin(1+x^2)$ with respect to x, or perhaps solving a word problem involving related rates of change. 

The expectation is that the student correctly apply the chain rule to derive the correct answer, and show enough work to be believed. In this sense, the student is a consumer of mathematics. They are given the chain rule as a tool to be accepted without question, and then use the tool to solve a narrow range of problems.

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