A Note to Students

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Preface A Note to Students

This work was compiled with some strong opinions.

The first is that, as with a sport, instrument, or nearly any other skill, you can’t learn mathematics without doing mathematics. Thus, there are few worked-out examples in this book. We would rather spend a long time in productive struggle to understand an idea deeply than be spoon-fed solutions.

The second is that most people’s ideas of what counts as a mathematical question are far too narrow. Mathematics is not merely geometry, algebra, and calculus (maybe with a dash of statistics for good measure). Mathematics is a way of thinking; it’s about abstraction, deductive reasoning, and problem-solving. This way of thinking can be applied in surprising places, and can lead to delight and wonder at the world around us. We will explore some of these questions this semester.

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