Preface

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Preface Preface

This is a text about proofs and problem solving in pure mathematics. The text will evolve over the course of the semester. What we do here is not dissimilar to what is in Liebeck's Concise Introduction to Pure Mathematics, but our focus is a little different. Here, we will be focused on a very precise development of the concepts at the very foundations of mathematics. The notion that will guide us is that of number. What kinds of numbers are there? How do they behave? What purposes do they serve? What kinds of techniques help us to understand them? What branches of mathematics study them? These are questions that we will start to answer in this book.

At the same time, we will be interested in what makes a precise, correct, and legible proof, and we will talk about the craft of proof-writing — our first impressions, development of different possible strategies, clarification of details, notation, and understandability to your target audience.