Page 8 - 'Blast_Into_Math

Blast into Math! Preface

Preface

The purpose of this book is to offer readers a fun mathematical learning experience without sacrificing
or oversimplifying the mathematics. Pure, rigorous mathematics is presented with concise definitions,
theorems and proofs; accompanying the mathematics are lively descriptions, colorful exposition, and
analogies. My goal is to share with readers through an active reading experience how mathematicians
perceive and experience mathematics. It is vibrant, exciting, and dynamic, like the analogies used in

this book to describe it.

Readers will notice that each chapter has a theme color. According to psychological research [W-S-G],
people remember things better when they are in color. The theme color is used for emphasis within the
chapter and is also an associative mnemonic for each chapter’s topic. The first chapter, “To the Reader,”
explains how the reader should actively read the book. Mathematics is experiential; one must do math to
understand it. The second chapter introduces the fundamental topics in logic upon which all mathematical
proofs are based, teaching readers what constitutes a mathematical proof and guiding them to begin

writing their own proofs. The next three chapters cover set theory and basic topics in number theory.
Chapter six teaches readers to be creative by changing their mathematical perspective, by writing numbers
in different bases. The last chapter introduces analysis.

Traditional textbooks tend to focus on a specific area of mathematics without explaining how
mathematicians do research. In this book a parallel is made between the reader’s experience and the
experience of research mathematicians. The basic principles and process of mathematics research are
analogous to the reader’s process of working through the book. When the reader is asked to complete
part of the proof of a theorem as an exercise this is compared to collaboration amongst mathematicians.
This book not only presents fundamental topics in pure mathematics but also shares with readers the

basic principles of pure mathematics research.

The intended audience includes undergraduate students in “Transition to Higher Mathematics” courses
and advanced high school students. The pre-requisite knowledge has most likely been met by a standard
high-school education, and so this book could also be used in community college and continuing
education or read by a general audience. It offers readers active participation, in the spirit of Sudoku, but
unlike Sudoku it delves deeper into the world of mathematics research. By the end of the book readers
will have worked on problems which no mathematician has ever solved!

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