Rowlett J. Blast Into Math! A Fun and Rigorous Introduction to Pure Mathematics

JuRo, BoBoCoAE, 2013. — 215 p. — ISBN: 8740303308, 9788740303308.This book is suitable for both students and a general audience interested in learning what pure mathematics is all about. Pure mathematics is presented in a friendly, accessible, and nonetheless rigorous style. Definitions, theorems, and proofs are accompanied by creative analogies and illustrations to convey the meaning and intuition behind the abstract math.
You don’t need much background for the first few chapters, but the material builds upon itself, and if you don’t do the exercises, eventually you’ll have trouble understanding.
If you read this book and do all the exercises, you will not only learn how to prove theorems, you’ll also experience what mathematics research is like: exciting, challenging, and fun!To the reader.
Pure mathematics: the proof of the pudding is in the eating.
Sets of numbers: mathematical playgrounds.
The Euclidean algorithm: a computational recipe.
Prime numbers: indestructible building blocks.
Mathematical perspectives: all your base are belong to us.
Analytic number theory: ants, ghosts and giants.
Afterword.