Books to read or review

Introduction

This is a collection of books that I wish to read at some point or have already read.

Books to read

A Gentle Introduction to the Art of Mathematics

GIAM (a Gentle Introduction to the Art of Mathematics) is a free, open-source textbook -- the current version is 3.1. GIAM covers several topics in the foundations of mathematics (logic, sets, relations, functions and cardinality) and introduces the reader to many techniques of mathematical proof (direct, indirect, contradiction, contrapositive, mathematical induction, combinatorial proofs and magic). There are amusing quotations at the start of each chapter.
Download (GIAM.pdf) version 3.1 2013 Homepage Source code (GitHub) Version 3.2 page 2023

BOOK OF PROOF

This book is an introduction to the standard methods of proving mathematical theorems. It has been approved by the American Institute of Mathematics' Open Textbook Initiative

Author:Richard Hammack

Homepage Download (Main.pdf)

How To Prove It: A Structured Approach, Second Edition

Author:Daniel J. Velleman (Department of Mathematics and Computer Science Amherst College)

Unofficial download

Proofs: A Long-Form Mathematics Textbook

Author:Jay Cummings

Homepage