Number, Space, and the Structures of Mathematics
This page provides access to a review copy of the textbook Number, Space, and the Structures of Mathematics by Scott Taylor. Please don’t distribute this text or use it in the classroom without written permission. The book is still in draft form – comments are welcome!
This book is intended for mathematics courses that transition students from beginning calculus to upper-level mathematics courses including algebra, analysis, geometry, topology, and graph theory. Much of the basic content is traditional, though particular attention is paid to motivating the material and making connections to the arts and sciences. For an overview of the purpose of the book and what makes it different from other texts, please read the Preface and take a look at the Table of Contents. An instructor’s manual is available if you email me. The book has been extensively classroom tested at Colby College, Bates College and California State University at Long Beach.
Please send comments and corrections to email@example.com . I’d love to hear from you.
You can download the entire book or individual chapters by following the links below. Downloading the entire book has the advantage that hyper-links between chapters will work.
(Note: The book was most recently revised on 8/17/19.)
- Entire book (approx. 38.1 MB)
- Front Matter: Preface/Introduction
- Chapter 1: Sets
- Chapter 2: Sets with Structure
- Chapter 3: Logic
- Chapter 4: Proof Techniques I
- Chapter 5: Building Sets
- Chapter 6: Set Theory Axiomatics
- Chapter 7: Partitions and Equivalence Relations
- Chapter 8: Functions
- Chapter 9: Proof Techniques II: Induction
- Chapter 10: The sizes of sets
- Chapter 11: Sequences: From numbers to spaces
- Chapter 12: New Number Systems, and
- Chapter 13: From Groups to Graphs (currently not available)
- Backmatter: List of Axioms/Proof Techniques/Typography/Index
About the author: Scott Taylor is an Associate Professor of Mathematics at Colby College. He is the author of research articles on knot theory and low-dimensional topology, as well as expository articles on the relationship between mathematics and art. He lives in Waterville, Maine with his wife Stephanie Taylor and two sons.