Topology of Numbers

by Allen Hatcher

The plan is for this to be an introductory textbook on elementary number theory from a geometric point of view, as opposed to the usual strictly algebraic approach. The title "Topology of Numbers" is intended to convey this idea of a more geometric slant, where we are using the word "Topology" in the general sense of "geometrical arrangement" rather than its usual mathematical meaning of a set with certain specified subsets called open sets. A fair portion of the book is devoted to studying Conway's topographs associated to quadratic forms in two variables, so perhaps the title could have been "Topography of Numbers" instead.

The current version of the book is still a preliminary draft, so it is incomplete and lacking in polish at certain points.

You can download a pdf file of what currently exists of the book, about 200 pages.

https://pi.math.cornell.edu/~hatcher/...

This version was posted in June 2018. The main changes from earlier versions occur in Chapters 5-7 which have been revised and expanded. Chapter 7 is still lacking about 20 pages which I plan to write in the next couple months (Summer 2018)..

Genres: Mathematics

200 pages, ebook

Published June 1, 2018

About the author

Allen Hatcher is an American research mathematician and author currently at Cornell University. He specializes in Topology.

Reviews

[Chris · Rating 5 out of 5]

like A.T. and his vector bundles book, this is a gem. It could be appreciated by a wider audience who want a slim introduction to the beauty of numbers. (genuine numbers, not knots or other mathematical objects)