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An infinite descent into pure mathematics

I have written an introductory pure mathematics textbook, entitled An infinite descent into pure mathematics. It is currently in the form of lecture notes, which are in their fifth iteration. A table of contents can be found below. (Please be aware that the book is still a work in progress!)

Download and licence information

An infinite descent to pure mathematics is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International Licence. This means that you are welcome to use, download and share the textbook, provided that credit is attributed to the author (Clive Newstead), that it is released under the same licence, and that it is not for commercial use.

Creative Commons Licence

The textbook can be downloaded for free here.


This textbook was born out of lecture notes I wrote for an introductory pure mathematics class at Carnegie Mellon University in summer 2015. I wanted to provide my students with a resource that emphasised not only the technical aspects of mathematics, but also the human aspects, particularly communication and inquiry—I was unable to find a resource that emphasised these aspects and also covered enough ground, so I decided to write my own. Particularly:


To date, this book has been used to teach seven courses over five semesters Carnegie Mellon University:

Table of contents

The following table of contents is subject to change.

* Close to completion
** Not yet written