This is an archived (June 2020) version of my Northwestern University academic web page. The URL will redirect to my Carnegie Mellon University web page when it has been created.

Clive Newstead · Home· Teaching· Book· Talks

Hello! I am a Postdoctoral Lecturer in the Department of Mathematics at Northwestern University in Evanston. Starting in Fall 2020, I will be an Assistant Teaching Professor at Carnegie Mellon University in Pittsburgh.

My contact info is as follows:

  • Email. cnewstead at northwestern dot edu
  • Office. Locy Hall 205
  • Phone. (847) 467-4078

This quarter (Spring 2020), I am (remotely) teaching:

  • Math 290-3 Linear Algebra and Multivariable Calculus (part 3 of 3)
  • Math 330-3 Abstract Algebra (part 3 of 3)
  • Math 300-CN Foundations of Higher Mathematics (evening course for SPS)

My mathematical background is in category theory, which I like to think of as the mathematics of mathematics: whereas mathematics looks at the real world, identifies patterns and structures and then studies those patterns and structures, category theory does the same thing for mathematics, relating results in one area of the subject to those in seemingly unrelated areas. I am also interested in pedagogy, and particularly in identifying the teaching strategies and course design principles that are most effective for promoting student learning in mathematics-based subjects.

I grew up in Yorkshire, a region in the north of England. I did my BA and MMath degrees at the University of Cambridge (Robinson College) from 2009 to 2013, and my PhD at Carnegie Mellon University in Pittsburgh from 2013 to 2018. My thesis was entitled Algebraic models of dependent type theory, advised by Steve Awodey.

My CV is available here (last updated some time in 2019).


The following calendar contains my scheduled meetings, classes, office hours, and other academic engagements. Please contact me if you would like to schedule a meeting.


I have written an introductory pure mathematics textbook, An Infinite Descent into Pure Mathematics.

My reason for writing the book is that I wanted to provide my students with a freely accessible 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 topics, so I decided to write my own. Particularly:

  • LaTeX support. The textbook contains a tutorial for typesetting mathematics using LaTeX, with code for all mathematical symbols provided when they are defined.
  • Proof-writing skills. There is an appendix that provides suggestions for writing mathematical proofs, from as low a level as choosing which words and symbols to use in a clause within a sentence in a proof, to structuring a substantial mathematical document.
  • Exercises. Though many proofs and examples are provided in the textbook, a large quantity of material is delivered as exercises for the reader. This is to promote inquiry-based learning, to encourage collaborative work, and to increase the book's feasibility as an instructional tool.
  • Completeness. I have tried to make sure that the material in the textbook is complete and coherent, with all details are included except when the details obfuscate the intuition, in which case they are still included, but are relegated to an appendix.

More information and a download link can be found here.

The book will eventually be published with ISBN 978-1-950215-00-3.