About me
Hello! I'm a fifth-year PhD candidate in the Department of Mathematical Sciences at Carnegie Mellon University in Pittsburgh, advised by Steve Awodey. Starting in September 2018, I will be a lecturer in the Department of Mathematics at Northwestern University in Evanston.
My research employs the tools of category theory to investigate algebraic and topological structures arising in mathematical logic. I also really enjoy teaching, and I work as a Senior Graduate Teaching Fellow at the Eberly Center, consulting with other graduate students and postdocs on their teaching.
I grew up in Yorkshire, a region in the north of England, and I did my BA and MMath degrees at Cambridge (Robinson College) from 2009 to 2013.
My CV is available here.
Teaching award presentation, April 2016. Photo: Carnegie Mellon.
Teaching
I have instructed three courses and served as a TA for five. I love all aspects of teaching mathematics, and it is a long term goal of mine to make mathematics a more accessible subject.
- Teaching portfolio. I have written a comprehensive teaching portfolio containing teaching statements, a list of my teaching experience, my teaching evaluation scores, and a selection of course materials that I have generated. It is available on request.
- Professional development. In December 2015 I completed the Future Faculty Program, and since January 2015 I have worked as a Graduate Teaching Fellow for the Eberly Center for Teaching Excellence and Educational Innovation. In this role, I provide consultations to graduate students and postdocs on their teaching, and I help facilitate workshops and seminars on teaching and learning.
- Awards. In April 2016, I received the CMU Graduate Student Teaching Award and the MCS Hugh D. Young teaching award. A press release from the Mellon College of Science is located here.
More information on individual courses I have taught can be found here.
Textbook
I have written an introductory pure mathematics textbook, entitled An infinite descent into pure mathematics. It is being used this semester by Prof Mary Radcliffe to teach 21-127 Concepts of Mathematics at CMU and can be downloaded here.
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 ground, 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.
- Writing guide. The finalised version of the textbook will contain tutorials on writing mathematics, 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.
AMS HoTT MRC group, Snowbird, UT, June 2017. Photo: Chris Kapulkin.
Pictured: Simon Cho, Cory Knapp, me, Liang Ze Wong
Research
My research is in the interactions between category theory and mathematical logic, and particularly in the categorical semantics of dependent type theory and related areas. Currently, I am working with Steve Awodey to investigate the algebraic structures associated with polynomials in locally cartesian closed categories, and using natural models to study their relationship with dependent types.
Additionally, this summer I participated in the Categories of Models of Type Theory group at the AMS Mathematical Research Community workshop on Homotopy Type Theory in Snowbird, UT. My group consisted of Simon Cho, Cory Knapp, Liang Ze Wong and myself; we were supervised by Chris Kapulkin and Emily Riehl. We worked on unifying the many approaches to the semantics of type theory by proving equivalences between various ∞-categories of models. This work was presented at the HoTT/UF workshop in Oxford in September 2017 (abstract) and will be presented at the Joint Mathematics Meeting in San Diego in January 2018.
A list of talks I have given at seminars and conferences can be found here.
Contact info
The best way to get hold of me is to send an email to cnewstead-at-cmu-dot-edu.