Copyright

Jan E. Grabowski

Published On

2025-09-22

Page Range

pp. 1–70

Language

  • English

Print Length

70 pages

1. Algebra

  • Jan E. Grabowski (author)
Chapter of: Representation Theory: A Categorical Approach(pp. 1–70)
The aim of this first chapter is to gather the definitions and some fundamental properties of the main protagonists in our story: groups, rings, fields, vector spaces, algebras and quivers. We start with those you are more likely to be familiar with and you should move through these at the pace that suits you.

Contributors

Jan E. Grabowski

(author)
Professor of Algebra at Lancaster University
https://www.maths.lancs.ac.uk/~grabowsj/

Jan Grabowski is an experienced researcher and educator in mathematics, with over 20 years’ experience of both, and currently holds the position of Professor of Algebra at Lancaster University. Jan has a strong research track record of publications in algebra and related topics, both as a single author and collaboratively. He has taught courses at Oxford and Lancaster across a range of levels and has been teaching abstract algebra for the majority of this time, including covering aspects of the material in the book in courses at both institutions. Jan has had recognition for his teaching, including a teaching prize at Oxford, obtaining a Postgraduate Certificate in Academic Practice and being awarded Senior Fellowship of the Higher Education Academy. He has championed innovation in teaching by presenting a mature exposition of ‘how mathematicians really think about these things’ as compared with other approaches that often defer more advanced ideas or techniques, rather than encouraging students to engage with challenging ideas early and repeatedly.