Groups, Fields, and Galois: Part 1 | UCLA Extension

Dr. Michael Miller, a retired researcher at RAND, has been teaching upper level undergraduate/graduate level math courses for fun at UCLA Extension for over 50 years. This fall he’ll be introducing the areas of groups, fields, and Galois theory from abstract algebra to those interested in abstract math: Groups, Fields, and Galois: Part 1. His intention is to do a follow-on class on Galois theory in the Winter which will use this class as a foundation. If you’re in the Los Angeles area his class starts on September 22, 2026 at UCLA on Tuesday nights from 7-10PM. Register here:
His courses are thorough and rigorous, but geared toward lifelong learners and beginners in abstract mathematics to allow people better entry points into higher level mathematics. His classes are interesting and relatively informal, and most students who take one usually stay on for future courses. The vast majority of students in the class (from 16-90+ years old) take his classes for fun and regular exposure to mathematical thought, though there is an option to take it for a grade if you like. There are generally no prerequisites for his classes, and he makes an effort to meet the students at their current level of sophistication. For this particular class, if you’ve got some experience in high school algebra and know some preliminaries about mathematical proofs you’ll be ready to dive in.

There are regular commuters joining from as far out as Irvine, Ventura County and even Riverside. Most in the class are dedicated hobbyist and professional mathematicians, engineers, physicists, and others from all walks of life (I’ve seen actors, directors, doctors, artists, poets, retirees, and even house-husbands in his classes.)

If you’re unsure of what you’re getting into, I recommend visiting on the first class to consider joining us for the Fall quarter. Sadly, this is an in-person course. There isn’t an option to take this remotely or via streaming, and he doesn’t typically record his lectures. I hope to see all the Southern California math fans next month!

Course Description

Group theory is recognized as one of the great unifying mathematical disciplines, with far-reaching applications in virtually all scientific (and many non-scientific) fields. This course, the first of a two-quarter sequence that concludes in Winter 2027 with a course on fields and Galois Theory, is geared toward developing the tools of group theory needed to establish the Abel-Ruffini theorem on the insolvability by radicals of the general polynomial of degree five or greater. Results established along this journey will also be applied toward addressing the three classical ruler and compass construction problems of antiquity: trisecting the angle, duplication of the cube, and squaring the circle, as well as Gauss’ surprising characterization of constructible regular polygons.
September 22 – December 1
Tuesday 7:00PM – 10:00PM PT
REG# 410697
Fee: $450.00

Recommended textbook: TBD

Dr. Miller provides enough background and thorough notes that if you’re taking notes on his lectures, you typically won’t need a textbook.

If you’ve never joined the class before (Dr. Miller has been teaching these for 53 years and some of us have been with him for nearly that long; I’m starting into my 20th year personally), I’ve written up some tips and hints.