Math 8510 (Abstract Algebra I), Fall 2023

Math 8510 (Abstract Algebra), Fall 2023


"Mathematics, rightly viewed, possesses not only truth, but supreme beauty." --Bertrand Russell

"Symmetry, as wide or narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty, and perfection." --Hermann Weyl

"If you are someone who prefers large vistas and powerful theories, then it is essential to be able to test general results by applying them to simple examples....where one can do concrete calculations, sometimes with elaborate formulas, that help to make the general theory understandable. They keep your feet on the ground...A good example is a thing of beauty. It shines and convinces. It gives insight and understaning. It provides the bedrock of belief." --Sir Michael Atiyah, in Advice to a young mathematician.

About the class

This will be a standard first-semester graduate course in abstract algebra, but there will be an extra effort to encorporate visuals to go along with the concepts. We will cover groups, homomorphisms, actions, extensions, universal properties, and rings. In the end, you will leave with a new appreciation of the beauty (and difficulty) of algebra, in a way that will develop your learning skills, which will be applicable to your other graduate courses and research.

Class essentials

Resources

Lecture notes

Homework

Homework should be written up carefully and concisely, and needs to be typeset in LaTeX (except for HW 1). Please write in complete sentences. Part of your grade will be based on the presentation and clarity of your answers. Enough of the problem statements should be copied down so that your homework solutions are self-contained and the textbook is not needed to read, understand, and grade them. Along with most assignments, I will post "supplemental material" consisting of blank images that you are free to use, rather than redraw by hand or remake with TikZ.

Exams

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