Name: Abstract algebra
ISBN: 9780471433347

Abstract algebra

This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics. The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises to aid the reader's understanding. In this way, readers gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings.

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nyrikkiAug 2024

Pi is transcendental but computable.

For an introduction to real real analysis is an old book typically called the 'Baby Rudin' Principles of Mathematical Analysis by Walter Rudin.

It is tiny and expensive, as most college math text books are once you get past a certain level. No idea if there is something better now, it is from the 1950's and there are used copies in most used book shops for cheap (or there was). It has no definition of 'equals' but does have a concept of equivalent relations.

Dummit and Foote's Abstract Algebra book is a great reference, especially with the problem with AI pollution. Coming from a General Relativity background, it still took me two years to work through on my own.

I don't know any suggestions on a more modern approach of starting with type or category theory.

I am not really interested in constructivist math, it is a problem to get around for me, so maybe someone who is can chime in on a better path.

While not rigorous, this paper does a good job at explaining just how muddy the concept of 'equality' is.

https://arxiv.org/abs/2405.10387

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GalenErsoMar 2023

Topics:

- Single variable calculus

- Multivariable calculus, vector calculus

- Linear algebra

- Tensor calculus

- Real analysis (see Walther Rudin)

- Complex analysis

- Ordinary differential equations

- Partial differential equations

- Abstract algebra

- Differential geometry

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savrynJan 2023

Abstract Algebra: A Student-Friendly Approach by Dos Reis

Paperback layout feels like a workbook, not overwhelming-- beginner friendly

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zomglingsAug 2021

I really like Abstract Algebra by Dummit and Foote.

Get an old, used, international edition.

Do exercises!

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chongliJan 2020

The best resource I know of is the textbook I bought for the course I took on group theory and ring theory [1]. It’s pretty expensive and the exercises are very challenging but if you’re a self-motivated student, you can learn a TON of abstract algebra from this one book. You may want to review some linear algebra before you dive in, if you haven’t done so in a while. You can find solutions to many of the exercises online though I can’t vouch for their accuracy.

[1] https://www.amazon.com/Abstract-Algebra-3rd-David-Dummit/dp/...

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impendiaDec 2019

If you want to understand Peluse's paper, I think the most directly relevant background reading would be Tao and Vu's Additive Combinatorics.

Dummit and Foote's Abstract Algebra is an excellent book -- even if not very directly relevant to additive combinatorics. Analysis background would be useful, such as to be found in Stein and Shakarchi's series. Some introductory combinatorics would also be good (e.g. Stanley's Enumerative Combinatorics, or Van Lint and Wilson).

Finally, analytic number theory would also be good to learn. For example, you might read Davenport's Multiplicative Number Theory. (Especially if you want to see integrals come into the picture.)

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