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As someone that finds themselves a little deficient with set theory, I would like to ask for an abstract algebra resource that really breaks down set theory and its related proofs. Videos, textbooks, or any other form of informational media would be appreciated.

If it helps, I am preparing to take my first course in Abstract Algebra in January, and this is an undergrad level class.

Alexander Gruber
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Eibhlín K
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    Try Pinter and see: https://math.stackexchange.com/questions/392374/guides-tutorials-to-learn-abstract-algebra?rq=1 – Moo Nov 08 '17 at 16:56
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    There are several similar questions already: https://math.stackexchange.com/questions/tagged/abstract-algebra+book-recommendation?sort=votes&pageSize=50 – Hans Lundmark Nov 08 '17 at 18:24
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    Most introductory algebra books contain a chapter 0 on such things... what else are you looking for that they don't provide? – rschwieb Nov 08 '17 at 19:39
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    I don't think you will find set theory to be the sticking point in abstract algebra. All the set theory you will need will probably be covered in the introductory chapter(s) of your textbook. Covering any more than that may be a waste of your time. More likely, the sticking point will be a lack of familiarity with the basic methods of proof. Your textbook may not be much help with that. To get you started, you might Google: software to teach the basic methods of proof. – Dan Christensen Nov 09 '17 at 04:01

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I haven't read it yet, but there is an Algebra entry in the Very Short Introductions series by Oxford University Press that may help you. In general those are little, quite-cheap books that can be easily read and give a good panoramic view of the subject, while keeping a good measure of insight (some of them are bland, but usually not those science-related). The themes touched in Algebra, a VSI are not exactly those which you will see in an Abstract Algebra class, but hopefully it may serve as a gentle introduction to other texts, by putting you in the right mindset.

Here I append the table of contents:

  • Numbers and algebra
  • The laws of algebra
  • Linear equations and inequalities
  • Quadratic equations
  • The algebra of polynomials
  • Introduction to matrices
  • Matrices and groups
  • Determinants and matrices
  • Algebra and the arithmetic of remainders
  • Vector spaces
  • Further reading
Jose Brox
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My first contact with Abstract Algebra was with a book in Portuguese (my mother tongue) called Introdução à Álgebra by Adison Gonçalves, published by the Brazilian Mathematical Society (SBM). I don't know if you can read in portuguese or if you have access to this kind of book, but anyway this books is very elementary, so I think it could help.

Filburt
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