Abstract Algebra

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( See also: [ vignettes ] ... [ functional analysis ] ... [ intro to modular forms ] ... [ representation theory ] ... [ Lie theory, symmetric spaces ] ... [ buildings notes ] ... [ number theory ] ... [ algebra ] ... [ complex analysis ] ... [ real analysis ] ... [ homological algebra ] )

... [ garrett@math.umn.edu ]


The main prerequisite for 8201 is good understanding of undergrad algebra and linear algebra, with substantial experience writing proofs .

Students coming into this course should have a range of experience in proof writing, not only in a previous course in abstract algebra, but also in analysis, rigorous linear algebra, and some point-set topology. All these play significant roles, both directly, and in terms of mathematical maturity and vocabulary.

Coherent writing is essential. Contrary to some myths, the symbols do not speak for themselves.

Prerequisite for 8202: 8201 or equivalent.

Grades fall and spring will be determined by four in-class midterms , scheduled as below. You are not competing against other students in the course, and I will not post grade distributions. Rather, the grade regimes are roughly 90-100 = A, 75-90 = B, 65-75 = C, etc., with finer gradations of pluses and minuses. So it is possible that everyone gets a "A", or oppositely. That is, there are concrete goals, determined by what essentially all mathematicians need to know, and would be happy to know.

There will be optional homework/example assignments preparatory to exams, as scheduled below, on which I'll give feedback about mathematical content and writing style. The homeworks will not directly contribute to the course grade, and in principle are optional, but it would probably be unwise not to do them and get feedback. No late homeworks will be accepted. Homework should be typeset, presumably via (La)TeX, and submitted by email. The notes contain discussions/solutions of the homework/examples. If you find useful things in prior years' example discussions, or elsewhere on the internet, or in books, cite . Also, collaboration with other people is fine, and acknowledge . It is ok to learn from other people, I think. :) This course is not a gauntlet to be run. The course is about increasing awareness and exposure to important, useful (also crazy and entertaining) ideas, so that in the future when they show up (seemingly out of the blue?) in your work, you can recognize them and act accordingly.

Text is below, with a few future updates along the way.


  • In 2023-24, MWF 11:15-12:05, Vincent 301, office hours after class MW, email anytime -->
    [ My book/notes on abstract algebra ] ... (updated Sat, 21 Jul '07, 12:39 PM) ... in individual chapters below. Various additions will be made along the way, but these notes are 90% correct as to what we'll cover.

    Miscellaneous notes: Solutions to standard exercises: s01 , s02 , s03 , s04 , s05 , s06 , s07 , s08 , s09 , s10 , s11 , s12 , s13 , s14 , s15 , s15b , s16 , s17 , s18 , s19 , s20 , s21

    Course notes ... individual chapters from notes linked-to above:


    Elementary exercises and notes: [Intro to Abstract Algebra]


    Sunday Monday Tuesday Wednesday Thursday Friday Saturday
    Sept 06 Sept 08
    Sept 11 Sept 13 Sept 15
    Sept 18 Sept 20 Sept 22
    Sept 25 hmwk 01 Sept 27 Sept 29 exam 01
    Oct 02 Oct 04 Oct 06
    Oct 09 Oct 11 Oct 13
    Oct 16 hmwk 02 Oct 18 Oct 20 exam 02
    Oct 23 Oct 25 Oct 27
    Oct 30 Nov 01 Nov 03
    Nov 06 Nov 08 Nov 10
    Nov 13 hmwk 3 Nov 15 Nov 17 exam 03
    Nov 20 Nov 22 Thanksgiving Nov 24
    Nov 27 Nov 29 Dec 01
    Dec 04 hmwk 04 Dec 06 Dec 08 exam 04
    Dec 11 Dec 13 last class

    Unless explicitly noted otherwise, everything here, work by Paul Garrett, is licensed under a Creative Commons Attribution 3.0 Unported License. ... [ garrett@umn.edu ]

    The University of Minnesota explicitly requires that I state that "The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by the University of Minnesota."