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 Spring 2024, MWF 11:15-12:05, Vincent 207, office hours immediately after class, 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]


    Exam and homework-example schedule, spring 2024:

    Sunday Monday Tuesday Wednesday Thursday Friday Saturday
    Jan 17 Jan 19
    Jan 22 Jan 24 Jan 25
    Jan 29 Jan 31 Feb 02
    Feb 05 hmwk 05 Feb 07 Feb 09 exam 05
    Feb 12 Feb 14 Feb 16
    Feb 19 Feb 21 Feb 23
    Feb 26 hmwk 06 Feb 28 Mar 01 exam 06
    Mar 04Spring Mar 06Break Mar 08
    Mar 11 Mar 13 Mar 15
    Mar 18 Mar 20 Mar 22
    Mar 25 Mar 27 Mar 31
    Apr 01 hmwk 07 Apr 03 Apr 05 exam 07
    Apr 08 Apr 10 Apr 12
    Apr 15 Apr 17 Apr 19
    Apr 22 hmwk 08 Apr 24 Apr 26 exam 08
    Apr 29 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."