Abstract Algebra

[ambient page updated Sat, 08 Apr '23, 05:09 PM] ... [ home ]

( 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 -->
    [Old Course Notes] ... (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]

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