Professor: Dan Abramovich
Office: Kassar-Gould 118
Telephone: (401) 863 7968
Web site: http://www.math.brown.edu/~abrmovic/MA/s1516/154/index.html
Preliminary Office hours: Wednesday 2:00-3:00; Monday and Friday 10:00-10:50
Canvas: direct link
Text: Abstarct Algebra, by Dummit and Foote, 3rd edition is most up-to-date (I think), but second edition is good if you can lay your hands on a cheaper copy. Excercise numbering may differ.
The book is hefty and could be intimidating - don't get scared. I chose it because (1) it was used in the fall so you might not need a new one and (2) it will serve you well for years to come.
I will supplement the book for the second topic with selections from Serre's Linear representations of finite groups and M. Artin's Algebra, Chapter 9.
Introductory statement. I find that Abstract Algebra is one of those topics in mathematics which have everything that makes us want to do mathematics for its own sake: you set up axioms of a few very simple structures, motivated by simple things like numbers and symmetry. Then you take a look just a little under the surface of these structures, and you discover a beautiful and rich theory. And, of course, the deeper you go, the more beautiful and interesting the theory becomes.
In this course we will cover two topics, working at cross
purposes. Galois theory is a spectacular theory
where the theory of groups informs the theory of fields in a
highly nontrivial way. Representation theory of finite groups
is a spectacular theory where linear algebra and the theory of fields
informs the theory of groups in a
highly nontrivial way.
Homework is given for every class, posted on class web page and canvas. Will be collected regularly. Homework for a given week is collected on the following Friday beginning the second Friday of the semester. No collaborative regular homework accepted (but see below for special assignments), though you are encouraged to discuss homework problems with other students.
Homework must be written out legibly. Write your name on your homework (preferably on every page), and staple the pages together.
Independent and group work will be assigne in a haphazard way. I sometimes assign independent reading; sometimes with required reports which could be individual or small group-work as I choose. There might be asignments which are too daunting for a person to do on ones own and assigned as group projects - some skills in working in a group might be valuable!
It is the student's responsibility to know which rules govern each assignment and to adhere to the university's academic conduct code.
I'll announce the grade composition when the dust settles. There will be a final.
I will not be available most of reading period, but I will arrange for valuable things to happen during reading period, so you should prepare to be in class during reading period.