Math 8202: Graduate abstract algebra (2nd semester)

Spring 2014

Prerequisites: Math 8201, or an equivalent discussed with the instructor.
Instructor: Victor Reiner (You can call me "Vic")
Office: Vincent Hall 256,
Telephone (with voice mail): 625-6682,
Classes: Mon-Wed-Fri 9:05-9:55am, Vincent Hall 207. 
Office hours: Mon 2:30pm
Tues 9:05am.
Thurs 11:15am.
Required text: Abstract algebra, 3rd edition, by D.S. Dummit and R.M. Foote, Wiley, 2004.
Course content: This is the 2nd semester of the Math 8201-2 one-year graduate core sequence in abstract algebra.
Math 8201 dealt with groups, vector spaces, linear and multilinear algebra including spectral theory, and started discussing rings, covering roughly these parts of the Dummit and Foote text:
Chapters 1-6
Chapter 11
Chapter 7, Sections 7.1 and 7.2

Math 8202 continues discussing more rings, modules, and field theory, covering these parts of the text:
Chapters 7,8,9 on rings (possibly adding in Groebner bases)
Chapters 10,12 on modules
Chapters 13,14 on fields
and if there's some extra time, dip into Chapters 17 and/or 18
Other useful texts: Abstract Algebra: The basic graduate year, by R. Ash, a text in PDF
Abstract Algebra online, by J. Beachy, a set of HTML pages
Advanced Modern Algebra by J. Rotman, Amer. Math. Soc. 2010
Algebra, by S. Lang, Addison-Wesley, 1993.
Algebra, by T. W. Hungerford, Springer-Verlag, 2003
Algebra: A graduate course, by M. Isaacs, Amer. Math. Society, 2009.
Algebra, by M. Artin, Prentice Hall, 1991 (a somewhat lower level book)
Field theory resources: Field and Galois Theory, by P. Morandi, Springer Grad. Texts in Math. 167.
Field extensions and Galois theory, by J.R. Bastida, Cambridge Univ. Press, 1984.
Written prelim preparation: One role of this class is to prepare the students for the Math PhD program's Algebra Written Prelim Exams. Although we will go a long way toward this goal, those who intend to take the prelim exam should not miss Paul Garrett's Abstract Algebra page, containing links to his book for the class, solutions to many of the typical prelim exam problems, etc. Also, here were some practice problems from old prelims containing mostly material from the first semester course, that is, group theory and linear algebra.
Homework: There will be 6 homework assignments, mainly exercises from the book, due every two weeks on Wednesday at the beginning of class; see the table below for the tentative list of assignments. These homeworks will count for 35% of the course grade. Late homework will not be accepted. I encourage collaboration on the homework, as long as each person understands the solutions, writes them up in their own words, and indicates on the homework page with whom they have collaborated.
Exams:  There will be two take-home midquarter exams to be handed out on dates to be announced later, each contributing 20% to the grade. There will be a take-home final exam worth 25% of the grade given just before exam period. In contrast to the homework, there is to be no collaboration allowed with other humans allowed on any of the take-home midquarter or final exams. 
Homework and exams
Assignment Due date Problems
Homework 1 Wed Feb. 5 7.3 # 2,4,13,17,26,28,29,30,31
7.4 # 8,11,15,19,26,30,31,32,37,38,39
7.5 # 3,5
7.6 # 1,2,3,4,5
Homework 2 Wed Feb. 19 8.1 # 2(a),3,4,5(a),9,10,12
8.2 # 1,2,3,5
8.3 # 5,6,7,8(a)
9.1 # 5,7,9,13,14
9.2 # 1,2,3,4,7,8
Midterm exam 1 Wed Feb. 26 Here is Midterm Exam 1
Homework 3 Wed Mar. 12 10.1 # 8,11,12,18,19,20
10.2 # 5,8,13
10.3 # 2,4,5,9,10,11
Homework 4 Wed Apr. 2 12.1 # 1,2,3,4,6,13
12.2 # 3,4,11,17,18
12.3 # 5,16,17,22,24,26,32
Midterm exam 2 Wed Apr. 9 Here is Midterm Exam 2
Dept. algebra prelim
written exam
Mon. Apr. 14 Dept. prelims page
Homework 5 Wed Apr. 23 13.1 # 1,5
13.2 # 3,7,8,12,14,16,18
13.4 # 1,2,3
13.5 # 7,8,9
13.6 # 3,4,5,6,9
Homework 6 Wed May 7 14.1 # 4,7
14.2 # 3,4,5,11,13,17,18,29,31
14.3 # 3,5,10
14.6 # 2
Final exam Wed May 14
during finals week
Here is the Final Exam.
Back to Reiner's Homepage.