Math 5285: Honors fundamental structures of algebra

Fall 2007

Prerequisites: Some previous exposure to linear algebra (vectors, matrices, determinants) would help.
One should either have the ability to write and read mathematical proofs, or have the desire and drive to learn how.  
Instructor: Victor Reiner (You can call me "Vic"). 
Office: Vincent Hall 256
Telephone (with voice mail): 625-6682
Classes: Mon-Wed-Fri 10:10-11:00am, Vincent Hall 311. 
Office hours: Mon and Fri at 11:15am, Tues at 3:35pm; also by appointment. 
Course content: This is the first semester of a course in the basic algebra of groups, ring, fields, and vector spaces.
Roughly speaking the Fall and Spring semesters should divide the topics as follows:
Fall-- Vector spaces, linear algebra, group theory and symmetry
Spring-- Rings, modules, and field theory
To give a feeling for the Fall subject matter, group theory can be thought of as the study of symmetry.
Some nice examples of finite groups are the symmetries of regular polyhedra (like the Platonic solids).
You can get a feel for these symmetries by playing with some manipulable regular polyhedra
on the web site of my colleague Joel Roberts.
Required text: Algebra, by Michael Artin, Prentice-Hall, 1991.
The (very) tentative plan for proceeding through Artin's book goes like this:
Fall-- some (but not all) of Chapters 1-7
Spring-- some (but not all) of Chapters 10,11,13,14
Other useful texts
Level Title Author(s), Publ. info Location
Lower A concrete introduction
to higher algebra
Childs, Springer-Verlag 1995 On reserve in math library
Lower Contemporary abstract algebra Gallian, Houghton-Mifflin 1998 On reserve in math library
Same Topics in algebra Herstein, Wiley & Sons 1999 On reserve in math library
Higher Abstract algebra Dummit and Foote, Wiley & Sons 2004 On reserve in math library
There will be 5 homework assignments due usually every other week, but
  • 2 weeks where there will be a week-long take-home midterm exam,
  • a week at the end with a week-long take-home final exam.
Tentative dates for the assignments and exams are in the schedule below.

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 their collaborators.

The take-home midterms and final exam are open-book, open-library, open-web,
but in contrast to the homework on exams, no collaboration or consultation of human sources is allowed.

Late homework will not be accepted. Early homework is fine, and can be left in my mailbox
in the School of Math mailroom near Vincent Hall 105.

Homework solutions should be well-explained-- the grader is told not to give credit for an unsupported answer.
Complaints about the grading should be brought to me.

Final course grade basis :
  • Homework = 50% of grade
  • Each of 2 midterms = 15% of grade
  • Final exam = 20% of grade
Homework assignments
Assignment or Exam Due date Problems from Artin,
unless otherwise specified
Homework 1 9/19 1.1: 6,7,10,16,19,20
1.2: 2,12,13,14,15,16
1.3: 1,8,11
1.4: 1,2,4
1.5: 1,3
Chap 1 Misc Probs: 3
Homework 2 10/3 2.1: 4,10
2.2: 1,3,4,11(hint: do 2.3.2 first),17,19,21
2.3: 2,3,8,10,12,14
2.4: 6,7,12,16,22
Exam 1 10/10 Midterm exam 1 in PostScript, PDF.
Homework 3 10/24 5.5: 5
5.7: 2
5.8: 2
2.5: 10
2.6: 3,5,7(a),10
2.7: 1,5
2.8: 4,9,10
2.9: 4,5
2.10: 1,5,10
Homework 4 11/7 5.9: 4
6.1: 3,6,8(d),14
6.2: 6
6.3: 9,13
6.4: 1,2,5(a,b),13
Chap 6 Misc Probs: 7
Exam 2 11/14 Midterm exam 2 in PostScript, PDF.
Homework 5 12/5 3.1: 1
3.2: 11,16
3.3: 5,7,15
3.4: 5,11
Chap 3 Misc Probs: 5,6
4.1: 4
4.2: 1,2,8
Final Exam 12/12 Final exam in PostScript, PDF.
Back to Reiner's Homepage.