Math 430 - Algebra II - Spring 2009

General Information:

Meeting Time:MWF, 12:00 - 12:50
Location: Jones 306
Instructor:Ryan Vinroot
Office: Jones 130
Office Hours (Tentative): Mon 3:30-4:30, Wed 3:30-4:30, Thurs 9-10:30, or by appointment/walk-in.
Textbook:A First Course in Abstract Algebra, Seventh Edition, by John B. Fraleigh
2 Tests - 100 points each, Homework - 100 points, Final Exam - 200 points, for a total of 500 points. The grading scale will roughly be a 10 percentage point scale, so that a final score of 450 (90%) is in the A range, a score of 400 (80%) is in the B range, etc.
Prerequisites: Math 307 - Algebra I.
Syllabus: We will be covering topics in Groups, Rings, Fields, and Galois Theory, which extend the concepts covered in Math 307. We will start with Sections 16 and 17 of the text, which cover Group Actions, and then we will cover the Sylow Theorems in Sections 36 and 37. We will then move to Rings, and quickly review some of the topics in Sections 22, 23, 26, and 27 which were covered in Math 307. Ring theory continues in Chapter IX (Sections 45-47), which concentrates on the various classes of rings based on factorization properties. This will be followed by Chapter VI (Sections 29-33), which covers the topic of Extension Fields. Finally, we will finish the semester by covering as much as Chapter X as time allows, which covers the topic of Galois Theory. Galois Theory will link all of the topics covered previously in the following way: Field extensions are contructed by polynomial rings modulo a maximal ideal, and Galois theory connects the subgroup structure of the automorphism group of a field extension (which is an instance of a group action) to the subfield structure of that field extension.

Dates & Course Announcements:

  • Important Dates and Class Holidays:
    • Sat, March 7 - Sun, March 15: NO CLASS (Spring Break)
    • Fri, May 8: FINAL EXAM
  • Here is a pdf of some notes on Group Actions. There is some material in these notes which is not in Section 16 of Fraleigh, and likewise, some material in Section 16 of Fraleigh which is not in these notes.
  • Here are some notes on the conjugacy classes of symmetric groups. Use them as a guide if you get stuck on Problem 8 on page 333 of the homework.
  • I will be in (or near) my office the following times before the Final: Mon (May 4) 9-12, 2-5; Tues (May 5) 9-1, 3-5; Wed (May 6) 8:30-11:30; Thurs (May 7) 9-1, 2:30-5.
Exam Calendar:
Test 1 Wed, Feb 25 In class Jones 306
Test 2 Fri, Apr 3 Take home Jones 306
Final Exam Fri, May 8 9-12 Jones 306


For each homework problem assigned, a complete solution with each step explained should be written up. Be sure to explain your steps and reasoning for calculations as well as for proofs. Homework is due at the beginning of class on the due date of the assignment, and credit will not be given to late homework. Problems will be assigned roughly on a weekly basis. You may work with other students on problems, but each student must turn in their own write-up of their assignment. If any problems are completed in a collaborative effort, please indicate so on the paper turned in. The overall homework grade will be 20% of the final grade.
Assignment Problems Due Date
1 pgs. 159-160 #9, 11, 12, 14
pgs. 164-165 #6, 8
Mon, Feb 2
2 pg. 327 #11, 14
pg. 333 #8, 9
Mon, Feb 9
3 pg. 327 #17, 18, 22
pg. 333 #5, 6, 7
Fri, Feb 20
4 pg. 208 #24, 25
pgs. 244-245 #17, 30
pg. 253 #24
Wed, Mar 4
5 pg. 400 #26, 31
pgs. 406-407 #12, 17, 18
pg. 413 #9, 15
Fri, Apr 3


  • There are some very useful links related to abstract algebra on the homepage of Professor Joseph Gallian (the author of another Abstract Algebra text), which is here.
  • There are several opportunities for undergraduates through the William & Mary mathematics department, including research in mathematics. If you are interested, feel free to ask me or someone else in the Mathematics department about these opportunities. Information is available here.