## Welcome to Tom Roby's Math 3121 homepage! (Fall 1999)

(last updated: 11 November 1999)

### Class Information

Coordinates: Lectures meet Tues/Thur. 6:00--7:50 (#11719) in Sci Science 213.

Text: J. Gallian Contemporary Abstract Algebra 4th Ed. (Houghton-Mifflin, 1998)

Web resource: http://seki.mcs.csuhayward.edu/~troby/3121.html will be my Math 3121 homepage. It will include a copy of the syllabus and list of homework assignments. I will keep this updated throughout the quarter.

Grading: There will be daily homework assignments (handed in weekly on Thursday), weekly quizzes (given on Tuesdays), one midterm exam given in class, and a final. Late homework will generally not be accepted, and no makeup exams will be given, but your two lowest homework and quiz scores will be dropped before grades are computed. If you do not take the midterm or you miss more than two quizzes, your final exam score will also be the score for your midterm or missing quizzes.

The breakdown of points is:

Homework Quizzes Midterm Final
25% 25% 25% 25%

Content: The goal is to cover the first 11 chapters of the text, which comprise an introduction to group theory. We may omit some applications for lack of time, but you are encouraged to read all eleven chapters. The next course in the sequence, Math 3122, will start with ring theory, which Gallian covers in later chapters.

The only way to learn mathematics is by doing it! Complete each assignment to the best of your ability, and get help when you are confused. Come to class prepared with questions. Don't hesitate to seek help from other students. Sometimes the point of view of someone who has just figured something out can be the most helpful.

### Lecture and Assignment Schedule

Please read the sections from the book listed before the date of the first lecture on that material.

 Midterm Exam: Chapters 0-5 on October 28 (Thurs.) Final Exam: 9 December (Thurs.) Chapter: Topic Lect. Date Homework problems Due 0: Integers, GCD & Mod n 9/23 R HW1: p. 21: #3,6,8,13,17,18,19,21,22,24,31,40,43 9/30 0-1: Induction, Eq. Rel., 9/28 T 1-2: D_4, Group axioms 9/30 R HW2: p. 35: #5,6,14,22; p. 51: #2,4,6, 12-24even 10/7 2: Elementary props. & EG's 10/5 T 3: Subgroups, Finite Groups 10/7 R HW3: p. 65: #4,5,8,12,14,17,22,28,34,42,48 10/14 3: Centers and commutators 10/12 T 4: Cyclic Groups 10/14 R HW4: p. 79: (Read #3-6),#8,11,16,20,30,34,36,46-50even,56,57 10/21 4: More Cyclic Groups 10/19 T 5: Permutations 10/21 R HW5: p.107: #4-10even, 17,18,38,40 11/2 REVIEW DAY 10/26 T Chapters 0-5 5: More Permutation Groups 11/2 T HW6: p. 109: #20,24,28,32,34,36; p. 126: 4,5,10,14 11/11 6: Isomorphisms & Cayley's 11/4 R 6: Automorphisms 11/9 T HW7: p. 126: #7,17,20,30,36,38; p. 143: #10,14,17,24,26,35,36. 11/23 7: Cosets and Lagrange's 11/11 R 8: External Direct Products 11/16 T HW8: p. 143: #21,30,34; p. 161: 2-10even,16,24,34,42 11/30 9: Quotients & Normality 11/18 R 10: Homomorphisms & Ker. 11/23 T HW9: p.185: #8,12-20even,26,28,36,40,42; p.203: #2,6,12,14,16,28 12/2 11: FTFAG 11/30 T Catchup Day 12/2 R Chapters 0-11 SPECIAL REVIEW 12/7 T Chapters 0-11

Homework: Homework will be given for each lecture, and all the homework assigned the previous week will be due the following Thursday. Please attempt all the problems by Tuesday, so that you can ask any questions you may have in class then. Except for routine computations, you should always give reasons to support your work and explain what you're doing. Not all the problems will be graded, but only a small subset; most of the ones assigned have answers in the back so you can tell if you're on the right track. This makes it more important that you write your solutions carefully.

Quizzes: There will be a short quiz at the end of class each Tuesday on the previous week's material. I will try to be very specific about what you should know. If you're not sure, please ask!

Midterm Exam: Thursday, 28 October 6:00-7:50 in class. Rearrange your schedule NOW if necessary.

Final Exam: Thursday, 9 December 6:00-7:50 in our usual classroom. There will be no make-up final exams. If you are unable to attend the final exam due to documented and unexpected circumstances beyond your control, and you have at least a C average on the previous coursework, an incomplete may be assigned.