This class will cover groups, fields, rings, and ideals. More explicitly: Groups acting on sets, examples of finite groups, Sylow theorems, solvable and simple groups. Fields, rings, and ideals; polynomial rings over a field; PID and non-PID. Unique factorization domains.

Math 120 will be a fast-moving, high-workload class. This is also a
*Writing in the Major* class.
Most students
interested in this material will find Math 109 (offered in spring quarter) more appropriate.

**Professor:** Ravi Vakil, 383-Q, vakil-at-math.stanford.edu.

**Course assistant:** Francois Greer, 381-A, fgreer-at-math.stanford.edu.

** Office hours:** Tuesday 8-10 am and 11 am-noon (Francois Greer), Wednesday 9-10:30 am (Ravi Vakil), Thursday 8-10 am and 11 am-noon (Francois Greer), Friday 10:30 am - noon (Ravi Vakil). (In the week of the final exam, these office hours are replaced by 12 hours of bonus office hours shown below.)

**Text:** Dummit and Foote's *Abstract Algebra*, third edition
(be careful to get the right edition!).

**Grading scheme:**

Short online assignments 5%

Problem sets 20%

Writing in the Major Assignment 15%

Midterm 20%

Final exam 40%

**Short online assignments.**
There will be weekly short online assignments on Coursework.
You needn't answer more than one or two sentences per question.
This is intended to be low-stress: you will get full marks for any
good-faith answer.
This is intended to give us feedback on how the reading has been
going. Because I will have to review your feedback in a limited time
period on Sunday afternoon, the deadlines will be on Sunday at
noon sharp.

**Email lists and study groups.**
There is a list of email addresses and dorm locations of people willing to be contacted to discuss homework or to form study groups. If you are interested in being on the list and seeing the list, just let me know.

**Problem sets.** There will
be weekly homework assignments, posted here.
You are encouraged to
work together to solve problems. But you must write up your solutions
individually, and give credit for ideas that others had. You should
give complete proofs. Because the graders will need to process a huge
volume of homework in a small amount of time: Please staple your homework, and write your
name on each page.

Homework due dates: Thursday at 3 pm outside my office.
**No lates** will be allowed (so the graders can just grade one problem
set at a time, and hence have a better chance of getting them back promptly).
But to give everyone a chance to get sick, or have busy periods, the lowest
problem set will be dropped.

- Problem set 1 is due on Thursday October 9. Do 12 of the following problems, including at least one from each section. Section 1.1: 1, 23, 26. Section 1.2: 5. Section 1.3: 2 (answers only). Section 1.4: 3, 10. Section 1.6: 6, 18, 20. Section 1.7: 3, 4, 17, 23. Section 2.1: 12, 13. Section 2.2: 3, 10. Section 2.3: 3, 21. Section 2.4: 7, 13.
- Problem set 2 is due on Thursday October 16. Do 12 of the following problems, including at least one from each section in chapter 3. Section 2.3: 9, 23. Section 3.1: 3, 6, 9, 16, 22, 24, 25, 27, 41, 42. Section 3.2: 4, 8, 10, 11, 17. Section 3.3: 1, 3, 4, 7, 9. Section 3.4: 4, 5, 6.
- Problem set 3 is due on Thursday October 23. Do 12 of the following problems, including at least one from each section. Section 3.5: 9, 10, 12. Section 4.1: 1, 4, 9, 10. Section 4.2: 1, 6, 8, 10, 11, 12. Section 4.3: 2a, 4, 5.
- Problem set 4 is due on Thursday October 30. Do 11 of the following, including at least one from each section. Section 4.3: 17, 22, 25, 26, 29, 33. Section 4.4: 1, 2, 3, 8, 16, 18 (worth 2 problems), 19 (worth 2 problems). Section 4.5: 3, 7, 30.
- Problem set 5 is due on Thursday November 20. Do 11 of the following, including at least one from each section. Section 4.6: 1, 6. Section 5.4: 2, 5, 15. Section 5.5: 2, 8. Section 7.1: 14, 23, 26. Section 7.2: 3, 12. Section 7.3: 10, 13, 18, 19, 22, 30, 34.
- Problem set 6 is due on Thursday December 4. Do 10 of the following problems, including at least one from each section excpt 7.5. Section 7.4: 8, 9, 10, 15. Section 7.5: 5 (worth 2). Section 7.6: 1, 5 (worth 2), 7. Section 8.1: 1(d)+2(b) (together worth 1), 3, 6, 7, 12. 8.2: 3, 5. Also, for each of the 6 problem sets, pick one problem you particularly liked, and explain why in a sentence or two.

**Writing in the major assignment.** Clear writing is essential
to mathematical communication, as you probably realize from reading
better and worse mathematical texts. Clarity in writing may be more
important in mathematics than in any other science, for a number of
reasons. Good exposition is an acquired and important
skill. Throughout this class, you'll received feedback on solutions to
your problem sets, and you should use this to refine your ability to
communicate your ideas clearly and effectively. This writing project
will give you an opportunity to focus on your exposition, as opposed
to absorbing new mathematical content. This course will emphasize
both exposition in communciating mathematics and the structure of
proofs. Part of your grade on each assignment and on the exams will
be on your exposition of your solutions to problems. **Information about the Writing in the Major assignment is here.** Deadlines to be aware of: Fri. Oct. 31, Friday Nov. 7, Fri. Nov. 21.

**Syllabus.**

**Miscellaneous:** Josh Meisel (who took 120 in 2009) found this link about a Futurama episode whose plot involved group theory.

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