**Office Hours:** M 9:30-10:30, T 2:30-3:30, W 4:00-5:00 (or by appointment).

- Learn a lot of abstract algebra, in particular ring, field, and Galois theory.

- Thoroughly understand what
**definitions and theorems**are. The student will be able to precisely state definitions and theorems and understand how they are applied. - Practice writing
**proofs.**It is expected that the student will have a fair amount of experience writing proofs. The student will further refine this skill. - Practice good
**mathematical writing**. In mathematics, as indeed in everything else, it is important not only to be correct but to explain yourself clearly and as simply as possible.

**Warning.** You should expect 8-10 hours of homework a week in this class, which is more than most other instructors assign;
in my experience there is no other way to learn the material. Your consistent effort will certainly lead to improved understanding,
and it will almost certainly lead to you earning high grades.

** Warning. I assign a lot of homework.**

The homework is intended to take 8-10 hours a week. That is a lot. Please count on making a consistent effort to do well in this class! Starting the night before is a bad idea.

If homework takes you more than 10 hours on any given week, then that is more than I intended; please let me know.

There will be at least one **bonus** problem on each homework, each worth one or two points, up to a maximum
score of 12/10 on each week's homework. This is the only way to earn extra credit; please note that bonus problems
will not be accepted late.

**Graduate credit:** If you want graduate credit, you are required to do at least one bonus problem from
every other homework (i.e., do one from HW1 or HW2, etc.) Bonus problems on top of that count for extra credit.

**Please note**. You will be graded both on correctness and on quality of exposition. Indeed, a major
focus of Math 547/702I is the ability to communicate mathematical ideas clearly.
**The standard is that someone who doesn't know the answer should be able to easily follow your work.**
In particular, please write in **complete English sentences** and draw **clear diagrams** where appropriate.
Any work that is confusing, ambiguous, or poorly explained will not receive full credit.

**Grading scale **: You are guaranteed the following: A = 88+, B+ = 82+, B = 74+, C+ = 68+, C = 60+, D = 50+.
Actual cutoffs might be more generous. Note that the grading scale is more generous than the usual 10-point scale
-- not because I am a softie, but because the material will be difficult.

Grade component | % of grade |

Two midterm exams |
15% x 2 |

Final exam: |
30% |

Homework: |
40% |

*Please note:* If you come to office hours, please don't be shy about interrupting me! I'm usually in
the middle of something, but it can wait.

If you have a legitimate conflict with any of the exams it is your responsibility to inform me **at least a week before** the exam.
Otherwise makeup exams will be given only in case of documented emergency.

Late homework will be accepted **once per student**, up to a week late; after that, no late homework please
except in case of emergency.

**Academic honesty** and **attendance** are expected of all students.

**Calculators** will not be needed or allowed.

Homework 1, due Wednesday, January 21.

Homework 2, due Monday, February 2.

Handout on polynomials. **Homework 3**, due Monday, February 9: the problems given there; and Ch. 17: 19, 20, and 25.

Partial solutions to the previous handout.

**Homework 4**, due Monday, February 23: Ch. 17: 26, 30; Ch. 18: 1, 2, 3, 6, 7, 8, 9, 13, 15, 18.

Some solutions to a couple of homework problems.

Exam 1, with partial solutions.

Some solutions to some later homework problems.