# Attendance

Attendance will be checked at the beginning of each class meeting, but it does not affect your grade. However you are responsible to know the material covered in class and that from the corresponding sections of your textbook.

# Homework

Working on example problems is the key to understand abstract concepts. Therefore there will be a homework assignment for each lecture in the course schedule. You turn in your solutions at the end of the lecture at the given due date. If there is no class meeting that day, you put your solutions in the drop box at the math office MS401 before noon. Make sure that you write your and my name and the course and section number on the front page. Late submissions will not be accepted. Your homework score is part of your final grade. Example solutions for selected problems will be posted in the solutions section after the due date. Feel free to ask me for solutions for specific problems that you could not solve.

# Quizzes

Be prepared for 5-minutes in-class quizzes that count toward your final grade. These quizzes will not be announced and there are no make-up quizzes. Books, notes, and electronic devices are not permitted during quizzes.

# Examinations

There will be 3 midterm exams and a final exam which contribute to your final grade. Each exam will be announced in class and appear online in the course schedule. Make-up exams will be given only under exceptional circumstances and if you contact me in advance. Books, notes, and electronic devices are not permitted during exams. Example solutions for the exams can be found in the solutions section after each exam.

The contributions to your total score will be weighted as follows.

Contribution Weight (final grade) Weight (6-weeks grade) Homework + Quizzes Midterm Exams Final Exam 20% 3 x 20% 20% 50% 1 x 50% 0%

Your total score will be truncated to an integer percentage and determines your final grade as follows.

 Total Score Letter Grade 0-59% 60-69% 70-79% 80-89% 90-100% F D C B A

Curving may be applied in form of a linear adjustment to all scores on a particular exam. I reserve the right to decide borderline cases based on class attendance and subjective impressions such as effort and conscientiousness.

# How to learn?

Your starting points are the textbook and the lecture. It is easier to follow the lecture if you have seen the material before and presented from a slightly different point of view. I strongly recommend that you read each section in your textbook at home before it is covered in class. Try to isolate what you do not understand and be prepared to ask questions during the lecture.

Do not hesitate to ask questions. If something is unclear to you in class, just ask. You can be sure that many of the other students have the same question but do not dare to ask. If you let me know what your problems are, I can adapt the lecture and make it easier for you to follow. There are no stupid questions. On the contrary, asking the right question is often an important step in the process of solving a problem.

The importance of working on example problems can not be overemphasized. Try to work on the homework problems intensively and pick additional similar problems from your textbook.

Discussion is crucial to understand mathematics. I strongly encourage you to discuss both the material covered in class and your solutions of the homework problems with other students. The best way to check your own understanding of a subject is to explain it to someone else.

# Where to get help?

Ideally you solve the homework problems on your own, or working with other students. If you realize that you do not understand the homework problems, seek help immediately. With a backlog of not understood material it extremely difficult to catch up with the class again.

You are always welcome to see me in my office hour, or contact me by email if you have any questions or problems. If my office hours do not fit your schedule, please contact me by email for an appointment.

# Course Schedule

The following course schedule is preliminary.

Class
Meeting
Date Sections
from
Textbook
Subject Homework
Assignment
Due Date
101/107.1Rings: Basic Definitions and Examples3,5,6,12,14,2301/14
201/127.1
7.2
Continued
Polynomial, Group, and Matrix Rings

1b,7,10cd,12

01/19
301/147.3Ring Homomorphisms and Quotient Rings
-01/17-Holiday
401/197.3Continued12,15,17,27,30,3301/24
501/217.4Properties of Ideals
6,701/247.4ContinuedExam 1: 3,7,10,13,15,31,39,4102/14
801/267.5Rings of Fractions
901/287.5Continued7.5:1,2; 15.4:18,21,2201/31
10,1101/317.6
8.1
Chinese Remainder Theorem
Euclidean Domains

3,5b,10,11,12

02/14
1202/02-Campus Closed
1302/048.1Continued
-02/07-No Class
-02/09-No Class
-02/11-No Class
1402/148.2Principal Ideal Domains
1502/168.3Unique Factorization Domains
1602/189.1-2Polynomial Rings9.1:13,14,15,17; 9.2:4,5,6d,1002/28
1702/219.3Polynomial Rings over UFDs
1802/239.4Irreducibility Criteria1bc,2cd,3,6,8,16,1903/04
1902/259.5Finite Multiplicative Subgroups of Fields
2002/289.6Hilbert's Basis Theorem and Gröbner Bases24,3203/11
2103/029.6Continued
2203/0410.1Modules, Definitions and Examples8,14,16,2203/11
2303/07Exam 2 (Solutions)
2403/0910.2Quotient Modules and Homomorphisms
2503/1110.3
10.5
Generators, Direct Sums, and Free Modules
Exact Sequences
11,12a,15
11ab,14a
03/23
-03/14-Spring Break
-03/16-Spring Break
-03/18-Spring Break
2603/2110.5Diagram Chasing
2703/2313.1Field Theory2,3,4,803/30
2803/2513.2Algebraic Extensions1,7,10,13,1604/04
-03/28-No Class
2903/3013.2
13.3
Continued
Straightedge and Compass Constructions
3004/0113.4Splitting Fields and Algebraic Closures1,3,5N/A
31,3204/0413.5
13.6
Separable Extensions
Cyclotomic Extensions
3,4,5
3,4,6
04/11
3304/0614.1Galois Theory1,3,4,5,9N/A
-04/08-No Class
3404/1114.1Continued
3504/1314.2The Fundamental Theorem of Galois Theory
3604/15Exam 3
37,3804/18-
14.2
Solutions of Exam 3
Continued
3904/2014.2Continued
4004/2214.2Examples
4104/2514.2ContinuedFinal Exam: 3,7,13,1605/02
4204/2714.2Norm and Trace
4304/29-Review
4405/02-Final Exam8:00am-9:50am

# Disclaimer

This syllabus may be subject to future changes and it is your responsibility to be informed. Any change of the syllabus will be announced in class and appear online.