MWF 11:15 a.m. - 12:05 p.m. in Lind Hall 302
Math 2283 (or 3283) Sequences, Series, and Foundations (W)
Christine Berkesch Zamaere
Office: Vincent Hall 254
Email: cberkesc -at- math.umn.edu (For faster response time, please include "Math4281" in the subject line.)
Office hours:
M 10:00 a.m. - 11:00 a.m., F 2:30 p.m. - 3:30 p.m., or by appointment (in Vincent Hall 254).
Abstract Algebra: a geometric approach by Theodore Shifrin, 1996. (On reserve in the Mathematics Library, Vincent Hall 310.) Errata and typos here.
This is an introductory course in modern algebra. It differs from Math 5285H: Fundamental Structures of Algebra by being less theoretical and having somewhat different subject matter (although there is some overlap).
Getting help:
  • You are strongly encouraged to work in study groups and learn from each other, although all final work submitted must be your own. Lind Hall 150 is available for small group meetings and individual study.
  • Free tutoring services are available. See Tutoring Resources at the Undergraduate Math page for more information.
  • Hire a tutor. A list of tutors is available in Vincent Hall 115 or by email request at ugrad@math.umn.edu.
  • Attend my office hours (see above).
  • Email me (above) short questions or comments. Please allow at least one working day for a response.

Staple the appropriate problem set sheet to the front of your assignment.

Assignment     Due date
Problem Set 1   Wednesday, September 14
Problem Set 2   Wednesday, September 21
Problem Set 3   Wednesday, September 28
Problem Set 4   Wednesday, October 5
Problem Set 5   Wednesday, October 12
Problem Set 6   Wednesday, October 19
Problem Set 7   Wednesday, October 26
Problem Set 8   Wednesday, November 2
Problem Set 9   Wednesday, November 9
Problem Set 10   Wednesday, November 16
Problem Set 11   Wednesday, November 23
Problem Set 12   Wednesday, November 30
Problem Set 13   Wednesday, December 7

Below is a list of topics and corresponding reading. As they become available, I will add the lecture dates. No topic next to a date means that we will continue with the previous topic.

Date      Topic                                                               Shifrin 
09-07   Preliminaries   A.1, A.2
09-09   Properties of the integers   1.1
09-09   Division and Euclidean algorithms   1.2
09-16   Modular arithmetic   1.3
09-16   Solving congruences   1.3
09-21   Equivalence relations   A.3
09-21   Rings, domains, and fields   1.4
09-28   The complex numbers   2.3
09-30   Introduction to polynomials   3.1
10-03   Euclidean algorithm for polynomials   3.1
10-07   Roots of polynomials   3.2
10-10   Irreducible polynomials   3.3
10-12   Review for Midterm 1  
10-14   Midterm 1  
10-17   Irreducible polynomials   3.3
10-21   Ring homomorphisms and ideals   4.1
10-26   Quotient Rings   4.1
10-28   Ring isomorphisms   4.2
11-02   Vector spaces and field extensions   5.1
11-07   Groups   6.1
11-09   Review for Midterm 2  
11-14   Midterm 2  
11-16   Cyclic groups   6.1
11-18   Permutation groups   6.4
11-21   Group homomorphisms and isomorphisms   6.2
11-28   Cosets   6.3
11-30   Normal subgroups and quotient groups   6.3
12-05   Solving polynomial equations   Handout
12-07   Review for Midterm 3  
12-09   Midterm 3  
12-12   Galois theory   7.6

September 7   First Math 4281 class meeting
September 12   Last day to register without instructor approval and drop with a 100% refund
September 19   Last day to drop without receiving a "W" and with a 75% refund
October 14   Midterm 1
November 11   Midterm 2
November 14   Last day to change to recieve a "W" without college approval
December 9   Midterm 3
December 14   Last day of class

Weekly problem sets are posted under homework above. Problem sets will typically be collected in class on Wednesday. Late homework will not be accepted, but early hard copy submission is welcomed. Your two lowest problem sets will be dropped from your grade. If you have an unavoidable and legitimate university sanctioned excuse for missing an assignment, please contact me as soon as possible about this issue. In particular, if you have more than three such excuses, it is possible to drop more assignments.

The homework in this course is intended to be challenging; it is training to help you build stronger mathematical muscles. There will be problems whose solutions are not immediate; there will be times that you will even need to sleep on a problem before fully grasping its solution. With this in mind, I recommend that you give yourself a full week to do the homework, so that only a few challenges remain by the Wednesday before the assignment is due. This gives you time to discuss any difficulties with your classmates and attend office hours in order to complete the problem set.

While you are encouraged to consult with your classmates on the homework, your final work must be your own. Copying a classmate's work constitutes plagiarism and violates the University of Minnesota Student Conduct Code. When you collaborate to reach an answer, include the name(s) of your classmate(s) with your solution.

Selected homework problems (or similar) may be given on exams. This is another reason why you should do the homework before each class and, moreover, remember the ideas and techniques used in your solutions.
Homework presentations:
Each Wednesday, class will begin with homework presentations. Every student will be required to present homework problems in rotation. If no students volunteers, someone will be selected at random by the instructor. The presentation grade will be based on your ability to be heard in the room, your ability to make your boardwork visible and clear to the class, the justification of your strategies and solution, your ability to take and apply feedback, and the correctness of your final work. The presentation will be weighted as a single homework assignment. A copy of the grading sheet is available here.
There will be three midterms in class. All exams are closed book, closed notes, and no calculators. A definition list will be provided with the exam.
Your grade is based on homework and exams, which will be weighted as follows:
Homework and presentation   34%
Midterm exams (x3)   22% each
Missed exams:
No make-up exams will be given; however, it is possible to take a quiz or exam early if you have a valid reason. If you have an unavoidable and legitimate university sanctioned excuse for missing an exam, please contact me as soon as possible about this issue.
Written work:
We write to communicate. Please keep this in mind as you complete written work for this course. Work must be neat and legible in order to receive consideration. You must explain your work in order to obtain full credit; an assertion is not an answer. The logic of a proof must be completely clear in order to receive full credit.
You will find the lectures easier to follow if you spend time with your textbook before class. The lectures section will tell you the topics for the coming class meetings. Before class, skip proofs, but seek to understand the "big idea" of each section, the key definitions, and statements of the main theorems. After class, read all statements and proofs carefully, and stop to identify useful proof techniques along the way.
Definitions and Theorems:
In order to be successful in this course, it is imperative that you become adept at using definitions and important theorem statements in proofs. I suggest having a special, separate place in your notebook to record this information. This will be very helpful when doing your homework. Also, be sure to memorize anything there that is not going to be given on the exam.
You should expect to spend about 9 hours a week outside of class on reading and homework for this course. This course builds upon itself, so in order to be successful, it is important to not fall behind.
Students are encouraged to use technology available to them for homework, but no technical aids will be allowed on the exam.
Students with disabilities who will be taking this course and may need disability-related accommodations are encouraged to make an appointment with me as soon as possible. Also, please contact UMN's Disability Services to register for support.
Academic integrity:
It is the obligation of each student to uphold the University of Minnesota Student Conduct Code regarding academic integrity. You will be asked to indicate this on your homework assignments. Students are strongly encouraged to discuss the homework problems but should write up the solutions individually. Students should acknowledge the assistance of any books, software, students, or professors.


Christine Berkesch Zamaere  ***  School of Mathematics  ***  University of Minnesota