Lectures:
MWF 11:15 a.m. - 12:05 p.m. in Vincent Hall 211
Prerequisites:
Math 2283 or 3283
Instructor:
Christine Berkesch Zamaere, Office: Vincent Hall 250, Email: cberkesc -at- math.umn.edu (For faster response time, please include "Math4281" in the subject line.)
Office hours:
(In Vincent Hall 250) M 12:15 - 1:30 p.m. and W 1:30 - 2:45 p.m., or by appointment.
Textbook:
Abstract Algebra: Theory & Applications by Thomas Judson, 2013 ed. (Available free online at the given link.)
Description:
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. 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.

Policies for Spring 2013

Homework:
Weekly problem sets are posted under homework below. Problem sets will be collected at the beginning of class on Friday and typically cover the material from the previous week. Late homework will not be accepted, but early submission is welcomed. If you have an unavoidable and legitimate university sanctioned excuse for missing an assignment, please contact me as soon as possible about this issue. Also note that 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.
Exams:
There will be three midterms during the following class meetings: October 4, November 1, and December 11. All exams are closed book, closed notes, and no calculators.
Grading:
Your grade is based on homework and the midterm exams, which will be weighted as follows:
Homework   40%
Midterm exams   20% each
Missed exams:
No make-up exams will be given; however, it is possible to take an exam early if you have a valid reason. If you miss an exam, your grade on it will be a prorated grade of the following exam. If you miss the last exam, your grade will be the minimum of your two previous exam scores. If you miss two tests, one of them will be graded as zero. If you miss three, they will all be graded as zero. You must tell me before the exam (an email is fine) that you want to exercise one of these options and skip the exam.
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.
Reading:
You will find the lectures easier to follow if you spend time with your textbook before class. The lectures section below will tell you the topics for the coming class meetings. Before class, skip proofs, but instead 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.
Workload:
You should expect to spend about 9 hours a week outside of class on reading and homework for this course.
Technology:
Students are encouraged to use technology available to them for homework, but no technical aids will be allowed on the exam.
Disabilities:
Students with disabilities, who will be taking this course and may need disability-related accommodations, are encouraged to make an appointment with the instructor as soon as possible. Also, please contact U of M'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.
Important dates:
September 10   Last day to register without instructor approval and drop with a 100% refund
September 16   Last day to drop without a "W" and with a 75% refund
October 4   Midterm 1
November 1   Midterm 2
November 27-28   Thanksgiving break
December 11   Midterm 3 and last day of class

Lectures

Below is a list of topics and corresponding reading for the semester, which is subject to change. 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   Reading
09-04   Properties of the integers   1.1, 1.2 thru p. 14, 2.1
09-06   Division and Euclidean algorithms   2.2
09-09   Modular arithmetic   3.1 thru top of p. 40, 6.3 (skip Theorems 6.11 and 6.12)
09-11   Solving congruences   16.5
09-13   Equivalence relations   1.2
09-16   Rings, domains, and fields   16.1, 16.2 (Only need a special case of textbook from Theorem 16.4 to Theorem 16.6, as abbreviated in class notes)
09-18   The complex numbers   4.2 (skip Prop. 4.10)
09-20    
09-23   Introduction to polynomials   17.1 (skip Theorem 17.3)
09-23   Euclidean algorithm for polynomials   17.2
09-25    
09-27   Irreducible polynomials over the integers   17.3 (stop after Example 7)
09-30   Roots of polynomials   21.1 (stop after Example 1), 21.2 (stop after Example 11)
10-02   Midterm 1 review   Email questions by 3 p.m. on Tuesday, Oct. 1
10-04   Midterm 1   Material through 09-25
10-07   (Continue with) Roots of polynomials  
10-09   Ring homomorphisms and ideals   16.3, Theorem 17.3
10-11   Quotient Rings   16.3
10-14   Ring isomorphisms   16.3, 21.1 through Theorem 21.2, 21.2 through Theorem 21.17
10-16    
10-18    
10-21   Vector spaces and field extensions   20.1, 20.2, 20.3, 21.1 after Theorem 21.3 through Example 9
10-23    
10-25   Geometric constructions   21.3
10-28   Groups   3.1, 3.2, 3.3
10-30   Midterm 2 review + (Continue with) Groups   Email questions by 3 p.m. on Tuesday, Oct. 29
11-01   Midterm 2   Material through 10-25
11-04   (Continue with) Groups  
11-06   Cyclic groups   4.1
11-08   Permutation groups   5.1, 5.2
11-11   Group homomorphisms and isomorphisms   11.1 (skip Theorem 11.2), 9.1 up to Theorem 9.5
11-13    
11-15   Cosets   6.1, 6.2
11-18    
11-20   Normal subgroups and quotient groups   10.1, Theorem 11.2, 11.2 through Example 8
11-22   Group actions   14.1, 14.2, Theorem 9.6
11-25    
11-27    
12-02   Galois theory   21.2, 23.1, 23.2, 23.3
12-04    
12-06    
12-09   History of solving polynomials + Review for Midterm 3  
12-11   Midterm 3   Material through 12-09

Homework

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

Assignment     Due date
Problem Set 1   Friday, September 13
Problem Set 2   Friday, September 20 (Typo: In #5, if you have x^3, it should be x^2.)
Problem Set 3   Friday, September 27
Problem Set 4   Friday, October 4
Problem Set 5   Friday, October 11
Problem Set 6   Friday, October 18
Problem Set 7   Friday, October 25 (Typos: In #4b, phi should be a ring isomorphism. In #5a, it should say sigma(alpha).)
Problem Set 8   Friday, November 1
Problem Set 9   Friday, November 8
Problem Set 10   Friday, November 15
Problem Set 11   Friday, November 22
Problem Set 12   Monday, December 2
Problem Set 13   Monday, December 9

Links

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