Math 3140 Fall 21

MATH 3140: Abstract Algebra 1 (Fall 2021)

MWF 9:10-10:00 am, ECCR 131

Peter Mayr

Schedule and assignments

Office hours

Math 310
Monday 12:30-1:30 pm
Friday 10:00-11:00 am or by appointment

Course description

Algebra appears in the study of symmetries of objects, construction of computer chips, cryptography... After a brief overview of various algebraic structures we will study the elementary theory of groups. In particular we will cover the following topics:

Textbooks

There are many good textbooks on the topic, including the ones listed below. We will mainly follow Goodman's book. You can find the others online or at the Mathematics Library for additional reading.
  1. J. Fraleigh, A First Course in Abstract Algebra (Seventh Edition), Addison Wesley 2002.
  2. J. Gallian, Contemporary Abstract Algebra (Fifth Edition), Cengage Learning 2016.
  3. F. Goodman, Algebra: Abstract and Concrete (Edition 2.6), 2015. [pdf]
  4. T. Hungerford, Abstract Algebra: An Introduction (Second Edition), Brooks Cole 1996.
  5. I. Herstein, Abstract Algebra, John Wiley 1996.
  6. T. Judson, Abstract Algebra: Theory and Applications. [pdf]
  7. S. Lang, Undergraduate Algebra (Third Edition), Springer 2005. [pdf]

Details on requirements for COVID-19, accomodations, etc

According to campus policy students who have tested positive for COVID-19, have symptoms of COVID-19, or have had close contact with someone who have tested positive for COVID-19, have symptoms of COVID-19 must stay home. If you must stay home, notify me as soon as possible to set up a plan to obtain lecture notes and take quizzes remotely.

Assignments

Homework problems are posted every Wednesday on the course website. Please submit your solutions as pdf on Canvas before class on the following Wednesday. I expect clearly organized and worded solutions (if you are able to type even better). Anything not legible will be marked as wrong. You are allowed and encouraged to discuss your assignments with others. However I ask you to follow this approach: First try to solve your problem on your own. If you get seriously stuck, discuss it with your colleagues, me, etc. In any case write up the solutions that you hand in alone.

Exams

Grading

Your final grade will be determined by the scores of your assignments, quizzes, midterms, and final exam. To combine these items the following weights will be used: Late homework will not be accepted. There is no make-up for missed quizzes. However the 3 lowest homework scores and the 3 lowest quiz scores will not count towards the final grade.

Scientific writing

There is a variety of word-processing software for writing Mathematics. LaTeX is the most widespread. You can use it with many text editors or via some cloud-based service, like OverLeaf.

How to succeed in this class

  1. Go to class! It seems obvious, but learning the material in small portions 3 times a week is easier than reading up on it in some book by yourself. Always keep up with the topics. You also get nerdy Math jokes.
  2. Ask questions early and often! If you are not sure about something, ask about it immediately -- no matter whether in class, in office hours, or by mail. Do not assume that you can skip or figure out things later that you do not understand now. If you are missing the basics, you may fall behind and struggle with more complicated concepts later in class.
  3. Do the work! The only way to learn stuff is to try it yourself. Strive to do all the homework assignments. Some will be more challenging than others. If you are stuck on the hard ones, discuss them with colleagues or ask for possible hints in office hours or by mail.
  4. Learn from mistakes! Look at all feedback you get on graded homework, quizzes, exams, etc. Make sure you understand where you went wrong and how to get the correct solution. In particular revise all relevant graded work before exams.
  5. Organize in study groups! Meet with classmates a couple of times a week to discuss lectures and homework. Still write up your solutions to assignments when you are alone, never in a group.
  6. Take advantage of office hours! If you cannot make it to the official hours, ask to meet at some other time. Office hours are an additional resource for you to discuss stuff for which there is no time during class. Come prepared! Try to solve homework problems alone before you ask for help and be ready to explain your thoughts and where you are stuck.