Math 330. Abstract Algebra

Spring 2020

Instructor: Enrique Treviño
Lectures: MWF 10:00 - 10:50 am in Young Hall 126
Office Hours: MWF between 11 am to 12 pm. You can also arrange a meeting by appointment.
Office: Young Hall 105
Email:
Phone Ext.: #6187

Announcements

Practice Exam 1. This file contains helpful problems. Other things worthy of practicing are proving the operations are associative, or commutative, finding identities, calculating subgroups generated by an element.
Practice Exam 1 Solutions.

All the homework assignments and their solutions are here:
Homework

Course Description

A study of algebraic structures with emphasis on groups, rings, and fields. Prerequisite: Mathematics 230. (Under the old GEC, this course meets the Natural Science & Mathematics requirement.) Textbook

Abstract Algebra: Theory and Applications by Tom Judson.

The textbook is an open-source book, you can download it free at the textbook's website. If you prefer a hardcover version of the book, the book can be ordered at the Lake Forest bookstore or it can be ordered online at Amazon or at Barnes and Noble for the inexpensive price of $20.

The following books have been placed on reserve in the library for more references:
Abstract Algebra by Dummit and Foote and
A First course in Abstract Algebra by Fraleigh
Visual Group Theory by Nathan Carter. The library has an ebook copy of this book too.

Topics we will cover

We will cover basic group theory, i.e., groups, subgroups, cyclic groups, permutation groups, cosets, Lagrange's theorem, Euler's theorem, group actions and basic ring theory. If we have time we'll also cover Sylow's theorems.

Student Learning Outcomes

Main Goals:

Understand what a group is.
Be able to prove that something is a group.
Understand what a subgroup is.
Be able to prove that something is a subgroup.
Understand and be able to prove Lagrange's Theorem
Understand what it means for a group to be cyclic and how to prove that something is cyclic.
Understand the permutation group Sn and be able to make calculations inside it
Understand orders and how to calculate them.
Ability to classify all abelian groups of small order.
Understand what a ring is.

Grading

The course grade will be based on:
Homework 20%,
Midterms 45% (15% each),
Final Exam 35%.

Homework

There will be written homework roughly every week. All homework assignments can be accessed here. The homework assignments require a username and password. Your username is "lakeforest\username" (where you place username with your Lake Forest account username), and the password is the password from your Lake Forest account. The due dates for each homework assignment will be updated as the semester progresses. Each homework assignment will consist of roughly 10 problems I want you to work on. I provide the solutions for several of the problems. The problems without a solution are the problems you must turn in. Each student will submit the solutions to the problems written in LaTeX. Collaboration on the homework is permitted (and encouraged), however the solutions turned in must be written individually. You are not allowed to use the internet or any book not listed in the textbook section above to answer the homework exercises. Furthermore, the homework submissions must be your own. I take plagiarism seriously as detailed below in the Academic Honesty section.

LaTeX Resources

As described above, the homework assignments should be written in LaTeX (and compiled to a pdf).

For each homework assignment, I provide my LaTeX code for the solutions to some of the problems. I suggest you use that code as your template. You should only turn in the problems I assigned to turn in, but you can use the exercise text I already provided and the same structure.
Slides from a talk on LaTeX created by Vadim Ponomarenko of San Diego State University.
The TeX source code for the slides. (Right-click to Save Link As).
LaTeX on Wikibooks. A very useful online manual.
For PC users, you can use TeXnicCenter to compile. You'll need to install MiKTeX. After you install MikTeX, you wil also have TeXWorks in your computer. You can use this compiler instead of TeXnicCenter if you prefer. Or find your own.
For Mac users the things to install are different. You can use MacTeX or find one of your liking online.
Another option is to compile things online in Overleaf. Many of my students have liked how easy it was to use.
Bates College has a very nice manual in their Math departmental website: The Bates LaTeX Manual.

Exams

There will be three midterms and one final exam. On the midterms and the final exam you must work on the problems on your own. No collaboration permitted in the exams.

The midterms might be outside of class so that you have more time to try the problems.

The tentative dates are:

The first midterm will be on Wednesday February 12 from 9am to 10:50am.
The second midterm will be on Friday March 9 from 9am to 10:50am.
The third midterm will be on Friday April 17 from 9am to 10:50am.
The final exam will be on Friday May 1 from 8:30am to 11:30am.

Attendance

Students are expected to come to every lecture and every exam.

If the dates of the exams conflict with Lake Forest approved events, inform me as soon as possible.

Description of instructional time and expectations:

This course meets 3 times per week for 3 hours per week. The course carries 1.0 course credit (equivalent to four semester credit hours). Students are expected to devote a minimum of 12 hours of total work per week (in-class time plus out-of-class work) to this course.

Academic Honesty

Please read the College's information on Academic Honesty. If a student cheats in an exam, quiz or homework assignment, I will proceed with charging the student with the Academic Honesty Judicial Board. The usual (first) penalty is a 0 in the assignment on which the cheating occured plus some ethics lectures the student would take. The second penalty is usually suspension.

Accommodations Statement

If you are a student who needs an accommodation because of a disability or medical or psychological condition that limits your ability to fully participate in this course, please contact Kara Fifield, Director of Disability Services, to document your disability with the College and with the professor of this course. Academic accommodations should be reasonable and not alter the fundamental nature of this course. Because it can take a week or more to arrange requested accommodations, you are encouraged to establish your semester accommodations as early in the semester as possible. Contact Kara Fifield by email or phone: kfifield@lakeforest.edu or 847-735-5167. For more information about services for students with disabilities at Lake Forest College, see: http://www.lakeforest.edu/academics/resources/disability/

You are also welcome to contact me privately to discuss your academic needs. However, all disability-related accommodations must be arranged through Kara Fifield.

Last modified on February 10, 2020.