Math 330. Modern Algebra I

Fall 2018

Instructor: Enrique Treviño
Lectures: MWF 10:00 - 10:50 am in Young Hall 117
Office Hours: MW between 2:30pm to 4pm. You can also arrange a meeting by appointment.
Office: Young Hall 105
Email:
Phone Ext.: #6187

Announcements

Announcements will be displayed here.

All the homework assignments and partial solutions are here:
Homework

Course Description

A study of algebraic structures with emphasis on groups, rings, and fields. Prerequisite: Mathematics 230.

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. One caveat is that the homework exercises are taken from the 2013th edition, so for homework is better to access the book online.

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:
Quizzes 20%,
Midterms 45% (15% each),
Final Exam 35%.

Homework and Quizzes

There will be written homework roughly every week. A copy of all homeworks can be accessed here. The dates of the quizzes will be updated as the semester progresses. Collaboration in the homework is permitted. The homework won't be turned in, instead there will be quizzes to test you on the homework exercises. There will be approximately 9 quizzes throughout the semester (roughly every week). The quizzes will consist of 2 or 3 problems which will be similar to the questions assigned on the homework assignment that week (but not necessarily identical).

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 will be outside of class so that you have more time to try the problems.

The tentative dates for the exams:

The first midterm will be on Wednesday September 26.
The second midterm will be on Wednesday November 7.
The third midterm will be on Friday December 7.
The final exam will be on Monday December 17 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 believe that you need accommodations for a disability, please consult with The Learning and Teaching Center. Since accommodations may require early planning and are not retroactive, please contact the center as soon as possible. For details about the services for students with disabilities and the accomodations process, visit 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 Teryn Robinson at the Learning and Teaching Center.

Last modified on August 30, 2018.