# Math 331. Modern Algebra II

Spring 2019

• Instructor:         Enrique Treviño

• Lectures:           MWF 10:00 - 10:50 am in Young Hall 117

• Office Hours:    MWF between 11:00am to 12pm. 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 are here:
Homework

Course Description

Additional topics in modern or linear algebra such as field extensions, Galois Theory, group conjugacy, modules, eigenvalue theory, dual spaces, and unitary spaces. Prerequisite: Mathematics 330 or permission of the instructor. ( 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. 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 ring and field theory. The highlight will be learning Galois Theory and applying it to classic problems such as
• Can an angle be trisected with straightedge and compass?
• Can a cube be doubled by straightedge and compass?
• Is there a formula involving only sums, products, quotients and radicals to find the roots of any polynomial of degree n? Clearly this is true for n = 2 as we have the quadratic formula. Is it always possible?

Student Learning Outcomes

Main Goals:
• Understand what a ring is.
• Understand what a field is.
• Be able to prove that something is a field.
• Understand what a field extension is.
• Understand properties of finite fields.
• Understand Galois Theory
• Be able to do proofs involving all of these algebraic structures.
• Understand the answers to the three classical problems listed above.

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. The homework will be posted here. Collaboration in the homework is permitted, however it must be your own.

Each homework problem should appear on its own page of a sheet of paper. This is because I might randomly select a subset of the problems to be graded. By having each problem on its own page, it is easier to grade only what's relevant. As a corollary, you should not staple your homework assignments.

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 February 20.
• The second midterm will be on Wednesday April 10.
• The third midterm will be on Monday April 29.
• The final exam will be on Saturday May 4 from 1:30pm to 4:30pm.

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.