f16-mas6331-syllabus

MAS 6331 Algebra 1

Fall 2016

Section Period Meeting Time Room
14BA MWF 3rd 9:35 – 10:25 LIT 221

Professor Alexandre Turull

480 Little Hall
(352) 294-2337
turull@ufl.edu

Office Hours

Monday Tuesday Wednesday Thursday Friday
12:50 – 1:40 12:50 – 1:40 12:50 – 1:40

 

Also by appointment

Prerequisites:

MAS 5312 Introduction to Algebra 2, or equivalent.

Textbook:

Algebra, by Thomas W. Hungerford.

Content:

As well as a subject in its own right, Algebra is the language of modern mathematics. As such, it plays a role for Mathematics, similar to the role Mathematics plays for all of Science. Hence, the study of Algebra is indespensible for serious work in modern mathematics.MAS 6331 Algebra 1 and its continuation MAS 6332 Algebra 2 are designed to introduce the student to the basic concepts and results of Modern Algebra. Having become familiar with basic algebraic thinking (in MAS 5312 or elsewhere), the student is expected to learn the basics of algebra as a language for all of mathematics. Hence, the student will learn about free objects, tensor products, localization, projective modules, injective modules, exact sequences, symmetric functions , Galois groups, simple rings and algebras, semi-simple rings and algebras, fractional ideals, Dedekind domains, the Jacobson radical , algebraic sets, Hilbert’s Basis Theorem , Hilbert’s Nullstellensatz, etc.

We will begin with Galois Theory, the theory that gave rise to modern algebra. This will include the study of solutions of algebraic equations by radicals, as well as Hilbert’s Theorem 90. We will then continue with Group Theory, with an emphasis on categorical concepts such as free groups, generators and relations, direct products and coproducts. These concepts readily generalize to other structures. We will prove the Krull-Schmidt Theorem for direct products of groups, and Hall’s Theorem on finite solvable groups.

The second semester will begin with a review of rings and ideals. Next, we will discuss Modules, including free , projective and injective modules. Then, we will discuss commutative rings and modules, including chain conditions, Dedekind domains, and algebraic sets and Hilbert’s Nullstellensatz. This will be followed by the study of simple and primitive non-commutative rings, the Jacobson radical, semisimple rings, algebras and division algebras.

Format and grade:

Lectures. Homework will be assigned regularly and discussed in class. Homework will not be graded. The grade will be earned through oral presentations and discussions, and a final test.

Tests:

Final: Thursday, December 15, 3:00 p.m. — 5:00 p.m.

UF grading policies for assigning grade points

See https://catalog.ufl.edu/ugrad/current/regulations/info/grades.aspx

Students with disabilities

Students with disabilities requesting accommodations should first register with the
Disability Resource Center (352-392-8565, http://www.dso.ufl.edu/drc/) by providing appropriate documentation. Once registered, students will receive an accommodation letter which must be presented to the instructor when requesting accommodation. Students with disabilities should follow this procedure as early as possible in the semester.

Attendance policy

Students are expected to attend class regularly.

The UF policy on attendance is here: https://catalog.ufl.edu/ugrad/current/regulations/info/attendance.aspx

Honor Code

UF students are bound by The Honor Pledge which states, “We, the members of the University of Florida community, pledge to hold ourselves and our peers to the highest standards of honor and integrity by abiding by the Honor Code.”

On all work submitted for credit by students at the University of Florida, the following pledge is either
required or implied: “On my honor, I have neither given nor received unauthorized aid in doing this assignment.”

The Honor Code (http://www.dso.ufl.edu/sccr/process/student-conduct-honor-code/) specifies a number of behaviors that are in violation of this code and the possible sanctions. Furthermore, you are obliged to report any condition that facilitates academic misconduct to appropriate personnel. If you have any questions or concerns, please consult with the instructor of this class.

Website:

https://people.clas.ufl.edu/turull/f16-MAS6331-syllabus