Prerequisite
MAS 4302, or consent of the instructor.

Text
Abstract Algebra: A Geometric Approach, Theodore Shifrin, 1st edition.

Content
Selected material from Chapters 5,6, and 7, plus supplemental material.

Objectives
MAS 4303 is a sequel to MAS 4302. Below is the objectives-statement for MAS 4302.

This course is designed for undergraduate mathematics majors and represents an introductory theory-based course in abstract algebra. The subject grew out of arithmetic and geometry and its roots go back hundereds of years. However, the abstract algebra course of today is substantially a product of efforts that took place in the 20th century to organize together algebra topics that should be "most basic" to a standard education in higher mathematics. In general this means an introduction to certain mathematical structures such as groups, rings, fields, and vector spaces. In practice there is considerable choice to be made because these mentioned topics are very broad and it would take far more than one or two semester to do them justice.

A major objective is to introduce students to the language and precision of modern abstract algebra. This means that the course will be proof-based, in the sense that students will be expected to understand, construct, and write proofs. A challenge for all students of mathematics is to balance the understanding with the communication. There is a tendency to think you are finished once you see why a mathematical statement is true or false. In fact you are just half-way there because constructing a legitimate proof involves different skills and expertise than the discovery part of the process. In this course both angles of problem-solving will be stressed.

Applications of abstract algebra are increasingly important in certain areas, for example in communication theory, electrical engineering, computer science, and cryptography. As the course proceeds applications will be introduced, and in some cases covered carefully. When applying algebra to a field other than mathematics the emphasis tends to shift away from mathematical rigor and towards practical constructions. This phenomenon, when it occurs, will tweak the goals of the course. Computational issues and algorithms upstage the formalality of proof in most applications, though logical precision is still important because algorithms must perform as expected in order to be useful.

Grading
Grades will be based on homework and at least one exam (probably take-home). Homework will be assigned regularly, collected, and graded. The graded homework will count for about one half of your grade, the exam(s) the other half. Homework assignments will be posted at my web site.

Attendance and the Academic Honor System
Class attendance is expected and students will be responsible for any course related information arising during regular class times. Students are also expected to adhere to FSU's Academic Honor System, a copy of which may be found in the Student Handbook.

American Disabilities Act Statement
Students with disabilities needing academic accommodations should: 1) register with and provide documentation to the Student Disability Resource Center (SDRC); 2) bring a letter to the instructor from SDRC indicating you need academic accommodations. This should be done within the first week of class.