## MAT351 Modern Algebra I

 Kevin J. CarlinOffice:  Fo 113 M-F 2:30-3:45 Telephone: 7563E-mail: kcarlin@assumption.edu

### Materials

Fraleigh, A First Course in Abstract Algebra, seventh edition, Addison-Wesley, 2003.

### Calculator Policy

Calculators may not be used in this course.

### Homework Journal

The homework journal is intended to be a complete record of your work outside class. None of your work should be done on scrap paper, erased, replaced, or destroyed. No one likes making mistakes. We want to forget them. That often means we repeat the same mistakes over and over. The goal is to be able to work a problem correctly from beginning to end, but the only way to reach that goal is to make mistakes, identify them, and correct them.

All of the work for a particular homework assignment should be kept together. Because you will work on the same homework topic at different times, you will need a ring binder and a supply of loose-leaf paper. If you use the same binder for class notes, use a separate section for your homework. Spiral-bound notebooks will not be accepted when the journal is collected.

When we go over a problem in class, compare the class notes to your own work in the journal. If there is a mistake, add a note to yourself explaining what went wrong. After class, work from the correction and see if you can finish the problem on your own.

To prepare for quizzes or exams, you should practice by doing whole problems. These practice problems should be included in the homework journal. Concentrate on the general techniques that you will need for the topic rather than trying to memorize a particular homework problem.

When you need help, bring your homework journal with you to my office hours or to the Academic Support Center.

### Topics

Preliminaries: Sets, functions, and equivalence relations.

Groups: binary operations, isomorphism, identities and inverses, group axioms, abelian groups, powers, subgroups, order, cyclic groups, generators, direct products, finitely generated abelian groups.

Permutations and Cosets: permutations, symmetry groups, Cayley’s Theorem, cycles, the symmetric group, the alternating group, left and right cosets, Lagrange’s Theorem.

Homomorphisms: images and kernels, normal subgroups, factor groups, the fundamental theorem, conjugation, simple groups, the center and commutator subgroups.

Rings and Fields: ring axioms, homomorphisms and isomorphisms, commutative rings, fields, zero divisors, integral domains, fields of quotients, rings of polynomials, factor rings, prime and maximal ideals.

There will be four quizzes, two exams (October 17 and December 5), and a cumulative final exam. The homework journal will be collected near the end of the semester. Your final grade will be based on 400 points:

 4 Quizzesand Homework Journal Best 4 @ 20 points 80 Exams 2 @ 100 points 200 Final Exam 1 @ 120 points 120 400

Grades are based on partial credit and will be scaled. Typically, the scale is A- = 75%, B- = 60%, C- = 50%, D- = 35%.

Make-up of any graded work due to serious illness or other emergency is possible only with prior or immediate notice and will be granted at my discretion. Unexcused absence from any exam will result in a failing grade for the course.

### Learning Objectives

• Students will understand the concept of an abstract group. They will know the principles and techniques of group theory. Students will be able to apply these in a variety of situations.

• Students will know the definitions and elementary properties of rings and fields.

### Course Description

MAT 351 Modern Algebra I
An introductory course in abstract algebra. This course will cover the theory of groups and the definitions of rings and fields. Prerequisite: MAT 202.

### Academic Honesty Policy

The college's academic honesty policy will be enforced as described in the Student Academic Honesty Policy booklet. Any use of a calculator in this course is a violation of the honesty policy.

### College ADA Policy

Assumption College provides accommodation to any student with documented disabilities. If you believe that you are entitled to accommodation, please contact the Director of Disability Services (ext. 7500).