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# Math 301: Abstract Algebra I

Course Coordinator: Clifford Bergman (cbergman@iastate.edu)

## Prerequisites

Math 166 (Calculus II), Math 317 or 407 (Linear Algebra), and Math 201 (Introduction to Proofs)

A student who has taken Math 207 in lieu of 317 may be prepared for the course. Discuss with the instructor. While the construction of sound proofs will be a central component of the course, a student with no previous experience writing simple proofs may find the course overly challenging.

## Learning Outcomes

Upon completion of this course, students…

1.     Will be familiar with properties of the integers such as prime factorization, divisibility, and congruence

2.     will be able to reason abstractly about mathematical structures

3.     will recognize and comprehend correct proofs of formal statements and be able to formulate proofs clearly and concisely

## Learning Objectives

1.     Students will be able to perform computations involving divisibility of integers.

2.     Students will be asked to identify ring-theoretic and group-theoretic properties and identify these properties in familiar rings and groups.

3.     Students will provide proofs to simple assertions of ring- and group-theoretic principles.

## Method of Instruction

1.     Lectures will emphasize ring- and group-theoretic properties. Weekly homework assignments will ask students to recognize these properties.

2.     Weekly homework assignments.

3.     Numerous proofs will be presented in class. Students will construct proofs on weekly homework assignments.

## Assessment

1.     Exam question: Which of the following rings is an integral domain…

2.     Exam question: Write the permutation as a product of disjoint cycles. Does the permutation lie in the alternating group?

3.     Exam question:  Prove the following assertion about rings…

Determine the proportion of students answering the questions correctly

## Textbook

“Abstract Algebra, An Introduction,” by Thomas W. Hungerford, third edition.

The text is available from the University Bookstore in both hardcopy and electronic format

## Course Topics

The course will cover roughly chapters 1-5 and 7 of the text.  Here is a list of topics.