Math 301: Abstract Algebra I

 

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 group-theoretic properties and identify these properties in familiar groups.

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

 

Method of Instruction

 

1.     Lectures will emphasize 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 groups is cyclic…

2.     Exam question: Show that N is a normal subgroup of G. Prove that G/N is isomorphic to H.

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


Determine the proportion of students answering the questions correctly

 

Textbook

“Abstract Algebra: theory and applications,” by Thomas W. Judson, 2016 edition.

This is an open-source text available for download at no cost. A bound, published version is for sale at the University Bookstore. (Note: the 2017 edition is also available. We will use the 2016 version in Spring 2018.)

Exams and Grading

The class will require weekly homework submissions, 2 in-class exams, and a final exam. Exam dates and content will be determined by the individual instructor. Class components will be weighted as follows.

Homework

45%

Exam 1

15%

Exam 2

15%

Final Exam

25%