Topics in Algebra (SU22)

Course Info:

• Lectures: Monday, Wednesday, Friday, block 11 (11:30 - 12:35 p.m. EDT)
• x-period: Tuesday, block 11X (12:15 - 1:05 p.m. EDT)
• Dates: 24 June 2022 - 24 August 2022
• Room: Kemeny 007
• Zoom Link: Use navigation bar.  Email if you have any problems.
• Instructor: John Voight
• Instructor office: Kemeny 341
• E-mail: jvoight@gmail.com
• Office hours:
  • Wednesdays, 3:30 - 5:00 p.m.
  • Thursdays, 4:00 - 5:00 p.m.
  • ...or please make an appointment by email!
• Course Web Page: https://canvas.dartmouth.edu/courses/53762 (or http://www.math.dartmouth.edu/~m31x22/ redirects)

• Prerequisites: Math 22 or 24.  If you are unsure about your preparation, please talk to the instructor!
• Required Texts:
  • Laura L. Dos Reis and Anthony J. Dos Reis, Abstract Algebra: A Student-Friendly Approach, 1st ed., 2017.  See errata.
    
  • David S. Dummit and Richard M. Foote, Abstract Algebra, 3rd ed., 2003.  See errata.
    
• Grading: Grade will be based on daily homework, weekly homework, a short exam, a final paper, and a final exam.

Course Catalogue Description:

This course will provide an introduction to fundamental algebraic structures, and may include significant applications. The majority of the course will consist of an introduction to the basic algebraic structures of groups and rings. Additional work will consist either of the development of further algebraic structures or applications of the previously developed theory to areas such as coding theory or crystallography.

As a result of the variable syllabus, this course may not serve as an adequate prerequisite for MATH 81. Students who contemplate taking MATH 81 should consider taking MATH 71 instead of this course.

Learning Outcomes:

By the end of this course, you should be able to:

1. Understand of the basic structures of algebra: define terms, explain their significance, and apply them in context;
2. Solve mathematical problems: utilize abstraction and think creatively; 
3. Write clear mathematical proofs: recognize and construct mathematically rigorous arguments.

Additional Pages:

1. Academic Honor Principle
2. Expectations
3. Homework
4. Consent to Record
5. Student Accessibility Needs
6. Mental Health
7. Title IX
8. Religious Observances
9. Additional Support for your Learning