Program Overview

Program Overview

The Math 31 program provides an introduction to fundamental algebraic structures, focusing on groups, rings, and fields. The course also explores the representation of groups as Cayley graphs and includes a hands-on project to solve the 2x2 Rubik's cube and understand its connection to abstract algebra.

Course Details

General Information

• Instructor: Bjoern Muetzel
• Office: 318 Kemeny Hall
• Office Hours: Monday 3:30-5 and Tuesday 2-3:30
• Lectures: MWF 11:30-12:35 in 004 Kemeny Hall
• X-hour: Tuesday 12:15-1:05 in 004 Kemeny Hall

Content

The course covers the study of groups, rings, and fields, with an additional focus on the geometric representation of groups through Cayley graphs. A key component of the course is a project where students solve the 2x2 Rubik's cube and analyze its connection to abstract algebra.

Textbook

• Charles C. Pinter: A Book of Abstract Algebra, 2nd edition

Exams and Assessments

• Midterm Exam I: Thursday, October 4 from 4:30-6:30 pm in KH 105
• Midterm Exam II: Thursday, October 25 from 4:30-6:30 pm in KH 105
• Solving the cube: Tuesday, November 6 from 12:15-1:05 pm in KH 004
• Essay about the cube: Due Thursday, November 15 at 4 pm in KH 318
• Final Exam: Sunday, November 18 from 3-6 pm in KH 007

Grades

The course grade is based on:

• Written homework: 20%
• Essay about the cube: 5%
• Solving the cube: 5%
• Midterm exams and final exam, with two grading options:
  • Option 1: Midterm I (15%), Midterm II (20%), Final Exam (35%)
  • Option 2: Midterm I (23.33%), Midterm II (23.33%), Final Exam (23.33%)
  • The better score from the two options will be used.

Homework Policy

• Written assignments are assigned weekly.
• Extensions may be granted if requested before the due date.
• Late homework will not be accepted.
• The lowest homework grade will be dropped.
• Solutions must be written in English, with references to theorems or propositions used from the text and class.

The Honor Principle

Academic integrity is core to the mission. Collaboration on homework is permitted but no copying is allowed. On exams, no assistance is allowed from any source except the professor. Matters of clarification should be directed to the professor.

Religious Observances

Students with religious observances that conflict with course participation should meet with the instructor by the end of the second week to discuss accommodations.

Disabilities

Students with disabilities should see the instructor privately as early in the term as possible and must consult the Student Accessibility Services office for authorized services. Confidentiality is maintained.