Egbert Rijke

Introduction to Abstract Algebra

Math 401 — Spring 2026

• Meeting time and place: Mon/Wed 12:00-1:15PM, Bloomberg 276
• Instructor: Egbert Rijke (erijke1[at]jh.edu)
• Office: Krieger Hall 405
• Office Hours: Tue 3:00-4:00PM and Thu 2:00-3:00PM, or by appointment.
• Teaching Assistant: Jiacheng Liang, (jliang66[at]jh.edu)

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Course Policies

• Homework: There will be weekly homework, counting to 50% of the grade.
• Exams: There will be one midterm and a final, which each count 25% of the grade. In both cases I will prepare practice exams.
• Letter grade: Any score of 75% or higher will be worth an A.
• Homework extension policy: If you need an extension for any reason, please send us an email. Extensions of 48h will always be granted, provided that you requested one. Longer extension will be considered on a case-by-case basis.

Remarks: Mistakes are part of learning, so it is important to me that there is room for making mistakes and still earn a top grade. We’re here to facilitate your learning.

You’re welcome to discuss and collaborate on homework with your friends. Anything that facilitates your learning is greatly encouraged. But submitted homework must not be copied, and should be your solution in your own words. AI generated homework solutions will not be graded and will be reported and scored 0.

Overview of the course

Lecture 1, January 21 2026, Platonic Solids

[Download Handout 1, Platonic Solids]

Homework for week 1: 1.1, 1.3, 1.5, 1.7, 1.9.

Lecture 2, January 28 2026, Axioms of a Group

Homework for week 2: 2.3, 2.5, 2.7, 2.8, 3.2.

Lecture 3, February 2 2026, Dihedral Group

Lecture 4, February 4 2026, Subgroups

Homework for week 3: 5.1, 5.3, 5.5, 5.8, 5.12.

Lecture 5, February 9 2026, Permutations

Lecture 6, February 11 2026, Isomorphisms

Homework for week 4: 6.4, 6.6, 7,5, 7.7, 7.12

Lecture 7, February 16 2026, Cayley’s Theorem

Lecture 8, February 18 2026, Matrix Groups

Homework for week 5: 8.6, 8.7, 8.8, 8.9, 9.1

Lecture 9, February 23 2026, Products

Lecture 10, February 25 2026, Lagrange’s Theorem

Homework for week 6: 10.7, 10.11, 11.2, 11.3, 11.7.

Lecture 11, March 2 2026, Partitions

Lecture 12, March 4 2026, Cauchy’s Theorem

Lecture 13, March 9 2026, Conjugacy

Lecture 14, March 11 2026, Quotient groups

Spring Break, March 16-20 2026

Lecture 15, March 23 2026, Homomorphisms

Midterm 1, March 25 2026

The material tested on the midterm consists of lectures 1 through 14, up to and including quotient groups. A practice midterm with questions much like the midterm questions will be provided in the week of Friday March 6th. Office hours on Tuesday March 24th will be 2-4pm.

Lecture 16, March 30 2026, Actions, orbits and stabilizers

Lecture 17, April 1 2026, Counting orbits

Lecture 18, April 6 2026, Finite rotation groups

Lecture 19, April 8 2026, The Sylow theorems

Lecture 20, April 13 2026, Finitely generated abelian groups

Lecture 21, April 15 2026, Row and column operations

Lecture 22, April 20 2026, Automorphisms

Lecture 23, April 22 2026, The Euclidean group

Final exam, April 27 2026