Math 401 (Spring 2026)

• Lectures: MW 11:45am-1pm, Gross Hall 304B
• Office hours: Thu 11:45am-1pm, Fri 2pm-3:45pm, Physics 274E, or by appointment
• Textbook: Algebra (2nd Ed.) by Michael Artin
• Email: danielle.wang@duke.edu
• Gradescope

Syllabus

See syllabus document.

Problem sets

• Problem set 1 due Jan 16
• Problem set 2 due Jan 23
• Problem set 3 due Jan 30
• Problem set 4 due Feb 13
• Problem set 5 due Feb 23 (Monday)
• Problem set 6 due Mar 2 (Monday)
• Problem set 7 due Mar 9 (Monday)
• Problem set 8 due Mar 20 (Friday)
• Problem set 9 due Apr 3 (Friday)
• Problem set 10 due Apr 10 (Friday)
• Problem set 11 due Apr 22 (Wednesday)

Midterm 1

Monday, February 9

• Practice exam 1, Solutions to practice exam 1
• Solutions to bonus problems from psets 1-3

Midterm 2

Monday, March 30

• Practice exam 2, Solutions to practice exam 2
• Solutions to bonus problems from psets 5-8

Final Exam

Friday, May 1

• Galois theory review, Solutions to Galois theory practice problems, but the final will cover material from the whole semester.
• Solutions to bonus problems from psets 9-11 + additional info

Schedule

Here are notes which will be updated as we progress.

• Jan 7: 2.3, 2.7, 2.9
• Jan 12: 1.5, 2.1-2.4, 2.11
• Jan 14: Dihedral group, 2.5, 2.6
• Jan 21: 2.8, 2.11
• Jan 26: 2.10, 2.12
• Jan 28: 2.10, 6.7, 6.8
• Feb 2: 6.9, Burnside’s lemma, 6.11
• Feb 4: 7.1, 7.2, 7.3
• Feb 11: 7.4, 7.5, conjugacy classes in A_5
• Feb 16: 7.7 Applications of Sylow theorems
• Feb 18: 6.10, 7.6, 7.7 Proof of Sylow theorems
• Feb 23: 11.1, 11.2, 11.3
• Feb 25: 11.3, 11.4
• Mar 2: 11.4, 11.5, 11.6
• Mar 4: 11.7, 11.8
• Mar 16: 11.8, prime ideals
• Mar 18: 12.1, 12.2
• Mar 23: 12.3
• Mar 25: 14.1, 14.2, 14.7 Statement of structure theorem
• Apr 1: 15.1, 15.2, 15.3
• Apr 6: 15.4, 15.6, 15.7
• Apr 8: 15.8, 16.1, 16.2
• Apr 13: 16.4, 16.5, 16.6
• Apr 15: 16.7, 16.8
• Apr 20: 16.8, 16.9, 16.10
• Apr 22: 16.11, 16.12