← Teaching
Abstract Algebra I — Fall 2026
MATH 3551, Section A · MWF 12:00–12:50, Lafayette L107 · first class Wednesday, September 9
Taylor Dupuy · Innovation E439 · office hours Wednesday 8:30–9:20AM
Lectures
Text
- Dummit and Foote — Abstract Algebra, 3rd edition (Wiley), ISBN 0-471-43334-9.
Errata.
Exam Schedule
- Midterm 1 (Monday, October 12, in class —
§§0.1–0.3, §§1.1–1.6, §2.1, and §§2.3–2.5)
- Midterm 2 (Friday, November 6, in class —
§1.7, §2.2, and §§3.1–3.3)
- Midterm 3 (Monday, November 30, in class —
§§3.4–5.2)
- Final (Thursday, December 17, 10:30 AM–1:15 PM, Lafayette L107 — cumulative)
Practice Exams
Open an exam below to choose a question sheet or its complete solutions.
Midterm 1 — current coverage: §§0.1–0.3, §§1.1–1.6, §2.1, and §§2.3–2.5
Midterm 2 — current coverage: §1.7, §2.2, and §§3.1–3.3
Midterm 3 — current coverage: §§3.4–5.2
Final Exam
Suggested Problems
Each section of the suggested-problems PDF opens with warm-up computations
and then lists the Dummit and Foote exercises below. Nothing is collected or graded.
Part I — through Midterm 1
(§§0.1–0.3, §§1.1–1.6, §2.1, and §§2.3–2.5)
- §0.1 Basics — 4, 6
- §0.2 Properties of the Integers — 1–5, 10, 11
- §0.3 Z/nZ: The Integers Modulo n — 3–9
- §1.1 Basic Axioms and Examples — 1, 5, 11, 20, 22, 25, 26, 32
- §1.2 Dihedral Groups — 1, 2, 3, 4, 5, 6
- §1.3 Symmetric Groups — 1, 2, 3, 4, 5, 14, 15, 18
- §1.4 Matrix Groups — 1, 2, 3, 4, 5, 7. Required independent reading; included on Midterm 1.
- §1.5 The Quaternion Group — 1, 2, 3. Required independent reading; included on Midterm 1.
- §1.6 Homomorphisms and Isomorphisms — 1, 2, 4, 6, 7, 9, 14, 20
- §2.1 Subgroups: Definition and Examples — 1, 2, 3, 4, 5, 6, 8, 10
- §2.3 Cyclic Groups and Cyclic Subgroups — 1, 2, 3, 4, 5, 8, 10, 16
- §2.4 Subgroups Generated by Subsets of a Group — 1, 2, 3, 6
- §2.5 The Lattice of Subgroups of a Group — 1, 2, 3, 4, 5, 6
Part II — through Midterm 2
(§1.7, §2.2, and §§3.1–3.3)
- §1.7 Group Actions — 1, 2, 3, 4, 5, 6, 12
- §2.2 Centralizers and Normalizers, Stabilizers and Kernels — 1, 2, 3, 4, 5, 6, 7, 10
- §3.1 Quotient Groups and Homomorphisms: Definitions and Examples — 1, 2, 3, 4, 6, 7, 14, 36, 37
- §3.2 More on Cosets and Lagrange's Theorem — 1, 2, 4, 5, 6, 8, 11, 16
- §3.3 The Isomorphism Theorems — 1, 2, 3, 7
Part III — through Midterm 3
(§§3.4–5.2)
- §3.4 Composition Series and the Hölder Program — 1, 2, 3, 4, 5
- §3.5 Transpositions and the Alternating Group — 1, 2, 3, 4, 5, 6, 7
- §4.1 Group Actions and Permutation Representations — 1, 2, 3, 4, 7, 8, 10
- §4.2 Cayley's Theorem — 1, 2, 3, 4, 7, 8, 9, 10
- §4.3 The Class Equation — 1, 2, 3, 4, 5, 6, 13
- §4.4 Automorphisms — 1, 2, 3, 4
- §4.5 The Sylow Theorems — 1, 2, 3, 4, 5, 13, 19, 24, 26
- §4.6 The Simplicity of An — 1, 2
- §5.1 Direct Products — 1, 2, 3, 4
- §5.2 The Fundamental Theorem of Finitely Generated Abelian Groups — 1, 2, 3
Part IV — final only (§5.4, §5.5, §6.1)
- §5.4 Recognizing Direct Products — 1, 2, 3, 4
- §5.5 Semidirect Products — 1, 2
- §6.1 p-groups, Nilpotent Groups, and Solvable Groups — 1, 2
Previous versions of this course
Notes