MAT 5173 — Algebra I Fall 2026 · UT San Antonio
The opportunity for development of basic theory of algebraic structures. Areas of study may include monoids, semigroups, groups, isomorphism theorems, free groups, group extensions and group actions, Sylow theorems, group chains and composition series, nilpotent and solvable groups, cohomology of groups.
MAT 4233 or consent of instructor.
3
Traditional in-person
| Duration | Wed 19 Aug – Thu 3 Dec |
| Campus | Main Campus |
| Location | MH 3.03.10 |
| Time | Mon Wed 7:30PM–8:45PM |
By the end of this course you should be able to:
Eduardo Dueñez, Associate Professor of Mathematics.
| Department | Mathematics |
| Office | FLN 4.01.11 |
| Student hours | Mon 5:30PM – 6:30PM & Tue 1:30PM – 2:30PM |
| eduardo.duenez@utsa.edu | |
| Homepage | https://supernumero.us/about |
Email is the preferred method of communication.
| Component | Weight | |
|---|---|---|
| Q&A sessions | 40% | 4 sessions, 10% each; none dropped |
| Problem sets | 15% | 4 sets, 3.75% each; graded for completeness |
| Midterm Exam 1 | 20% | In class, Wed 7 Oct |
| Midterm Exam 2 | 25% | Wed 2 Dec in class |
Four class meetings throughout the semester (roughly every other Wednesday except when adjacent to an exam) will be Q&A sessions in which each student will be asked to explain and defend their solution to a homework problem submitted as part of a written assignment. You will only be asked questions related to an assigned problem and about the solution you submitted.
Each Q&A session is scored 0–3:
A correct answer you cannot explain is worth less than an explainable honest failure.
Note: A low Q&A average caps the course grade, whatever the other components come to:
(An average below 1.0 is of course also below 1.5; in that case the ‘D’ cap is the one that applies.)
Four sets of theoretical problems. Maximum six pages.
Computational (SageMath) material is supplementary and entirely optional: it is never part of a problem set or a Q&A session, and it is not graded.
Each item will be scored only based on the degree of completion (not on correctness): 2 for a nominally complete solution, 1 for a clearly partial one, 0 for nothing submitted or for obvious filler with no substance.
Note: Any submission containing non-human-readable content, stray characters, or artifacts revealing non-proofread AI output scores 0 for that item.
AI assistance is allowed in preparing work for submission, as are any solution keys, collaboration, and internet sources. You are ultimately responsible for your submissions; any part of your work that has clearly not been proofread (e.g., includes non-human readable characters or LLM artifacts) automatically earns a zero grade. Include one line noting what resources you used in your submission.
This policy is by design, and it reflects how the course is graded: 85% of the grade comes from Q&A sessions and in-class exams where only what is truly understood and can be explained counts. Assignments submitted but not written/understood by you result in failing grades in Q&A sessions and exams. Use AI to learn faster —not to prepare and turn in papers you cannot defend, blocking you from passing exams as well.
All audiovisual (or audio only, or video only) recordings of lectures are explicitly forbidden; all uses of AI agents or apps to capture, process, or analyze any lecture contents are strictly forbidden. The only limited exceptions are explicitly allowed recordings per official memorandum of the office of Student Disability Services. Under no circumstances is any processing or analyzing of such recordings allowed. Any sharing of confidential course materials with individuals who are not enrolled students in the course is a violation of FERPA privacy laws.
Both exams are traditional in-class (written and closed book). Exams are based primarily on the assigned problem sets —expect some context and phrasing to differ from the homework, plus a minority of other unseen problems. Memorizing solutions will not result in good exam grades; preparing by understanding the assigned problems will make the exams straightforward and earn high Q&A grades as well.
No extensions on problem sets. A single missed Q&A session in the semester may be made up during office hours within seven days (no documentation is required). No Q&A scores are dropped.
| Grade | Range | Grade | Range |
|---|---|---|---|
| A | [90%, 100%] | A- | [85%, 90%) |
| B+ | [80%, 85%) | B | [76%, 80%) |
| B- | [72%, 76%) | C+ | [69%, 72%) |
| C | [65%, 69%) | C- | [60%, 65%) |
| D | [50%, 60%) | F | [0%, 50%) |
Expect an average of about 9 hours per week, and no fewer than 7.
This is a writing-intensive course. Standard professional standards for technical writing (mathematical writing) apply. The style is mathematical prose written for a human reader, An otherwise “correct” argument presented as a disorganized or unintelligible pile of symbols is not a solution will be returned without grading and earn no credit. For detailed requirements and required reading refer to the Writing Mathematics page.
Each student should be intimately familiar with the contents of any work submitted for grading. The instructor has the right to request adequate verbal explanation of methodology and content for any submitted work. Credit will not be awarded when such an explanation is requested but not satisfactorily provided.
| Date | Topic |
|---|---|
| Wed 19 Aug | Lecture — Course launch; groups and subgroups |
| Mon 24 Aug | Lecture — Permutation groups; cyclic groups; the order of an element |
| Wed 26 Aug | Lecture — Cosets, normal subgroups and homomorphisms |
| Mon 31 Aug | Lecture — The isomorphism theorems |
| Wed 2 Sep | Lecture — Direct products |
| Wed 9 Sep | Lecture — Quotient groups and the isomorphism theorems; direct products |
| Mon 14 Sep | Lecture — Quotient groups and the isomorphism theorems; direct products (continued) |
| Wed 16 Sep | Q&A (Due: Set 1) |
| Mon 21 Sep | Lecture — Rings: basic definitions and properties; ideals, homomorphisms and quotient rings |
| Wed 23 Sep | Lecture — The isomorphism theorems for rings; maximal and prime ideals |
| Mon 28 Sep | Lecture — Polynomial rings; unique factorization |
| Wed 30 Sep | Lecture — Polynomial rings and unique factorization (continued) |
| Mon 5 Oct | Q&A (Due: Set 2) |
| Wed 7 Oct | Exam — Midterm Exam 1 — Sets 1 and 2 |
| Wed 14 Oct | Lecture — Principal ideal domains and Euclidean domains; rings of fractions; irreducible polynomials |
| Mon 19 Oct | Lecture — Field extensions; degree; simple extensions |
| Wed 21 Oct | Lecture — Splitting fields; algebraic closures |
| Mon 26 Oct | Lecture — Separability; normal extensions; finite fields |
| Wed 28 Oct | Lecture — Separability, normal extensions and finite fields, continued |
| Mon 2 Nov | Q&A (Due: Set 3) |
| Wed 4 Nov | Lecture — Affine varieties; V(I) and I(V); the Nullstellensatz and the Hilbert basis theorem (stated, not proved) |
| Mon 9 Nov | Lecture — Fixed fields and Galois groups |
| Wed 11 Nov | Lecture — The fundamental theorem of Galois theory |
| Mon 16 Nov | Lecture — The fundamental theorem, continued; computing Galois groups |
| Wed 18 Nov | Q&A (Due: Set 4) |
| Mon 23 Nov | Lecture — Survey: the unsolvability of the quintic |
| Mon 30 Nov | Review — Review — the exam pool |
| Wed 2 Dec | Exam — Midterm Exam 2 — Sets 3 and 4 |
Readings for each meeting are on the Weekly Schedule (also available as a printable PDF).
The ombudsperson is an advocate who investigates complaints about a specific section or instructor and attempts to resolve them through mediation. Comments or complaints sent to this person will be brought to the attention of department leadership, who will follow up. If you have questions about the logistics of your class, please contact the instructor.
Contact Ilse Rosales Martinez at ilse.rosalesmartinez@utsa.edu.
As the instructor of this course, I may record meetings and lessons. You are expected to follow appropriate University policies and maintain the security of passwords used to access recorded lectures. Recordings may not be published, reproduced, or shared with those not in the class. If the instructor or a UTSA office plans any other uses for the recordings, consent of the students identifiable in the recordings is required before such use unless an exception is allowed by law.
The syllabus is subject to change at the instructor’s discretion. Any changes or corrections to the course materials, assignment dates, or other updates will be communicated to students ahead of time. You are responsible for checking Canvas for corrections or updates to the syllabus.