Spring 2027

Modern Algebra 2

Modern Algebra 2 covers field extensions, roots of polynomials, splitting fields, simple extensions, linear transformations, matrices, characteristic roots, canonical forms, and determinants.

offering recorded3 credits
Recorded instructors · Spring 2027 Uri Andrews3.4/5

Summary

1 / 6

Past student reviews · Uri Andrews

Homework was tough with over ten proof-based problems per week, but Andrews was flexible and accommodating with the workload.

What you’ll be able to do

  • Recall and state the formal definitions of the mathematical objects and their properties used in advanced abstract algebra (e.g., rings, modules, fields, Galois groups, etc.).

  • Use such definitions to argue that a mathematical object does or does not have the condition of being a particular type or having a particular property (e.g. whether a field extension is normal, whether a ring is a principal ideal domain, classifying abelian groups, etc.).

  • Recall and state the standard theorems of advanced abstract algebra (e.g. the fundamental theorem of Galois theory, the classification of modules over principal ideal domains, results on canonical forms of matrices, etc.) and recall the arguments for these theorems and the underlying logic of their proofs.

  • Use such theorems in the context of longer arguments by examining their premises (e.g., determining if a polynomial is solvable over a given field, finding the normal and Jordan canonical forms of linear transformations and applying these to problems in various fields like differential equations, etc.).

  • Prove or disprove statements related to the above definitions, properties, and theorems using techniques of mathematical argument (direct methods, indirect methods, constructing examples and counterexamples, induction, etc.).

  • Convey arguments using English and appropriate mathematical terminology, notation and grammar.

  • Identify applications of course content in current areas of research.

Source: UW Guide

Grade history

↗
average GPA
letter grades
A
AB
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All recorded terms · compare terms & instructors

Prerequisites

Course map

MATH 541, graduate/professional standing, or declared in Mathematics VISP (undergraduate or graduate)

    • MATH 541
    • graduate/professional standing
    • declared in Mathematics VISP (undergraduate or graduate)
    take one
MATH 542

This is a best-effort interpretation; check the catalog requirements above.

Prerequisite text tree
  • Any of
    • MATH 541
    • graduate/professional standing
    • declared in Mathematics VISP (undergraduate or graduate)

Professors

Spring 2027
Adjusted rating
RMP difficulty
captured reviews
About this rating

Raw average: 3.37/5 from 94 quality ratings. The adjusted rating blends this with the UW review average (3.66/5), weighted as 20 additional ratings. Smaller samples stay closer to that average. Each captured review is counted once in the prior; this does not correct who chooses to leave a review.

For this course: 4.8/5 raw quality · 2.8/5 difficulty · 4 reviews

RMP profile ↗ · All captured review dates; profile matched by name.

Past student reviews · Uri Andrews

Uri Andrews gave superb lectures and explained content very clearly, while assigning a heavy volume of homework. He was described as very flexible and accommodating with these assignments, and one student found him to be an incredibly kind person.

Recent recorded grades — Spring 2013: 2.92 GPA, 63.2% A/AB (n=19 letter grades); Spring 2026: 3.34 GPA, 61.3% A/AB (n=31 letter grades).

Historical instructors & teaching patterns

Past student reviews · Andrei Caldararu, Tullia Dymarz

Past students described Andrei Caldararu as an engaging lecturer who made abstract algebra fun and well-articulated, though one noted the grading could be tough. Tullia Dymarz began classes with a review of prior material and provided interesting homework, which a student found helpful for catching up and learning the material effectively.

ANDREI CALDARARU is recorded teaching in Spring 2008, Spring 2011, Fall 2018, Fall 2022. Recorded history may be incomplete and does not establish a future schedule.

DMYTRO ARINKIN is recorded teaching in Spring 2017, Fall 2017, Spring 2018, Fall 2021, Spring 2024. Recorded history may be incomplete and does not establish a future schedule.

DONALD PASSMAN is recorded teaching in Spring 2009. Recorded history may be incomplete and does not establish a future schedule.

JOSHUA MUNDINGER is recorded teaching in Spring 2025. Recorded history may be incomplete and does not establish a future schedule.

MICHAEL KEMENY is recorded teaching in Spring 2020. Recorded history may be incomplete and does not establish a future schedule.

PAUL APISA is recorded teaching in Fall 2023. Recorded history may be incomplete and does not establish a future schedule.

PAUL M TERWILLIGER is recorded teaching in Spring 2016. Recorded history may be incomplete and does not establish a future schedule.

TONGHAI YANG is recorded teaching in Fall 2025. Recorded history may be incomplete and does not establish a future schedule.

TULLIA DYMARZ is recorded teaching in Fall 2015, Spring 2019. Recorded history may be incomplete and does not establish a future schedule.

URI ANDREWS is recorded teaching in Spring 2013, Spring 2026. Recorded history may be incomplete and does not establish a future schedule.

YOUSHENG SHI is recorded teaching in Spring 2022. Recorded history may be incomplete and does not establish a future schedule.

Recorded history may be incomplete and does not establish a future schedule.

Calendar & sections

Spring 2027

Schedule loads here as you scroll.

SectionModeEnrolled / capacityWaitlist
LEC 001Classroom Instruction0 / 400

Times are Central. Select a meeting for details; export includes recorded dates for the selected sections. Enrollment reflects scan time.

Meeting source records
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Student experience

the class

Past student reviews · Uri Andrews

Students found Uri Andrews to be a talented lecturer who explains content clearly and is an incredibly kind person.

Recent recorded grades — Spring 2025: 3.30 GPA, 60.9% A/AB (n=23 letter grades); Fall 2025: 3.16 GPA, 45.5% A/AB (n=22 letter grades); Spring 2026: 3.34 GPA, 61.3% A/AB (n=31 letter grades).

difficulty & workload

Past student reviews · Uri Andrews

Homework was tough with over ten proof-based problems per week, but Andrews was flexible and accommodating with the workload.

Past student reviews · Uri Andrews

A student noted that while homework was difficult and no exam reviews were given, exams were easier and self-completion of homework could pretty much guarantee an A.

Topics

  • Field extensions, roots of polynomials, splitting fields, simple extensions
  • Linear transformations, matrices, characteristic roots, canonical forms, determinants
  • Advanced abstract algebra objects including rings, modules, fields, and Galois groups

Skills

  • Field extensions, roots of polynomials, splitting fields, simple extensions, linear transformations, matrices, characteristic roots, canonical forms, determinants.
  • Argue that a mathematical object does or does not have the condition of being a particular type or having a particular property.
  • Use theorems in the context of longer arguments by examining their premises.
  • Prove or disprove statements using techniques of mathematical argument.
  • Convey arguments using English and appropriate mathematical terminology, notation and grammar.

Grades

Latest available · Spring 2026— not enough history to project Spring 2027.

average GPA
A / AB grades
letter grades
Instructor

Grade distribution · % of letter grades

A
AB
B
BC
C
D
F

Grades over time

Through Spring 2026

More grade details Grade mix, volume & source data

Where this course fits relative to

Latest available grades · Spring 2026 · all course levels

GPA

Higher than % of other courses in this group.

Course GPAs · red marks this course’s range

letter grades

More recorded grades than % of other courses in this group.

Typical course in this group: letter grades.

About this comparison

1280 courses over the same term, each with at least 30 recorded letter grades. Cross-listed courses count once. GPA is not a measure of difficulty or teaching quality. The typical course is the median by recorded grade count; tied values are not counted as lower. Grade counts describe course scale, not unique students or typical section size.

Descriptions compare GPA with this group’s average: at least 0.20 higher or lower; otherwise close to average. Section size uses median recorded enrollment: small up to 30, mid-sized 31–99, large 100+. Lectures and discussion/lab sections are described separately.

Sources & history

UW–Madison

Catalog & offerings

Descriptions, prerequisites, and recorded course offerings.

Catalog observation history

Observations at scan time; dates do not imply when a catalog change took effect.

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Selected offering source records
MATH 542 · Spring 2027

Modern Algebra 2

Recorded 2026-10-14
Raw records 
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    "semester": "1274",
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    "offering_id": "1274:600:011686",
    "course_id": "MATH 542",
    "course_uid": "course_60c2767a206a079d3af2a1a4",
    "term_id": "1274",
    "source_course_id": "011686",
    "source_subject_id": "600",
    "title": "Modern Algebra 2",
    "credits_min": 3,
    "credits_max": 3,
    "typically_offered": "Spring"
  }
]
Rate My Professors

Student reviews

Original comments behind the course and instructor summaries.

Read original reviews
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Madgrades

Grade history

Recorded grade distributions by term, section, and instructor.

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Dataset & model

Recorded 2026-10-14

View the dataset on Hugging Face
Model outputs & technical records
Qwen/Qwen3.8-27B
LLM outputs across runs
Download part 1
Full model traces

Recorded model configuration, reasoning, and tool conversations.

Download part 1
Model & dataset provenance 
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  "model_revision": "1d4bf0f2ff6012fd82039f2fa52739d0dd7c60c0",
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  "requirements_status": "needs_review",
  "dataset_revision": "fc1811fa52e581ea57a35c0cf3343f8740a8ffbf",
  "observed_at": "2026-10-14 17:50:09.728220+00:00"
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