Spring 2027

Point-set Topology

Point-set topology covering topological spaces, connectedness, compactness, separation axioms, and metric spaces.

offering recorded3 credits
Recorded instructors · Spring 2027 Paige Hillen4.0/5

Summary

1 / 6

Past student reviews · Paige Hillen

A student found the homework fair and noted that quizzes and exams were very manageable if they stayed on top of the material.

What you’ll be able to do

  • Recall and state the formal definitions of the mathematical objects and their properties used in elementary point set topology (e.g., abstract topological spaces, metric spaces, Hausdorff spaces, compact spaces, 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., connected, compact Hausdorff).

  • Recall and state the standard theorems of point set topology (e.g., Extension theorems, Tychnoff Theorem, 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., proving a map is a homeomorphism).

  • 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 areas of modern research.

Source: UW Guide

Grade history

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average GPA
letter grades
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All recorded terms · compare terms & instructors

Prerequisites

Course map

(MATH 234 or 375) and (MATH 341, 375, 421, 467, or 521), graduate/professional standing, or declared in Mathematics VISP (undergraduate or graduate)

MATH 551 used by

“Used by” includes alternatives; linked courses may have other requirements. This is a best-effort interpretation; check the catalog requirements above.

Prerequisite text tree

Professors

Spring 2027
Adjusted rating
RMP difficulty
captured reviews
About this rating

Raw average: 5.00/5 from 6 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: 5.0/5 raw quality · 2.0/5 difficulty · 3 reviews

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

Past student reviews · Paige Hillen

Paige Hillen explains difficult topology concepts clearly and keeps lectures organized. Students found the homework fair, noting it prepared them well for manageable quizzes and exams.

Students described Hillen as a caring and wonderful professor, with one noting that the easy homework and tests might have limited deeper learning.

Recent recorded grades — Spring 2026: 3.31 GPA, 62.5% A/AB (n=40 letter grades).

Historical instructors & teaching patterns

Past student reviews · Alex Waldron, Botong Wang

Alex Waldron explained content clearly and was described as funny, though students noted a fair amount of homework. Botong Wang’s lectures were well-received for providing recorded sessions and shared notes, making the nuanced material more accessible. Exams were considered fair, and homework was tricky but manageable.

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

AMIR ASSADI is recorded teaching in Spring 2016. Recorded history may be incomplete and does not establish a future schedule.

AUTUMN KENT is recorded teaching in Fall 2014. Recorded history may be incomplete and does not establish a future schedule.

BOTONG WANG is recorded teaching in Fall 2016, Spring 2017, Spring 2018, Fall 2018, Fall 2020. Recorded history may be incomplete and does not establish a future schedule.

LU WANG is recorded teaching in Fall 2015, Fall 2017. Recorded history may be incomplete and does not establish a future schedule.

MARISSA LOVING is recorded teaching in Fall 2022, Spring 2024, Fall 2025. Recorded history may be incomplete and does not establish a future schedule.

MUSTAFA KALAFAT is recorded teaching in Fall 2007, Fall 2008. Recorded history may be incomplete and does not establish a future schedule.

NOAH SCHWEBER is recorded teaching in Spring 2019. Recorded history may be incomplete and does not establish a future schedule.

PAIGE HILLEN is recorded teaching in Spring 2026. Recorded history may be incomplete and does not establish a future schedule.

SEAN PAUL is recorded teaching in Spring 2009, Spring 2014, Spring 2015, Fall 2020, Spring 2022. Recorded history may be incomplete and does not establish a future schedule.

XIUXIONG CHEN is recorded teaching in Spring 2008. Recorded history may be incomplete and does not establish a future schedule.

YONG-GEUN OH is recorded teaching in Spring 2011. 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 / 500

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 · Paige Hillen

Paige Hillen explained difficult topology concepts clearly and kept lectures organized. Students described her as caring and a great professor for the course.

Recent recorded grades — Spring 2025: 3.03 GPA, 44.8% A/AB (n=29 letter grades); Fall 2025: 3.20 GPA, 55.4% A/AB (n=65 letter grades); Spring 2026: 3.31 GPA, 62.5% A/AB (n=40 letter grades).

difficulty & workload

Past student reviews · Paige Hillen

A student found the homework fair and noted that quizzes and exams were very manageable if they stayed on top of the material.

Past student reviews · Paige Hillen

One student felt the homeworks and tests were pretty easy, resulting in less learning than expected.

Topics

  • Topological spaces, connectedness, compactness, separation axioms, and metric spaces
  • Standard theorems of point set topology, including Extension theorems and Tychnoff Theorem

Skills

  • State formal definitions of topological objects and properties
  • Prove or disprove statements using mathematical argument techniques
  • Convey mathematical arguments with appropriate terminology and notation

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
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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 551 · Spring 2027

Point-Set Topology

Recorded 2026-10-14
Raw records 
[
  {
    "run_id": "20261014T203208-0851c9a1",
    "semester": "1274",
    "observed_at": "2026-10-14 17:50:09.728220+00:00",
    "offering_id": "1274:600:011687",
    "course_id": "MATH 551",
    "course_uid": "course_7d3f055b392d74c588d35d0b",
    "term_id": "1274",
    "source_course_id": "011687",
    "source_subject_id": "600",
    "title": "Point-Set Topology",
    "credits_min": 3,
    "credits_max": 3,
    "typically_offered": "Fall, Spring"
  }
]
Rate My Professors

Student reviews

Original comments behind the course and instructor summaries.

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Madgrades

Grade history

Recorded grade distributions by term, section, and instructor.

Explore recorded grades
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.

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Model & dataset provenance 
{
  "model": "Qwen/Qwen3.8-27B",
  "model_revision": "1d4bf0f2ff6012fd82039f2fa52739d0dd7c60c0",
  "task_version": "17",
  "output_id": "c7850bbb0e8a0e3966370d8f574d2b8e734223770d852222c9c49237e13af3b2",
  "requirements_status": "needs_review",
  "dataset_revision": "fc1811fa52e581ea57a35c0cf3343f8740a8ffbf",
  "observed_at": "2026-10-14 17:50:09.728220+00:00"
}