Spring 2027

Analysis I

Analysis I covers real numbers, set theory, metric spaces, basic topology, sequences and series, limits, continuity, differentiation, integration, and uniform convergence.

offering recorded3 credits
Recorded instructors · Spring 2027 Yayi Fu3.0/5Mihaela Ifrim2.9/5Sean Paul1.9/5

Summary

1 / 6

Past student reviews · Yayi Fu

Yayi Fu covered a massive amount of material that could feel overwhelming. The final exam was worth 40% of the grade and was harder than the midterms, which were derived directly from review exercises.

What you’ll be able to do

  • Recall and state the formal definitions of the mathematical objects and their properties used in classical real analysis (e.g., the of a set, continuity of a function, limit of a sequence, etc.).

  • Use the above definitions to prove if a mathematical construct does or does not have the condition of being a particular mathematical object or having a particular property (e.g., that a given function is continuous, that a given set is compact, that a series converges absolutely, etc.).

  • Recall and state the standard theorems of classical real analysis. (e.g., the Bolzano- Weierstrass theorem, monotone bounded sequences converge, the fundamental theorem of calculus, etc.). Moreover, the student will be able to recall the arguments for these theorems and the underlying logic of their proofs.

  • Use the above theorems in the context of longer arguments by examining their premises (e.g., proving that a function has a maximum by verifying that it is continuous on a compact set).

  • 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 in oral and written forms using English and appropriate mathematical terminology, notation and grammar.

  • Identify applications of course content in areas of modern 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 234 and 467), (MATH 322, 341, 376, or 421), graduate/professional standing, or member of the Pre-Masters Mathematics (Visiting International) Program

MATH 521 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: 2.29/5 from 17 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: 3.3/5 raw quality · 3.0/5 difficulty · 4 reviews

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

Past student reviews · Yayi Fu

Yayi Fu’s lectures were often described as fast-paced and dry, with students reading directly from notes or textbooks. However, she was consistently rated as fair, with midterm questions taken verbatim from review exercises and generous grading. While the course covered a massive amount of material, students found exams straightforward if they prepared properly and supplemented lectures with her notes.

Recent recorded grades — Fall 2025: 3.29 GPA, 58.3% A/AB (n=36 letter grades); Spring 2026: 3.03 GPA, 50.9% A/AB (n=57 letter grades).

Mihaela Ifrim

Adjusted rating
RMP difficulty
captured reviews
About this rating

Raw average: 2.39/5 from 33 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: 3.0/5 raw quality · 4.0/5 difficulty · 2 reviews

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

Past student reviews · Mihaela Ifrim

Students reported that Mihaela Ifrim's tests were hard but grading was generous, while advising participation and study groups to succeed. However, one student described the experience as horrible, highlighting a significant disagreement in satisfaction levels.

Recent recorded grades — Fall 2020: 3.24 GPA, 58.8% A/AB (n=51 letter grades).

Sean Paul

Adjusted rating
RMP difficulty
captured reviews
About this rating

Raw average: 1.73/5 from 242 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: 3.0/5 raw quality · 4.0/5 difficulty · 2 reviews

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

Past student reviews · Sean Paul

Sean Paul's lectures were disorganized but informative, with video recordings provided for each class. Students reported that diligent study allowed them to learn a lot and achieve good grades without significant difficulty.

Sean Paul was described as cold and lacking in empathy, with one student noting he treated them and others with disrespect. Despite being good at answering questions in office hours, his interactions were characterized as aloof.

Recent recorded grades — Fall 2025: 2.36 GPA, 24.1% A/AB (n=29 letter grades).

Historical instructors & teaching patterns

Past student reviews · Xianghong Gong

In Xianghong Gong's past sections, he held extra problem-solving sessions to help students understand difficult exercises in the course material.

BRIAN COOK is recorded teaching in Fall 2013, Fall 2016. Recorded history may be incomplete and does not establish a future schedule.

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

MIHAELA IFRIM is recorded teaching in Fall 2020. Recorded history may be incomplete and does not establish a future schedule.

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

SIGURD ANGENENT is recorded teaching in Spring 2016, Spring 2017. Recorded history may be incomplete and does not establish a future schedule.

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

TIMO SEPPALAINEN is recorded teaching in Spring 2011. Recorded history may be incomplete and does not establish a future schedule.

TONGOU YANG is recorded teaching in Fall 2022. Recorded history may be incomplete and does not establish a future schedule.

TRINH NGUYEN is recorded teaching in Spring 2023, Fall 2023. Recorded history may be incomplete and does not establish a future schedule.

XIANGHONG GONG is recorded teaching in Spring 2007, Fall 2010, Spring 2012, Fall 2012. Recorded history may be incomplete and does not establish a future schedule.

XIUXIONG CHEN is recorded teaching in Spring 2009, Fall 2011. Recorded history may be incomplete and does not establish a future schedule.

YANNAN QIU is recorded teaching in Fall 2006, Fall 2008. Recorded history may be incomplete and does not establish a future schedule.

YAYI FU is recorded teaching in Fall 2025, Spring 2026. 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 003Classroom Instruction0 / 400
LEC 001Classroom Instruction0 / 400
LEC 002Classroom Instruction0 / 400
LEC 004Classroom 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 · Sean Paul, Yayi Fu

Students described the course as challenging but manageable with diligent study. Yayi Fu covered a massive amount of material, while Sean Paul provided video recordings of each class.

Recent recorded grades — Spring 2025: 2.99 GPA, 46.7% A/AB (n=122 letter grades); Fall 2025: 3.01 GPA, 45.0% A/AB (n=140 letter grades); Spring 2026: 3.26 GPA, 61.1% A/AB (n=131 letter grades).

difficulty & workload

Past student reviews · Yayi Fu

Yayi Fu covered a massive amount of material that could feel overwhelming. The final exam was worth 40% of the grade and was harder than the midterms, which were derived directly from review exercises.

Past student reviews · Yayi Fu

Yayi Fu's lectures were described as fast-paced and sometimes unengaging, requiring students to supplement with notes. However, grading was considered fair and generous, making it feasible to earn good grades.

Topics

  • Real numbers and set theory
  • Metric spaces and basic topology
  • Sequences and series of functions
  • Uniform convergence

Skills

  • Formal definitions in real analysis
  • Proof construction
  • Application of standard theorems
  • Mathematical argumentation techniques

Grades

Historical instructor

Spring 2027 · Projected

Before grades are released

– average GPA

Approximate 80% prediction interval

About this estimate

The course’s semester-average GPA, not an individual student’s grade. The center uses 5 same-season terms, weighted toward recent results.

The range uses the finite-sample 80th-percentile rank of absolute errors from earlier same-season forecasts. Each forecast uses only records from earlier terms. At least four forecasts are required; bounds are rounded outward and limited to 0–4. This is an empirical estimate: changing instructors or grading policies can reduce its coverage.

8 earlier forecasts · 0.14 GPA average error.

Grades over time

Through Spring 2027

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 521 · Spring 2027

Analysis I

Recorded 2026-10-14
Raw records 
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    "run_id": "20261014T203208-0851c9a1",
    "semester": "1274",
    "observed_at": "2026-10-14 17:50:09.728220+00:00",
    "offering_id": "1274:600:011682",
    "course_id": "MATH 521",
    "course_uid": "course_364c50303ed83d1234b4ea51",
    "term_id": "1274",
    "source_course_id": "011682",
    "source_subject_id": "600",
    "title": "Analysis I",
    "credits_min": 3,
    "credits_max": 3,
    "typically_offered": "Fall, Spring, Summer"
  }
]
Rate My Professors

Student reviews

Original comments behind the course and instructor summaries.

Read original reviews
Download part 1
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.

Download part 1
Model & dataset provenance 
{
  "model": "Qwen/Qwen3.8-27B",
  "model_revision": "1d4bf0f2ff6012fd82039f2fa52739d0dd7c60c0",
  "task_version": "17",
  "output_id": "53683d354e056d677d2bbbb5a489e4403663548cdb3693c1a093d7b637921e2e",
  "requirements_status": "needs_review",
  "dataset_revision": "fc1811fa52e581ea57a35c0cf3343f8740a8ffbf",
  "observed_at": "2026-10-14 17:50:09.728220+00:00"
}