Fall 2026

The Theory of Single Variable Calculus

Covers first and second semester calculus material while teaching math majors to write and understand proofs.

offering recorded3 credits
Recorded instructors · Fall 2026 Fernando Al Assal3.5/5Yayi Fu3.0/5

Summary

1 / 6

Some students report that homework and exams are difficult, requiring memorization of proofs from notes rather than independent thinking. They criticize the lack of introductory proof instruction and contradictory materials.

Grade history

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

Prerequisites

Course map

MATH 234 or graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program

    • MATH 234
    • graduate/professional standing
    • member of the Pre-Masters Mathematics (Visiting International) Program
    take one
MATH 421 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
  • Any of
    • MATH 234
    • graduate/professional standing
    • member of the Pre-Masters Mathematics (Visiting International) Program

Professors

Fall 2026
/5Adjusted rating
/5RMP difficulty
captured reviews
About this rating

Raw average: 3.44/5 from 32 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.

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

No course-specific feedback yet.

/5Adjusted rating
/5RMP 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: 2.4/5 raw quality · 3.3/5 difficulty · 7 reviews

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

Yayi Fu receives harsh criticism for delivering dense, whispering lectures that rely on copying PDF notes rather than explaining concepts. Reviewers describe her exams as memorization-focused and disconnected from homework, with one noting contradictions between textbook and lecture proofs.

Other students find Fu knowledgeable and committed to rigor, praising her clear notes and helpful hints for individual thinking. These reviewers report lenient grading, easy exams, and strong preparation for advanced courses, though they also note the lectures are very dense.

Recent recorded grades — Fall 2024: 3.47 GPA, 71.9% A/AB (n=32 letter grades); Spring 2025: 3.62 GPA, 76.7% A/AB (n=30 letter grades).

Historical instructors & teaching patterns

Historical reviews of Grace Work: Grace Work teaches clearly and is well-prepared, with a kind and straightforward style that supports student success if they attend lectures. While some students report harsh homework grading, the instructor herself is not responsible for those grades.

ANDREAS SEEGER is recorded teaching in Fall 2008, Fall 2018. Recorded history may be incomplete and does not establish a future schedule.

DONGHYUN LEE is recorded teaching in Fall 2016. Recorded history may be incomplete and does not establish a future schedule.

FLORIAN BERTRAND is recorded teaching in Spring 2010, Spring 2011. Recorded history may be incomplete and does not establish a future schedule.

GLORIA MARI-BEFFA is recorded teaching in Fall 2007, Spring 2016. Recorded history may be incomplete and does not establish a future schedule.

GRACE WORK is recorded teaching in Spring 2022, Spring 2023, Spring 2024, Spring 2025, Fall 2025. Recorded history may be incomplete and does not establish a future schedule.

JENNIFER BEICHMAN is recorded teaching in Fall 2013. Recorded history may be incomplete and does not establish a future schedule.

SIGURD ANGENENT is recorded teaching in Fall 2019. Recorded history may be incomplete and does not establish a future schedule.

SIMON SCHULZ is recorded teaching in Fall 2021, Fall 2022. Recorded history may be incomplete and does not establish a future schedule.

STEFFEN LEMPP is recorded teaching in Spring 2015. Recorded history may be incomplete and does not establish a future schedule.

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

YAYI FU is recorded teaching in Fall 2024, Spring 2025. 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

Fall 2026

Schedule loads here as you scroll.

SectionModeEnrolled / capacityWaitlist
LEC 001Classroom Instruction39 / 402
LEC 003Classroom Instruction40 / 404
LEC 002Classroom Instruction39 / 400

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

Meeting source records

Student experience

the class

Yayi Fu is knowledgeable and committed to rigor, with clear notes and helpful hints that support learning. Some students find her lectures dense but appreciate her clarity and responsiveness.

Recent recorded grades — Spring 2025: 3.24 GPA, 56.6% A/AB (n=106 letter grades); Fall 2025: 2.98 GPA, 42.5% A/AB (n=106 letter grades); Spring 2026: 2.99 GPA, 47.7% A/AB (n=88 letter grades).

difficulty & workload

Some students report that homework and exams are difficult, requiring memorization of proofs from notes rather than independent thinking. They criticize the lack of introductory proof instruction and contradictory materials.

Students appreciate Fu’s responsiveness on Piazza and lenient grading, finding her notes and hints helpful for understanding dense material. They recommend the class for those with prior proof exposure.

Topics

  • First and second semester calculus.
  • Mathematical proofs in general and calculus.

Skills

  • Write and understand mathematical proofs.

Grades

Historical instructor

Fall 2026 · 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 · 0.15 GPA average error.

Grades over time

Through Fall 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

1283 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.

Selected offering source records
MATH 421 · Fall 2026

The Theory of Single Variable Calculus

Recorded 2026-09-07
Raw records
[
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "offering_id": "1272:600:021988",
    "course_id": "MATH 421",
    "course_uid": "course_4aa5bbed0c86993f5f0dc832",
    "term_id": "1272",
    "source_course_id": "021988",
    "source_subject_id": "600",
    "title": "The Theory of Single Variable Calculus",
    "credits_min": 3,
    "credits_max": 3,
    "typically_offered": "Fall, Spring"
  }
]
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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.

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Model outputs & technical records
nvidia/Qwen3.6-35B-A3B-NVFP4
LLM outputs across runs
Full model traces

Recorded model configuration, reasoning, and tool conversations.

Model & dataset provenance
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  "model_revision": "1355db6a052410cfd62085d94b58866fd0f2c3c5",
  "task_version": "14",
  "output_id": "8c4f7244b577a96a078da98178d160c4034f80fa2890d617f9dda8f97bbe442c",
  "requirements_status": "valid",
  "dataset_revision": "e243353dcb7d79b7247ced91d69443ef4c2a6349",
  "observed_at": "2026-09-07 15:55:43.033547+00:00"
}