Spring 2027

The Theory of Single Variable Calculus

Theory of single variable calculus teaching math majors to write and understand proofs in mathematics and calculus.

offering recorded3 credits
Recorded instructors · Spring 2027 Grace Work3.7/5Fernando Al Assal3.5/5

Summary

1 / 6

Past student reviews · Grace Work

Homework was challenging but directly prepared students for exams, which were tough yet fair and manageable for those who engaged with the material.

What you’ll be able to do

  • Understand and use the standard methods and tools of mathematical argument (e.g direct and indirect methods, the construction of examples and counterexamples, induction arguments, first-order logic, set theory, and quantifiers).

  • Recall and state the formal definitions of mathematical objects (e.g. sets, functions, and graphs) and their properties used in calculus.

  • Distinguish if a mathematical construct does or does not have the condition of having a particular property formally (e.g. limits, continuity, differentiability, and integrability).

  • Recall and state standard calculus theorems (e.g. Intermediate Value Theorem, Mean Value Theorems, and Fundamental Theorem of Calculus), and recall arguments for these theorems and the underlying logic of their proofs.

  • Prove or disprove statements related to the definitions, properties, and theorems of calculus using the techniques of mathematical argument.

  • Write mathematical proofs and concepts in logical, reasonable, and concise ways.

Source: UW Guide

Grade history

↗
average GPA
letter grades
A
AB
B
BC
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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

Spring 2027
Adjusted rating
RMP difficulty
captured reviews
About this rating

Raw average: 3.74/5 from 62 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: 3.9/5 raw quality · 3.7/5 difficulty · 7 reviews

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

Past student reviews · Grace Work

Grace Work's teaching style received mixed feedback, with some students describing her lectures as clear and engaging while others found her unhelpful when questions were asked. Exams were generally described as difficult but fair, with one student noting a median score of 50 and a specific grading curve. Homework was frequently cited as challenging, though several reviewers stated it effectively prepared them for exams, and office hours were noted as helpful by some.

Recent recorded grades — Spring 2024: 3.03 GPA, 45.8% A/AB (n=59 letter grades); Spring 2025: 3.09 GPA, 48.7% A/AB (n=76 letter grades); Fall 2025: 2.96 GPA, 38.9% A/AB (n=72 letter grades).

Adjusted rating
RMP 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.

Historical instructors & teaching patterns

Past student reviews · Andreas Seeger, Sigurd Angenent

Past students found Andreas Seeger accommodating, offering review sheets and fair homework deadlines, while Sigurd Angenent was described as friendly and helpful. Both instructors were considered excellent by students who took the course under their instruction.

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

Spring 2027

Schedule loads here as you scroll.

SectionModeEnrolled / capacityWaitlist
LEC 001Classroom Instruction0 / 400
LEC 002Classroom Instruction0 / 400
LEC 003Classroom 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 · Grace Work

Grace Work breaks down complex concepts clearly using motivating examples before formal proofs, creating an engaging and understandable learning environment for students.

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

Past student reviews · Grace Work

Homework was challenging but directly prepared students for exams, which were tough yet fair and manageable for those who engaged with the material.

Past student reviews · Grace Work

Students found Grace Work helpful during office hours and responsive to questions in lecture, with one noting that if you attend class, you will do well in the course.

Topics

  • Methods of mathematical argument including induction, logic, and set theory.
  • Standard calculus theorems such as IVT, MVT, and FTC.

Skills

  • Writing and understanding mathematical proofs using methods like induction, direct/indirect arguments, and logic.
  • Recalling and applying standard calculus theorems and their underlying logical structures.

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 · 0.22 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 421 · Spring 2027

The Theory of Single Variable Calculus

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": "1274:600:021988",
    "course_id": "MATH 421",
    "course_uid": "course_4aa5bbed0c86993f5f0dc832",
    "term_id": "1274",
    "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"
  }
]
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.

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": "4989a8a09da8c4415e053ca070fa19a55cf1014a841ed176b24de2989b0e4649",
  "requirements_status": "needs_review",
  "dataset_revision": "fc1811fa52e581ea57a35c0cf3343f8740a8ffbf",
  "observed_at": "2026-10-14 17:50:09.728220+00:00"
}