Fall 2026

Introduction to Combinatorics

Introduction to combinatorics covering enumeration, generating functions, graph theory, and matching problems.

offering recorded3 credits
Recorded instructors · Fall 2026 Mitch Keller3.1/5Paul Terwilliger3.1/5

Summary

1 / 6

The course is dense and challenging. Homework is feasible but requires reading the textbook, as lectures may not fully explain concepts. Exams often draw directly from the book and previous tests.

Grade history

average GPA
letter grades
A
AB
B
BC
C
D
F

All recorded terms · compare terms & instructors

Prerequisites

Course map

(MATH 320, 340, 341, 345, or 375), graduate/professional standing, or declared in Mathematics VISP (undergraduate or graduate)

COMPSCI/MATH/STAT 475 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

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

Raw average: 2.84/5 from 37 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: 2.0/5 raw quality · 4.0/5 difficulty · 2 reviews

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

Mitch Keller is described as a good instructor with great lectures, though one review notes the textbook is poorly written. His grading system is unique and restrictive, requiring full marks on all work or extra credit to achieve an A, otherwise capping the grade at an AB.

Recent recorded grades — Spring 2024: 3.17 GPA, 47.5% A/AB (n=40 letter grades); Fall 2025: 3.30 GPA, 63.0% A/AB (n=27 letter grades); Spring 2026: 3.37 GPA, 54.3% A/AB (n=46 letter grades).

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

Raw average: 2.76/5 from 38 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: 2.7/5 raw quality · 3.5/5 difficulty · 25 reviews

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

Paul Terwilliger is described as knowledgeable and clear, with some students finding him flexible and reasonable. Reviewers note that exam questions often come from the textbook, suggesting that reading ahead is important for success in the course.

Other reviewers criticize Terwilliger for being inflexible, illegible, and unhelpful with questions. They report harsh grading, lack of feedback, and lectures that are difficult to follow, though some note the material itself is manageable if read independently.

Recent recorded grades — Fall 2024: 3.44 GPA, 72.5% A/AB (n=40 letter grades); Spring 2025: 3.49 GPA, 66.7% A/AB (n=69 letter grades); Fall 2025: 3.07 GPA, 36.0% A/AB (n=50 letter grades).

Historical instructors & teaching patterns

Historical reviews of Matthew Ballard, Mikhail Ivanov: Matthew Ballard provided well-paced lectures and helpful homework, challenging students while ensuring success opportunities. Mikhail Ivanov was a very good professor who provided recorded lectures and notes, with lenient grading and generous partial credit despite the course being exam-heavy.

JOHN WILTSHIRE-GORDON is recorded teaching in Fall 2017. Recorded history may be incomplete and does not establish a future schedule.

JUN LE GOH is recorded teaching in Fall 2021. Recorded history may be incomplete and does not establish a future schedule.

LEV BORISOV is recorded teaching in Fall 2006. Recorded history may be incomplete and does not establish a future schedule.

MANLIO VALENTI is recorded teaching in Spring 2023. Recorded history may be incomplete and does not establish a future schedule.

MATTHEW BALLARD is recorded teaching in Fall 2011. Recorded history may be incomplete and does not establish a future schedule.

MIKHAIL IVANOV is recorded teaching in Fall 2020, Fall 2021, Fall 2023. Recorded history may be incomplete and does not establish a future schedule.

MITCH KELLER is recorded teaching in Fall 2023, Spring 2024, Fall 2025, Spring 2026. Recorded history may be incomplete and does not establish a future schedule.

PAUL M TERWILLIGER is recorded teaching in Fall 2012, Spring 2014, Fall 2014, Spring 2015, Spring 2016, Fall 2016, Fall 2017, Spring 2018, Fall 2018, Spring 2019, Fall 2019, Spring 2020, Fall 2020, Spring 2022, Fall 2022, Spring 2023, Fall 2023, Spring 2024, Fall 2024, Spring 2025, Fall 2025. Recorded history may be incomplete and does not establish a future schedule.

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

SHENGWEN GAN is recorded teaching in Spring 2024. Recorded history may be incomplete and does not establish a future schedule.

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

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

STEVEN SAM is recorded teaching in Fall 2015. 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 Instruction6 / 350
LEC 002Classroom Instruction5 / 350
LEC 003Classroom Instruction6 / 350
LEC 001Classroom Instruction23 / 350
LEC 002Classroom Instruction9 / 350
LEC 003Classroom Instruction19 / 350
LEC 001Classroom Instruction1 / 350
LEC 002Classroom Instruction0 / 350
LEC 003Classroom Instruction5 / 350

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

Paul Terwilliger is a knowledgeable mathematician who presents material clearly, though reviews disagree on his communication and flexibility. Mitch Keller is a good instructor but uses a unique grading system that restricts the maximum grade to an AB without perfect scores or extra credit.

Recent recorded grades — Spring 2025: 3.39 GPA, 60.2% A/AB (n=98 letter grades); Fall 2025: 3.15 GPA, 45.5% A/AB (n=77 letter grades); Spring 2026: 3.35 GPA, 55.6% A/AB (n=63 letter grades).

difficulty & workload

The course is dense and challenging. Homework is feasible but requires reading the textbook, as lectures may not fully explain concepts. Exams often draw directly from the book and previous tests.

Students report mixed experiences with Terwilliger, citing his flexibility and clear examples versus his inflexibility and poor communication. Keller's grading policy is a significant concern, as students must achieve perfect marks on all assessments to secure an A.

Topics

  • Enumeration, distribution, and arrangement
  • Inclusion-exclusion principle
  • Generating functions and linear recurrence relations
  • Combinatorial identities
  • Graph coloring problems
  • Finite designs
  • Systems of distinct representatives and matching problems
  • Applications in sciences and puzzles

Skills

  • Solving enumeration and arrangement problems
  • Applying the inclusion-exclusion principle
  • Using generating functions and recurrence relations
  • Deriving and using combinatorial identities
  • Solving graph coloring problems
  • Analyzing systems of distinct representatives and graph matchings
  • Studying finite designs
  • General problem solving techniques

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 · 0.05 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
COMPSCI/MATH/STAT 475 · Fall 2026

Introduction to Combinatorics

Recorded 2026-09-07
COMPSCI/MATH/STAT 475 · Fall 2026

Introduction to Combinatorics

Recorded 2026-09-07
COMPSCI/MATH/STAT 475 · Fall 2026

Introduction to Combinatorics

Recorded 2026-09-07
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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.

Explore recorded grades
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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