Spring 2027

Introduction to Combinatorics

Introduction to combinatorics covering enumeration, inclusion-exclusion, generating functions, graph coloring, finite designs, and matching problems with applications in science and puzzles.

offering recorded3 credits
Recorded instructors · Spring 2027 Mitch Keller3.1/5

Summary

1 / 6

Past student reviews · Mitch Keller

The grading system was unique and demanding: students needed full marks on all assignments and tests or extra credit to achieve an A; otherwise, the highest possible grade was an AB.

What you’ll be able to do

  • Understand basic counting strategies, such as staged thought-experiments, inclusion/exclusion, generating functions, and recurrence relations, and apply these strategies to solve a wide variety of counting problems.

  • Recall basic objects that are used in combinatorics, such as permutations and combinations of sets and multisets, binomial and multinomial coefficients, the Catalan numbers, the Stirling numbers, and the partition numbers.

  • Analyze a given combinatorial problem using the standard theorems of combinatorics, such as the pigeonhole principle, the Newton binomial theorem, the multinomial theorem, the Ramsey theorem, the Dilworth theorem, the Burnside theorem, and the Polya counting theorem.

  • Construct mathematical arguments related to combinatorial problems using the above definitions, properties, theorems, and counting strategies; including the construction of examples and counterexamples.

  • Convey arguments in oral and written form in English, using appropriate mathematical terminology, notation, and grammar.

Source: UW Guide 1 UW Guide 2 UW Guide 3

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

Spring 2027
Adjusted rating
RMP 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.

Past student reviews · Mitch Keller

Mitch Keller used a unique grading scale where an A required full marks on all tests and assignments or extra credit, otherwise capping the grade at AB. One student found the course difficult and noted the textbook was poorly written, though lectures helped, while another rated the instruction quality moderately.

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).

Historical instructors & teaching patterns

Past student reviews · Mikhail Ivanov

Mikhail Ivanov taught this course as an exam-heavy class where exams comprised 80% of the grade and homework 20%. He was described as a very lenient grader who provided generous partial credit, and the course was curved on top of that grading. His lectures were recorded and uploaded with notes, and attendance was not required.

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.

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.

STEFFEN LEMPP is recorded teaching in Spring 2019. 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 / 380
LEC 003Classroom Instruction0 / 380
LEC 001Classroom Instruction0 / 380
LEC 003Classroom Instruction0 / 380
LEC 001Classroom Instruction0 / 380
LEC 003Classroom Instruction0 / 380

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 · Mitch Keller

Mitch Keller’s lectures were considered great and helped compensate for a poorly written textbook, though the course required consistent effort across all assessments.

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

Past student reviews · Mitch Keller

The grading system was unique and demanding: students needed full marks on all assignments and tests or extra credit to achieve an A; otherwise, the highest possible grade was an AB.

Past student reviews · Mitch Keller

Students found the textbook poorly written, but the quality of the lectures helped make up for this deficiency during the course.

Topics

  • Enumeration, distribution, arrangement, inclusion-exclusion, generating functions, linear recurrences, and combinatorial identities.
  • Graph coloring, finite designs, systems of distinct representatives, and matching problems in graphs.
  • Applications in social, biological, and physical sciences, puzzles, and problem solving.

Skills

  • Apply counting strategies like inclusion-exclusion, generating functions, and recurrence relations to solve combinatorial problems.
  • Analyze combinatorial problems using standard theorems including the pigeonhole principle, Ramsey theorem, and Polya counting theorem.
  • Construct mathematical arguments and counterexamples for combinatorial problems.

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 · 0.17 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.

Download part 1
Selected offering source records
COMPSCI/MATH/STAT 475 · Spring 2027

Introduction to Combinatorics

Recorded 2026-10-14
COMPSCI/MATH/STAT 475 · Spring 2027

Introduction to Combinatorics

Recorded 2026-10-14
COMPSCI/MATH/STAT 475 · Spring 2027

Introduction to Combinatorics

Recorded 2026-10-14
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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 1Download part 2Download part 3
Model & dataset provenance 
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