Spring 2027

Probability Theory

Rigorous intro to probability theory covering Kolmogorov axioms, random variables, and classical results with proofs; uses minimal measure theory.

offering recorded3 credits
Recorded instructors · Spring 2027 Tatyana Shcherbyna

Summary

1 / 6

Past student reviews · Vadim Gorin

Homework varied drastically between manageable and really difficult, and one student felt the final exam was harder than past versions, though the midterm was not too bad.

What you’ll be able to do

  • State, explain, and apply the axioms, principal results, definitions, and theorems of undergraduate probability theory. This includes concepts such as probability spaces, random variables and random vectors and their probability distributions, conditional probability, independence, law of large numbers, and the central limit theorem.

  • Calculate probabilities and expectations in simple model problems.

  • Use probability theory to model simplified real-world situations with random outcomes. In particular, students can identify and apply the most common probability distributions, including the Bernoulli, binomial, geometric, Poisson, uniform, normal, and exponential distributions.

  • Analyze long-term behavior in simple model problems using the law of large numbers, the central limit theorem, and the Borel-Cantelli lemma.

  • Construct proofs of simple theorems in probability theory.

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 376, 421, or521 or graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program

    • MATH 376
    • MATH 421
    • MATH 521
    • graduate/professional standing
    • member of the Pre-Masters Mathematics (Visiting International) Program
    take one
MATH 531 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 376
    • MATH 421
    • MATH 521
    • graduate/professional standing
    • member of the Pre-Masters Mathematics (Visiting International) Program

Professors

Spring 2027

Recent recorded grades — Spring 2024: 2.94 GPA, 48.1% A/AB (n=27 letter grades); Spring 2025: 3.06 GPA, 56.0% A/AB (n=25 letter grades).

Historical instructors & teaching patterns

BENEDEK VALKO is recorded teaching in Spring 2015, Spring 2016, Spring 2019, Spring 2020, Spring 2023. Recorded history may be incomplete and does not establish a future schedule.

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

VADIM GORIN is recorded teaching in Spring 2022. 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

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 · Benedek Valko

One student described the class as a source of pure enjoyment, noting that grades did not kill the experience of thinking and learning.

Recent recorded grades — Spring 2024: 2.94 GPA, 48.1% A/AB (n=27 letter grades); Spring 2025: 3.06 GPA, 56.0% A/AB (n=25 letter grades); Spring 2026: 3.13 GPA, 46.7% A/AB (n=30 letter grades).

difficulty & workload

Past student reviews · Vadim Gorin

Homework varied drastically between manageable and really difficult, and one student felt the final exam was harder than past versions, though the midterm was not too bad.

Past student reviews · Benedek Valko

A former student found the instructor very responsible and always ready to help, noting his excellence in academic skills.

Topics

  • Kolmogorov axioms, conditional probability, independence, random variables, and expectation.
  • DeMoivre-Laplace limit theorems, simple random walk on one-dimensional lattice, and generating functions.
  • Law of large numbers, central limit theorem, and Borel-Cantelli lemma.

Skills

  • Apply axioms, results, and theorems of undergraduate probability theory including probability spaces, random variables, and limit theorems.
  • Model simplified real-world situations using common probability distributions like Bernoulli, binomial, Poisson, and normal.
  • Construct mathematical proofs for simple theorems in probability theory.

Grades

Latest available · Spring 2026— not enough history to project Spring 2027.

average GPA
A / AB grades
letter grades
Instructor

Grade distribution · % of letter grades

A
AB
B
BC
C
D
F

Grades over time

Through Spring 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

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 531 · Spring 2027

Probability Theory

Recorded 2026-10-14
Raw records 
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    "run_id": "20261014T203208-0851c9a1",
    "semester": "1274",
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    "offering_id": "1274:600:024224",
    "course_id": "MATH 531",
    "course_uid": "course_e0a93fa3466c39b6802e52a7",
    "term_id": "1274",
    "source_course_id": "024224",
    "source_subject_id": "600",
    "title": "Probability Theory",
    "credits_min": 3,
    "credits_max": 3,
    "typically_offered": "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": "79b02d4dff65a93e90faaaa2f6d2810c349bf8fa3dfe89de8bb138d8f7c7c71d",
  "requirements_status": "needs_review",
  "dataset_revision": "fc1811fa52e581ea57a35c0cf3343f8740a8ffbf",
  "observed_at": "2026-10-14 17:50:09.728220+00:00"
}