Spring 2027

Introductory Probability

Introductory Probability covers axioms, random variables, distributions, expectation, variance, conditional probability, inequalities, laws of large numbers, and the central limit theorem.

offering recorded3 credits
Recorded instructors · Spring 2027 Ander Aguirre Zarate

Summary

1 / 6

Past student reviews · Hyukpyo Hong

Exams followed a split structure where the first half mirrored practice problems exactly, while the second half was significantly more challenging.

What you’ll be able to do

  • Recall and state the formal definitions of the mathematical objects and their properties used in basic probability theory (e.g., probability spaces, random variables and their probability distributions, named distributions, conditional probability, independence, etc.).

  • Use such definitions to argue that a mathematical object does or does not have the condition of being a particular type or having a particular property (e.g., whether certain events or random variables are independent or not, whether a random variable has one of the named distributions, etc.).

  • Recall and state the standard theorems of probability theory. (e.g., Bayes’ theorem, the law of large numbers, the central limit theorem, Markov’s inequality etc.), and apply these theorems to solve problems in probability theory.

  • Use multiple approaches to compute and estimate probabilities and expectations.

  • Model simple real-life situations using techniques in probability theory and calculate probabilities and expectations associated with those models.

  • Express informal mathematical arguments in English using appropriate mathematical terminology and notation.

Source: UW Guide

Grade history

↗
average GPA
letter grades
A
AB
B
BC
C
D
F

All recorded terms · compare terms & instructors

Prerequisites

Course map

MATH 213 or 222. Not open to students with credit forMATH/​STAT 309 or STAT/​MATH 431.

MATH 331 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
Historical instructors & teaching patterns

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

HYUKPYO HONG is recorded teaching in Spring 2025, Fall 2025, Spring 2026. Recorded history may be incomplete and does not establish a future schedule.

SHI JIN is recorded teaching in Fall 2007, Fall 2012. Recorded history may be incomplete and does not establish a future schedule.

YUKUN YUE is recorded teaching in Fall 2024. 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 / 1900

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

Meeting source records
Download part 1

Student experience

the class

Past student reviews · Hyukpyo Hong

Past students described the course as unexpectedly difficult but noted that grading cutoffs were adjusted to match previous year distributions.

Recent recorded grades — Spring 2025: 3.09 GPA, 46.1% A/AB (n=89 letter grades); Fall 2025: 3.13 GPA, 45.8% A/AB (n=107 letter grades); Spring 2026: 3.14 GPA, 50.7% A/AB (n=146 letter grades).

difficulty & workload

Past student reviews · Hyukpyo Hong

Exams followed a split structure where the first half mirrored practice problems exactly, while the second half was significantly more challenging.

Past student reviews · Yukun Yue

One student found that studying practice problems effectively prepared them for the exams, allowing them to earn high scores despite one tough midterm.

Topics

  • Axioms of probability, random variables, discrete and continuous distributions, expectation, variance, conditional probability, inequalities, laws of large numbers, central limit theorem
  • Multivariate integration techniques

Skills

  • Formal definitions of probability theory objects
  • Argumentation regarding mathematical properties
  • Computing and estimating probabilities and expectations
  • Techniques of multivariate integration

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.

Download part 1
Selected offering source records
MATH 331 · Spring 2027

Introductory Probability

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": "1274:600:011652",
    "course_id": "MATH 331",
    "course_uid": "course_5d5f3a3f185baf9eaaa98221",
    "term_id": "1274",
    "source_course_id": "011652",
    "source_subject_id": "600",
    "title": "Introductory Probability",
    "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
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 2
Model & dataset provenance 
{
  "model": "Qwen/Qwen3.8-27B",
  "model_revision": "1d4bf0f2ff6012fd82039f2fa52739d0dd7c60c0",
  "task_version": "17",
  "output_id": "65ebb558ec3c9b71ead525bb3af574f840082a47ec0cc4f7a68b60648474ff19",
  "requirements_status": "valid",
  "dataset_revision": "fc1811fa52e581ea57a35c0cf3343f8740a8ffbf",
  "observed_at": "2026-10-14 17:50:09.728220+00:00"
}