Spring 2027

Introduction to the Theory of Probability

Introduction to the Theory of Probability covering axioms, random variables, distributions, expectation, conditional probability, multivariate distributions, inequalities, and limit theorems.

offering recorded3 credits

Recorded instructors · Spring 2027 Benedek Valko3.9/5 David Anderson

Summary

1 / 6

Past student reviews · Benedek Valko

The course required weekly homework and quizzes, with homework described as lengthy and exams as tough but fair. Lectures were dense, covering topics from the textbook, though students found them manageable if they practiced problems consistently.

What you’ll be able to do

Recall and state the formal definitions of the mathematical objects and their properties used in probability theory (e.g., probability spaces, random variables and random vectors and their probability distributions, named distributions, conditional probability, independence, linearity of expectation, 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, whether or not a sequence of random variables is exchangeable, etc.).
Recall and state the standard theorems of probability theory. (e.g., Bayes' theorem, the law of large numbers, the central limit theorem, etc.), and apply these theorems to solve problems in probability theory.
Use multiple approaches to compute and estimate probabilities and expectations (e.g., using the indicator method, using conditioning, estimating probabilities using normal or Poisson approximation etc.).
Construct mathematical arguments related to the above definitions, properties, and theorems, including the construction of examples and counterexamples.
Convey his or her arguments in oral and written forms using English and appropriate mathematical terminology and notation (and grammar).
Model simple real-life situations using techniques in probability theory and calculate probabilities and expectations associated with those models.

Source: UW Guide 1 UW Guide 2

Grade history

↗

average GPA
letter grades

All recorded terms · compare terms & instructors

Prerequisites

Course map

MATH 234 or 376 or graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program

- MATH 234
- MATH 376
- graduate/professional standing
- member of the Pre-Masters Mathematics (Visiting International) Program
take one

MATH/STAT 431 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
- MATH 376
- graduate/professional standing
- member of the Pre-Masters Mathematics (Visiting International) Program

Professors

Spring 2027

Benedek Valko

Adjusted rating

RMP difficulty

captured reviews

About this rating

Raw average: 4.07/5 from 28 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: 4.1/5 raw quality · 3.5/5 difficulty · 13 reviews

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

Past student reviews · Benedek Valko

Professor Benedek Valko taught a fast-paced course with weekly homework and quizzes, using dense lectures to build probability concepts from the ground up. While some students found exams tough and grading harsh without partial credit, others noted the material was clear and fair for those who practiced.

Recent recorded grades — Fall 2022: 3.13 GPA, 52.6% A/AB (n=38 letter grades); Fall 2023: 3.24 GPA, 60.0% A/AB (n=45 letter grades); Spring 2024: 3.06 GPA, 48.7% A/AB (n=39 letter grades).

David Anderson

Recent recorded grades — Spring 2014: 2.78 GPA, 42.5% A/AB (n=73 letter grades); Spring 2015: 2.86 GPA, 41.4% A/AB (n=29 letter grades); Fall 2016: 3.28 GPA, 55.2% A/AB (n=29 letter grades).

Historical instructors & teaching patterns

Past student reviews · Albert Ai, Chenxi Wu

Albert Ai wrote proofs on the board carefully and rigorously, providing motivation for concepts and organizing course content well. Chenxi Wu’s lectures were confusing but he offered on-the-spot examples to clarify things, cared about students, and solicited feedback, though he went deeper into theory than exams required.

ALBERT AI is recorded teaching in Fall 2020, Fall 2021, Spring 2024. Recorded history may be incomplete and does not establish a future schedule.

ALEXANDER KISELEV is recorded teaching in Spring 2007, Fall 2007, Fall 2010. Recorded history may be incomplete and does not establish a future schedule.

BENEDEK VALKO is recorded teaching in Spring 2009, Fall 2012, Spring 2013, Fall 2013, Fall 2015, Fall 2016, Fall 2022, Fall 2023, Spring 2024. Recorded history may be incomplete and does not establish a future schedule.

CHENXI WU is recorded teaching in Fall 2025. Recorded history may be incomplete and does not establish a future schedule.

DAVID ANDERSON is recorded teaching in Spring 2010, Spring 2011, Spring 2014, Spring 2015, Fall 2016. Recorded history may be incomplete and does not establish a future schedule.

GREGORIO MORENO-FLORES is recorded teaching in Fall 2011. Recorded history may be incomplete and does not establish a future schedule.

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

MIKHAIL IVANOV is recorded teaching in Fall 2021, Fall 2024, Spring 2025. Recorded history may be incomplete and does not establish a future schedule.

PHILIP WOOD is recorded teaching in Spring 2012, Spring 2015, Spring 2017. Recorded history may be incomplete and does not establish a future schedule.

SAMUEL STECHMANN is recorded teaching in Fall 2015. Recorded history may be incomplete and does not establish a future schedule.

SHAOMING GUO is recorded teaching in Fall 2019, Fall 2023. Recorded history may be incomplete and does not establish a future schedule.

STEPHEN WAINGER is recorded teaching in Spring 2008, Fall 2009. Recorded history may be incomplete and does not establish a future schedule.

XIAOQIN GUO is recorded teaching in Spring 2018. 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.

Section	Mode	Enrolled / capacity
LEC 001	Classroom Instruction	0 / 35
LEC 003	Classroom Instruction	0 / 35
LEC 001	Classroom Instruction	0 / 35
LEC 003	Classroom Instruction	0 / 35

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

Professor Valko is described as a strong instructor who builds probability concepts from the ground up. One student specifically recommended taking the course with him, citing his clear lectures and comprehensive approach to the material.

Recent recorded grades — Spring 2025: 3.17 GPA, 46.8% A/AB (n=126 letter grades); Fall 2025: 3.26 GPA, 43.7% A/AB (n=135 letter grades); Spring 2026: 3.21 GPA, 49.5% A/AB (n=97 letter grades).

difficulty & workload

Past student reviews · Benedek Valko

Feedback on grading was mixed; one student found exams harsh with little partial credit, while another noted Valko adjusted weights to reward improvement and offered extensions for personal difficulties.

Topics

Axioms of probability, random variables, discrete and continuous distributions, expectation, variance, moment generating functions, conditional probability, multivariate distributions, inequalities, laws of large numbers, and the central

Skills

Formal probability theory concepts including axioms, distributions, expectation, and limit theorems.
Application of standard probability theorems to solve problems.
Computing and estimating probabilities and expectations using various methods.

Grades

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 · 0.18 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/STAT 431 · Spring 2027

Introduction to the Theory of Probability

Recorded 2026-10-14

MATH/STAT 431 · Spring 2027

Introduction to the Theory of Probability

Recorded 2026-10-14

Raw records

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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

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 Download part 2

Model & dataset provenance

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}

Introduction to the Theory of Probability

Summary

What you’ll be able to do

Grade history

Prerequisites

Professors

Benedek Valko

David Anderson

Calendar & sections

Student experience

the class

difficulty & workload

Topics

Skills

Grades

Spring 2027 · Projected

Grades over time

Where this course fits relative to UW–Madison

Sources & history

Catalog & offerings

Student reviews

Grade history

Where this course fits relative to