Spring 2027

Introduction to Stochastic Processes

Covers discrete-time and continuous-time Markov chains, Poisson point processes, and renewal processes, with applications to queueing, branching, and models in science, engineering, and business.

offering recorded3 credits

Recorded instructors · Spring 2027 Timo Seppalainen4.4/5

Summary

1 / 6

Past student reviews · Timo Seppalainen

Homework assignments were challenging and time-consuming, but students noted there were only about ten. The homework was significantly harder than the exams, meaning thorough homework completion often reduced the need for additional exam study.

What you’ll be able to do

Recall and state the formal definitions of the mathematical objects and their properties for stochastic processes (e.g., discrete space Markov chains, Poisson processes, renewal processes, branching processes, 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., irreducibility, aperiodicity, recurrence, transience, the Markov property, etc.).
Recall and state the standard theorems of stochastic processes. (e.g., laws of large numbers for Markov chains, existence of limiting/stationary distributions, law of large numbers for renewal processes, etc.) and recall the arguments for these theorems and the underlying logic of their proofs.
Construct mathematical arguments related to the above definitions, properties, and theorems, including the construction of examples and counterexamples.
Convey arguments in oral and written forms using English and appropriate mathematical terminology, notation and grammar.
Model simple real life situations by means of discrete-space stochastic processes and calculate probabilities associated with those processes.
Identify applications of course content in current areas of research.

Source: UW Guide 1 UW Guide 2 UW Guide 3 UW Guide 4

Grade history

↗

average GPA
letter grades

All recorded terms · compare terms & instructors

Prerequisites

Course map

(STAT/MATH 431, 309,STAT 311, or MATH 531) and (MATH 320, 340, 341, 345, 375, 421, or 531), graduate/professional standing, or declared in Mathematics VISP (undergraduate or graduate)

- - take one
  - take one
  take all
- graduate/professional standing
- declared in Mathematics VISP (undergraduate or graduate)
take one

ISYE/MATH/OTM/STAT 632 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
- All of
  - Any of
  - Any of
- graduate/professional standing
- declared in Mathematics VISP (undergraduate or graduate)

Professors

Spring 2027

Timo Seppalainen

Adjusted rating

RMP difficulty

captured reviews

About this rating

Raw average: 5.00/5 from 22 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: 5.0/5 raw quality · 3.3/5 difficulty · 6 reviews

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

Past student reviews · Timo Seppalainen

Timo Seppalainen made complicated probability topics accessible, even for students without an analysis background. He explained why mathematical results were important and how they fit into broader contexts. Students found the homework challenging, noting it was harder than the exams, but valued the clarity of his lectures.

Recent recorded grades — Fall 2019: 2.87 GPA, 46.0% A/AB (n=50 letter grades); Spring 2020: 3.50 GPA, 73.1% A/AB (n=26 letter grades); Fall 2025: 2.98 GPA, 42.5% A/AB (n=40 letter grades).

Historical instructors & teaching patterns

Past student reviews · Erik Bates, David Keating

Historical students described Erik Bates as a talented professor who focused on deep understanding of probability, while David Keating was praised for clearly explaining tough concepts and answering questions proactively. Both instructors were highly recommended for their teaching quality, though feedback on workload and grading varied among other historical sections.

BENEDEK VALKO is recorded teaching in Fall 2011, Spring 2012, Fall 2014, Fall 2019, Fall 2021, Spring 2022, Fall 2025. Recorded history may be incomplete and does not establish a future schedule.

DANIELE CAPPELLETTI is recorded teaching in Spring 2017, Fall 2017, Spring 2018. Recorded history may be incomplete and does not establish a future schedule.

DAVID KEATING is recorded teaching in Fall 2022, Spring 2023, Fall 2023, Spring 2024. Recorded history may be incomplete and does not establish a future schedule.

DAVID S. GRIFFEATH is recorded teaching in Fall 2007, Spring 2008, Spring 2009, Fall 2009, Spring 2010, Spring 2011. Recorded history may be incomplete and does not establish a future schedule.

ERIK BATES is recorded teaching in Fall 2020, Fall 2022. Recorded history may be incomplete and does not establish a future schedule.

GREGORY SHINAULT is recorded teaching in Spring 2014, Fall 2018, Spring 2019. Recorded history may be incomplete and does not establish a future schedule.

JUN YIN is recorded teaching in Spring 2013, Spring 2015, Spring 2017. Recorded history may be incomplete and does not establish a future schedule.

SEBASTIEN ROCH is recorded teaching in Fall 2013, Fall 2014, Spring 2015, Fall 2015, Spring 2016, Fall 2016, Spring 2023. Recorded history may be incomplete and does not establish a future schedule.

SIGURD ANGENENT is recorded teaching in Fall 2018. Recorded history may be incomplete and does not establish a future schedule.

TIMO SEPPALAINEN is recorded teaching in Spring 2007, Fall 2008, Fall 2018, Fall 2019, Spring 2020, Fall 2025. Recorded history may be incomplete and does not establish a future schedule.

XIAOQIN GUO is recorded teaching in Spring 2020. 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 / 67
LEC 001	Classroom Instruction	0 / 67
LEC 001	Classroom Instruction	0 / 67
LEC 001	Classroom Instruction	0 / 67

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 · Timo Seppalainen

Professor Seppalainen delivers clear, rigorous lectures that contextualize probability within measure theory, making complex topics accessible to students without an analysis background.

Recent recorded grades — Spring 2025: 3.37 GPA, 66.7% A/AB (n=51 letter grades); Fall 2025: 3.18 GPA, 45.7% A/AB (n=81 letter grades); Spring 2026: 3.01 GPA, 41.1% A/AB (n=56 letter grades).

difficulty & workload

Past student reviews · Timo Seppalainen

Students appreciated the instructor's accommodating approach, which included using multiple grading formulas to determine the course grade and selecting the method that resulted in the highest final score.

Topics

Discrete-time and continuous-time Markov chains, Poisson point processes, and renewal processes.
Applications to queueing, branching, and other models in science, engineering, and business.

Skills

Formal definitions of stochastic process objects and properties.
Argumentation regarding mathematical object types and properties.
Standard theorems, proof arguments, and underlying logic.
Modeling real-life situations and calculating associated probabilities.

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 · 0.11 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

ISYE/MATH/OTM/STAT 632 · Spring 2027

Introduction to Stochastic Processes

Recorded 2026-10-14

ISYE/MATH/OTM/STAT 632 · Spring 2027

Introduction to Stochastic Processes

Recorded 2026-10-14

ISYE/MATH/OTM/STAT 632 · Spring 2027

Introduction to Stochastic Processes

Recorded 2026-10-14

ISYE/MATH/OTM/STAT 632 · Spring 2027

Introduction to Stochastic Processes

Recorded 2026-10-14

Raw records

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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.

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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.

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Model & dataset provenance

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  "output_id": "112432f854bd57e29664737111051b6456837dbdb3aa430479f2f8151613ac91",
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Introduction to Stochastic Processes

Summary

What you’ll be able to do

Grade history

Prerequisites

Professors

Timo Seppalainen

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