Spring 2027

Mathematical Methods in Data Science

Rigorous introduction to math for data science covering matrix factorizations, optimization, probabilistic models, and Markov chains with applications to machine learning.

offering recorded3 credits
Recorded instructors · Spring 2027 No instructors listed

Summary

1 / 6

Past student reviews · Hanbaek Lyu

A student said Hanbaek Lyu’s exam philosophy was to make exams pretty hard but grade them leniently, and the course felt like an extension of linear algebra with a focus on proofs.

What you’ll be able to do

  • State and calculate eigenvalue, singular value and QR decompositions and apply them to data science techniques such as spectral clustering, principal components analysis and least-squares problems.

  • State and derive properties of multivariate normal distributions and apply them to data science problems based on Gaussian models such as mixtures of Gaussians and Gaussian graphical models.

  • Formulate certain machine learning and statistics problems as optimization problems, solve these problems using simple optimization algorithms such as first-order methods and state results about the convergence of these algorithms.

  • State and derive basic properties of finite Markov chain models and apply them to data science techniques such as Markov chain Monte Carlo.

  • Construct proofs of simple theorems in matrix factorizations, Gaussian modeling, optimization theory, and finite Markov chains.

  • Implement data science methods based on matrix factorizations, Gaussian modeling, optimization theory, and finite Markov chains in a programming language such as Python.

  • Identify and use course content in the context of current/modern research in mathematics and data science.

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 320, 340, 341, 345, or 375) and (STAT/​MATH 309, 431,MATH 531, or STAT 311) and (MATH 322, 341, 375, 421, or 467, or COMP SCI 577), graduate/professional standing, or declared in Mathematics VISP (graduate or undergraduate)

MATH 535

This is a best-effort interpretation; check the catalog requirements above.

Prerequisite text tree

Professors

Spring 2027

No instructors recorded for this selection.

Historical instructors & teaching patterns

HANBAEK LYU is recorded teaching in Spring 2023. Recorded history may be incomplete and does not establish a future schedule.

SEBASTIEN ROCH is recorded teaching in Spring 2020, Fall 2020, Spring 2022, Fall 2022, Spring 2024, Spring 2025. 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 / 550

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 · Sebastien Roch

One student said Dr. Roch was a pretty good lecturer who focused on the most important topics and left time for questions.

Recent recorded grades — Spring 2025: 3.44 GPA, 63.8% A/AB (n=47 letter grades); Fall 2025: 3.46 GPA, 76.5% A/AB (n=34 letter grades); Spring 2026: 3.87 GPA, 91.3% A/AB (n=46 letter grades).

difficulty & workload

Past student reviews · Hanbaek Lyu

A student said Hanbaek Lyu’s exam philosophy was to make exams pretty hard but grade them leniently, and the course felt like an extension of linear algebra with a focus on proofs.

Past student reviews · Hanbaek Lyu

One student found Hanbaek Lyu knowledgeable and said they could get insights of machine learning techniques from a mathematical view. They also found the organization and lecture notes, provided by a previous professor, weak.

Topics

  • Matrix factorizations, optimization theory, probabilistic models, and finite Markov chains.
  • Applied problems from machine learning and statistics.

Skills

  • Calculate eigenvalue, singular value, and QR decompositions for data science applications.
  • Formulate and solve optimization problems using first-order methods.
  • Derive properties of multivariate normal distributions for Gaussian models.
  • Apply finite Markov chain properties to Markov chain Monte Carlo.

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 535 · Spring 2027

Mathematical Methods in Data Science

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": "1274:600:025408",
    "course_id": "MATH 535",
    "course_uid": "course_85a2851be919e3db46f0fbc1",
    "term_id": "1274",
    "source_course_id": "025408",
    "source_subject_id": "600",
    "title": "Mathematical Methods in Data Science",
    "credits_min": 3,
    "credits_max": 3,
    "typically_offered": "Not Applicable"
  }
]
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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": "c0391d188d9f2f74379f0cb328c15d0e0f117c8f7cedca95b6990fdbc9070f32",
  "requirements_status": "needs_review",
  "dataset_revision": "fc1811fa52e581ea57a35c0cf3343f8740a8ffbf",
  "observed_at": "2026-10-14 17:50:09.728220+00:00"
}