Spring 2027

Linear Algebra

Theory of linear algebra covering vector spaces, transformations, and eigenvalues, with an introduction to proofs and proof writing.

offering recorded3 credits
Recorded instructors · Spring 2027 Cassie Williams4.3/5

Summary

1 / 6

Past student reviews · Howard Becker

Homework was a moderate level, but exams required applying abstract concepts from class to create original proofs, making them moderate to difficult.

What you’ll be able to do

  • Recall and state the formal definitions of mathematical objects and their properties used in elementary linear algebra (e.g., dimension of a vector space, linear dependence of a set of vectors, etc.).

  • Use the standard methods and tools of mathematical argument in the context of linear algebra (e.g., direct and indirect methods, the construction of examples and counterexamples, induction arguments, 1st order logic, set theory, quantifiers, etc.).

  • Verify if a mathematical construct does or does not have the condition of having a particular property (e.g., that a matrix is invertible, that a set is a vector subspace, that a vector is an eigenvector, etc.).

  • Recall and state standard theorems used in elementary linear algebra (e.g., symmetric matrices are diagonalizable, linear operators with non-trivial kernel are not invertible, etc.).

  • Verify the premises of standard theorems in elementary linear algebra in order to apply their conclusions in the context of longer arguments (e.g., that a given matrix has zero determinant and therefore has nullity larger than one, etc.).

  • Prove or disprove statements related to the definitions, properties, and theorems of elementary linear algebra using the techniques of mathematical argument.

  • Perform standard computations in the context of linear algebra (e.g., finding the rank of a matrix, computing the determinant of a square matrix, etc.).

  • Convey formal mathematical arguments in English using appropriate mathematical terminology and notation.

Source: UW Guide

Grade history

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average GPA
letter grades
A
AB
B
BC
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All recorded terms · compare terms & instructors

Prerequisites

Course map

MATH 234. Not open to students with credit forMATH 375.

MATH 341 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

Cassie Williams

Adjusted rating
RMP difficulty
captured reviews
About this rating

Raw average: 4.54/5 from 54 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.

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

No course-specific feedback yet.

Historical instructors & teaching patterns

ALEXANDER HANHART is recorded teaching in Spring 2016. Recorded history may be incomplete and does not establish a future schedule.

ANDREI CALDARARU is recorded teaching in Fall 2023. Recorded history may be incomplete and does not establish a future schedule.

ANTOINE REMOND-TIEDREZ is recorded teaching in Fall 2021, Spring 2024. Recorded history may be incomplete and does not establish a future schedule.

FLORIAN BERTRAND is recorded teaching in Fall 2009. Recorded history may be incomplete and does not establish a future schedule.

HOWARD BECKER is recorded teaching in Fall 2014. Recorded history may be incomplete and does not establish a future schedule.

JACK BURKART is recorded teaching in Fall 2021. Recorded history may be incomplete and does not establish a future schedule.

JUSTIN SUKIENNIK is recorded teaching in Spring 2020. Recorded history may be incomplete and does not establish a future schedule.

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

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

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

YANG YANG is recorded teaching in Spring 2026. 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 / 350
LEC 002Classroom Instruction0 / 350

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 · Paul Apisa

A former math major described the course as the hardest thing they had ever done, stating that the rigor helped them later in their studies.

Recent recorded grades — Spring 2025: 3.18 GPA, 54.2% A/AB (n=96 letter grades); Fall 2025: 3.15 GPA, 51.6% A/AB (n=64 letter grades); Spring 2026: 3.09 GPA, 54.4% A/AB (n=90 letter grades).

difficulty & workload

Past student reviews · Howard Becker

Homework was a moderate level, but exams required applying abstract concepts from class to create original proofs, making them moderate to difficult.

Past student reviews · Antoine Remond-Tiedrez

One student found that using quizzes to examine definitions was an effective method for learning the material.

Topics

  • Vector spaces, linear transformations, and eigenvalues
  • Set theory, logic, and proof techniques

Skills

  • Mathematical argumentation and proof writing
  • Core concepts of linear algebra including vector spaces, transformations, and eigenvalues
  • Standard linear algebra computations such as rank and determinants

Grades

Historical instructor

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 · 0.25 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 341 · Spring 2027

Linear Algebra

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": "1274:600:021987",
    "course_id": "MATH 341",
    "course_uid": "course_fa53f4954bab469b5d4c4fe3",
    "term_id": "1274",
    "source_course_id": "021987",
    "source_subject_id": "600",
    "title": "Linear Algebra",
    "credits_min": 3,
    "credits_max": 3,
    "typically_offered": "Fall, 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 1Download part 2
Model & dataset provenance 
{
  "model": "Qwen/Qwen3.8-27B",
  "model_revision": "1d4bf0f2ff6012fd82039f2fa52739d0dd7c60c0",
  "task_version": "17",
  "output_id": "fcf989c9be248aa7f83ef64e2a6566b824c72c9d53815cd4bd8675e21289c346",
  "requirements_status": "valid",
  "dataset_revision": "fc1811fa52e581ea57a35c0cf3343f8740a8ffbf",
  "observed_at": "2026-10-14 17:50:09.728220+00:00"
}