Spring 2027

Topics in Multi-variable Calculus and Linear Algebra

Topics in Multi-Variable Calculus and Linear Algebra covering vector spaces, linear transformations, differential calculus, determinants, eigenvalues, and integrals.

no offering record for this termCredits unavailable
Recorded instructors · Spring 2027 No instructors listed

Summary

1 / 8

Past student reviews · Sean Paul, Laurentiu Maxim

Freshmen often underestimated the work required, noting that self-teaching was necessary. One student found the fast lecture pace difficult, requiring extra time after class to comprehend the material.

What you’ll be able to do

  • Identify the formal definitions of mathematical objects and their properties used in linear algebra and differential multivariable calculus (e.g., vector spaces, linear transformations, derivatives of multivariate functions, etc.).

  • Use the standard methods and tools of mathematical argument in the context of linear algebra and multivariate differential calculus (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 valued function is differentiable, etc.).

  • Identify standard theorems in linear algebra and differential multivariate calculus and recall arguments for these theorems and the underlying logic of their proofs (e.g., symmetric matrices are diagonalizable, chain rule for multivariate functions, etc.).

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

  • Perform standard computations in the context of linear algebra and differential multivariate calculus.

  • Write mathematical proofs and concepts in logical, reasonable, and concise ways.

Source: UW Guide

Grade history

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average GPA
letter grades
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All recorded terms · compare terms & instructors

Prerequisites

Course map

Consent of Instructor

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MATH 375 used by

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Prerequisite text tree
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Professors

Spring 2027

No instructors recorded for this selection.

Historical instructors & teaching patterns

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

AUTUMN KENT is recorded teaching in Fall 2020, Fall 2023. Recorded history may be incomplete and does not establish a future schedule.

GHEORGHE CRACIUN is recorded teaching in Fall 2011. Recorded history may be incomplete and does not establish a future schedule.

GLORIA MARI-BEFFA is recorded teaching in Fall 2006, Fall 2011. Recorded history may be incomplete and does not establish a future schedule.

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

LAURENTIU MAXIM is recorded teaching in Fall 2014, Fall 2016. Recorded history may be incomplete and does not establish a future schedule.

SAVERIO SPAGNOLIE is recorded teaching in Fall 2013, Fall 2025. Recorded history may be incomplete and does not establish a future schedule.

SEAN PAUL is recorded teaching in Fall 2008. Recorded history may be incomplete and does not establish a future schedule.

SERGUEI DENISSOV is recorded teaching in Fall 2019. Recorded history may be incomplete and does not establish a future schedule.

SIGURD ANGENENT is recorded teaching in Fall 2017. Recorded history may be incomplete and does not establish a future schedule.

TULLIA DYMARZ is recorded teaching in Fall 2015. 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

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Student experience

the class

Past student reviews · Tullia Dymarz, Autumn Kent

Students described the course as a challenging, proof-based class where some instructors used take-home exams and lenient grading to manage the theoretical workload.

Recent recorded grades — Fall 2023: 3.89 GPA, 92.0% A/AB (n=50 letter grades); Fall 2024: 3.43 GPA, 64.0% A/AB (n=50 letter grades); Fall 2025: 3.37 GPA, 57.4% A/AB (n=47 letter grades).

difficulty & workload

Past student reviews · Sean Paul, Laurentiu Maxim

Freshmen often underestimated the work required, noting that self-teaching was necessary. One student found the fast lecture pace difficult, requiring extra time after class to comprehend the material.

Past student reviews · Serguei Denissov, Saverio Spagnolie

Experiences varied widely; one student criticized skipped steps and poor explanations, while another found lectures good, exams fair, and homework time-consuming but manageable.

Topics

  • Vector spaces and linear transformations
  • Differential calculus of scalar and vector fields
  • Determinants, eigenvalues, and eigenvectors
  • Multiple, line, and surface integrals

Skills

  • Proving or disproving mathematical statements
  • Using standard methods of mathematical argument
  • Writing mathematical proofs

Grades

Latest available · Fall 2025— 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 Fall 2025

More grade details Grade mix, volume & source data

Where this course fits relative to

Latest available grades · Fall 2025 · 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

1316 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

No offering records for the selected term.

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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Dataset & model

Recorded 2026-10-14

View the dataset on Hugging Face
Model outputs & technical records
Qwen/Qwen3.8-27B
LLM outputs across runs
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Full model traces

Recorded model configuration, reasoning, and tool conversations.

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Model & dataset provenance 
{
  "model": "Qwen/Qwen3.8-27B",
  "model_revision": "1d4bf0f2ff6012fd82039f2fa52739d0dd7c60c0",
  "task_version": "17",
  "output_id": "d52a9bc51c21d6ad6d9b77fd96b3ca0441e125488811b7542236697912502978",
  "requirements_status": "valid",
  "dataset_revision": "fc1811fa52e581ea57a35c0cf3343f8740a8ffbf",
  "observed_at": "2026-10-14 17:50:09.728220+00:00"
}