Spring 2027

Complex Analysis

Complex Analysis covers elementary functions of a complex variable, conformal mapping, complex integrals, and the calculus of residues.

offering recorded3 credits
Recorded instructors · Spring 2027 Lars Niedorf4.0/5

Summary

1 / 6

Past student reviews · Betsy (Lindsay) Stovall

Lectures were proof-heavy, and exams included unexpected questions that required students to read extensively to develop a deeper understanding.

What you’ll be able to do

  • Recall and state the formal definitions of the mathematical objects and their properties used in complex analysis (e.g., principle branches, conjugates, holomorphic and analytic functions, 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., that a function is complex differentiable, that an infinite product converges, classification of singularities, etc.).

  • Recall and state the standard theorems of complex analysis (e.g., Cauchy's Integral formula, the maximum modulus principle, the Riemann mapping Theorem), and recall the arguments for these theorems and the underlying logic of their proofs.

  • Use such theorems in the context of longer arguments by examining their premises (e.g., computation of real integrals using path integration techniques, computation of residues of meromorphic functions, that a given function has an analytic continuation, etc.).

  • Prove or disprove statements related to the above definitions, properties, and theorems using techniques of mathematical argument (direct methods, indirect methods, constructing examples and counterexamples, induction, etc.).

  • Convey arguments in oral and written forms using English and appropriate mathematical terminology, notation and grammar.

  • Identify applications of course content in current areas of research.

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

MATH 321 or 521 or graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program

MATH 623

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

Prerequisite text tree

Professors

Spring 2027
Adjusted rating
RMP difficulty
captured reviews
About this rating

Raw average: 4.55/5 from 11 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

SERGUEI DENISSOV is recorded teaching in Fall 2017. 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 / 400

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 · Betsy (Lindsay) Stovall

Betsy (Lindsay) Stovall provided an elegant explanation of intricate concepts in this course.

Recent recorded grades — Fall 2023: 3.60 GPA, 85.0% A/AB (n=20 letter grades); Fall 2024: 3.51 GPA, 74.3% A/AB (n=35 letter grades); Fall 2025: 3.32 GPA, 50.0% A/AB (n=30 letter grades).

difficulty & workload

Past student reviews · Betsy (Lindsay) Stovall

Lectures were proof-heavy, and exams included unexpected questions that required students to read extensively to develop a deeper understanding.

Past student reviews · Betsy (Lindsay) Stovall

Betsy (Lindsay) Stovall was accessible outside of class, and students found her office hours to be helpful.

Topics

  • Elementary functions of a complex variable
  • Conformal mapping
  • Complex integrals
  • Calculus of residues
  • Standard theorems of complex analysis, including Cauchy's Integral formula, the maximum modulus principle, and the Riemann mapping Theorem.

Skills

  • Elementary functions of a complex variable, conformal mapping, complex integrals, and the calculus of residues.
  • Recalling and stating formal definitions of mathematical objects in complex analysis.
  • Arguing whether mathematical objects possess specific types or properties using definitions.
  • Using standard theorems in longer arguments, including computing real integrals via path integration and residues of meromorphic functions.
  • Proving or disproving mathematical statements using direct, indirect, and constructive techniques.

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
MATH 623 · Spring 2027

Complex Analysis

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": "1274:600:011698",
    "course_id": "MATH 623",
    "course_uid": "course_1351409acfb0d317ef52fedf",
    "term_id": "1274",
    "source_course_id": "011698",
    "source_subject_id": "600",
    "title": "Complex Analysis",
    "credits_min": 3,
    "credits_max": 3,
    "typically_offered": "Fall"
  }
]
Rate My Professors

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
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": "df26971021b24f6d04da463ff187f424ca7d3dcf9587e575544996b0fdfcc188",
  "requirements_status": "needs_review",
  "dataset_revision": "fc1811fa52e581ea57a35c0cf3343f8740a8ffbf",
  "observed_at": "2026-10-14 17:50:09.728220+00:00"
}