Spring 2027

Introduction to Number Theory

Introduction to Number Theory covering proof writing techniques, divisibility, primes, congruences, and Fermat's theorem.

offering recorded3 credits
Recorded instructors · Spring 2027 Niclas Technau3.7/5

Summary

1 / 6

Past student reviews · Botong Wang

Students reported that the homework directly prepares them for exams, which were described as very straightforward. The class involved lecture-heavy instruction.

What you’ll be able to do

  • Understand and use the standard methods and tools of mathematical argument (e.g. direct and indirect methods, the construction of examples and counterexamples, induction arguments).

  • State and describe the formal definitions of the mathematical objects and their properties used in elementary number theory (e.g., divisibility, prime numbers, congruences, etc.).

  • State and apply the main theorems in elementary number theory (e.g. theorems related to modular arithmetic, divisibility, prime numbers, Fermat's Little Theorem).

  • Prove or disprove statements and evaluate the validity of arguments related to the definitions, properties, and theorems of elementary number theory.

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 234, 320, 340, 345, 375, or (MATH 222 and COMP SCI/​MATH 240)

MATH 467 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
Adjusted rating
RMP difficulty
captured reviews
About this rating

Raw average: 4.00/5 from 3 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

ANANTH SHANKAR is recorded teaching in Fall 2022. Recorded history may be incomplete and does not establish a future schedule.

BOTONG WANG is recorded teaching in Fall 2025. Recorded history may be incomplete and does not establish a future schedule.

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

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

MITCH KELLER is recorded teaching in Fall 2024. 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 · Botong Wang

The course is lecture-heavy with engaging sessions that break down advanced concepts using examples. Homework directly prepares students for straightforward exams.

Recent recorded grades — Spring 2025: 2.97 GPA, 44.1% A/AB (n=34 letter grades); Fall 2025: 3.34 GPA, 58.8% A/AB (n=68 letter grades); Spring 2026: 2.48 GPA, 35.5% A/AB (n=31 letter grades).

difficulty & workload

Past student reviews · Botong Wang

Students reported that the homework directly prepares them for exams, which were described as very straightforward. The class involved lecture-heavy instruction.

Past student reviews · Botong Wang

Learners found the lectures engaging and appreciated that the instructor motivated almost everything with examples, making understanding easier.

Topics

  • Divisibility
  • Basic properties of primes
  • Congruences
  • Fermat's theorem
  • Proof writing techniques

Skills

  • Proof writing techniques
  • Standard methods and tools of mathematical argument
  • Formal definitions of mathematical objects in elementary number theory
  • Application of main theorems in elementary number theory
  • Proving or disproving statements and evaluating argument validity

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 467 · Spring 2027

Introduction to Number Theory

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": "1274:600:025252",
    "course_id": "MATH 467",
    "course_uid": "course_e7b7ff33c37b147a17b2d14d",
    "term_id": "1274",
    "source_course_id": "025252",
    "source_subject_id": "600",
    "title": "Introduction to Number Theory",
    "credits_min": 3,
    "credits_max": 3,
    "typically_offered": "Not Applicable"
  }
]
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": "9692ae9bdba8e1fad434a07a8859d0c75d524323244dc2a529e5d02d3344a281",
  "requirements_status": "valid",
  "dataset_revision": "fc1811fa52e581ea57a35c0cf3343f8740a8ffbf",
  "observed_at": "2026-10-14 17:50:09.728220+00:00"
}