Spring 2027

Modern Number Theory

Number theory covering fundamentals and modern applications like modular arithmetic, quadratic reciprocity, Diophantine equations, and the circle method.

offering recorded3 credits
Recorded instructors · Spring 2027 Andrei Caldararu2.9/5

Summary

1 / 6

Past student reviews · Andrei Caldararu

The course was not easy, and students needed to study diligently to perform well in the class.

What you’ll be able to do

  • Recall and state the formal definitions of the mathematical objects and their properties used in the field of Number Theory (e.g., congruence, quadratic residue, arithmetic function, elliptic curves, 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., a number is transcendental, a continued fraction is positive, etc.).

  • Recall and state the standard theorems of number theory. (e.g., quadratic reciprocity, Roth’s theorem, etc.). Moreover, the student will be able to 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., Applying the euclidean algorithm to show that rational numbers have a finite continued fraction expansion , 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 using English with appropriate mathematical terminology and notation.

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

Source: UW Guide

Grade history

↗
average GPA
letter grades
A
AB
B
BC
C
D
F

All recorded terms · compare terms & instructors

Prerequisites

Course map

MATH 541 or graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program

    • MATH 541
    • graduate/professional standing
    • member of the Pre-Masters Mathematics (Visiting International) Program
    take one
MATH 567

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

Prerequisite text tree
  • Any of
    • MATH 541
    • graduate/professional standing
    • member of the Pre-Masters Mathematics (Visiting International) Program

Professors

Spring 2027

Andrei Caldararu

Adjusted rating
RMP difficulty
captured reviews
About this rating

Raw average: 2.52/5 from 44 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.

For this course: 4.0/5 raw quality · 4.0/5 difficulty · 1 reviews

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

Past student reviews · Andrei Caldararu

Andrei Caldararu was described as knowledgeable and dedicated, though he did not make the classes easy. Students reported needing to study hard to do well, found him difficult to read, and noted that grades were assigned only at the semester's end, making progress hard to track.

Recent recorded grades — Fall 2017: 3.07 GPA, 52.2% A/AB (n=23 letter grades); Spring 2020: 3.44 GPA, 68.8% A/AB (n=16 letter grades); Spring 2026: 3.22 GPA, 68.8% A/AB (n=16 letter grades).

Historical instructors & teaching patterns

Past student reviews · Dmytro Arinkin, Daniel Erman

Historical reviews described Dmytro Arinkin as clear and helpful, with exams closely matching sample problems and somewhat difficult homework. Students also praised Daniel Erman for making number theory approachable through numerous examples and applications to fields like cryptography. These accounts suggest the course content was challenging but accessible under specific instructors who provided strong pedagogical support.

ANDREI CALDARARU is recorded teaching in Fall 2017, Spring 2020, Spring 2026. Recorded history may be incomplete and does not establish a future schedule.

DANIEL ERMAN is recorded teaching in Fall 2016, Fall 2018. Recorded history may be incomplete and does not establish a future schedule.

DMYTRO ARINKIN is recorded teaching in Fall 2013, Fall 2014, Fall 2015. Recorded history may be incomplete and does not establish a future schedule.

YOUSHENG SHI is recorded teaching in Spring 2022, Spring 2023. 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 / 280

Times are Central. Select a meeting for details; export includes recorded dates for the selected sections. Enrollment reflects scan time.

Meeting source records
Download part 1

Student experience

the class

Past student reviews · Andrei Caldararu

Andrei Caldararu was knowledgeable and dedicated, but the class was challenging and required significant independent study to succeed.

Recent recorded grades — Spring 2024: 2.93 GPA, 28.6% A/AB (n=7 letter grades); Spring 2025: 3.23 GPA, 55.0% A/AB (n=20 letter grades); Spring 2026: 3.22 GPA, 68.8% A/AB (n=16 letter grades).

difficulty & workload

Past student reviews · Andrei Caldararu

The course was not easy, and students needed to study diligently to perform well in the class.

Past student reviews · Andrei Caldararu

The instructor was hard to read, and grades were assigned at the semester's end, making it impossible to track progress until the very end.

Topics

  • Fundamental number theory topics
  • Probability and random matrix theory

Skills

  • Formal definitions of number theory objects
  • Argumentation regarding mathematical properties
  • Standard theorems and proof logic
  • Application of theorems in complex arguments
  • Mathematical proof techniques
  • Mathematical communication and notation
  • Identification of modern research applications

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

Not enough comparable courses for Spring 2027 in UW–Madison.

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.

Download part 1
Selected offering source records
MATH 567 · Spring 2027

Modern 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": "1274:600:011692",
    "course_id": "MATH 567",
    "course_uid": "course_a75fa380f07449fe8cb71571",
    "term_id": "1274",
    "source_course_id": "011692",
    "source_subject_id": "600",
    "title": "Modern Number Theory",
    "credits_min": 3,
    "credits_max": 3,
    "typically_offered": "Fall"
  }
]
Rate My Professors

Student reviews

Original comments behind the course and instructor summaries.

Read original reviews
Download part 1
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": "040c83cb01a291706b0637dfd7abe7dff79710b15e01a526a43c9d738012e04d",
  "requirements_status": "needs_review",
  "dataset_revision": "fc1811fa52e581ea57a35c0cf3343f8740a8ffbf",
  "observed_at": "2026-10-14 17:50:09.728220+00:00"
}