Math 4527: Number Theory 2 ~ Homepage

Math 4527 (Number Theory 2), Fall 2026

Course Information
Instructor		Class Times		Office Hours
Evan Dummit edummit at northeastern dot edu		MW 2:50pm-4:30pm Richards 160		W 4:45pm-5:45pm R 2pm-4pm 571 Lake Hall
We will use Piazza for any course-related discussion: here is the Piazza page.
For detailed information about the course, please consult the 4527 Course Syllabus. Note: any information given in class or on this webpage supersedes the written syllabus.
All homework assignments will be posted on this webpage (see below). Homework assignments will be submitted via Gradescope, which is accessible through Canvas. Please submit scans of your homework pages by 11:59pm Eastern on the due date. Late assignments may be penalized at the grader's discretion.
Use of large-language models ("generative AI", such as ChatGPT or Claude) or equivalent technology in any manner is expressly prohibited in this course. This includes, but is not limited to, summarizing course information, asking for hints or solutions to course assignments, and general information retrieval on course topics. Ask questions during class, in office hours, on Piazza, or via email instead.
The instructor will write lecture notes for the course (see below) in lieu of an official textbook as the semester progresses. Reference texts are available upon request.

Homework Assignments + Exams
Some Tips on Problem Solving are available as suggestions for the homework assignments.
Assignments to be posted here.

Handouts / Lecture Notes
Handout	Topics
Chapter 6: Rational Approximation and Diophantine Equations (35pp, v3.50, posted 9/7)	6.1 ~ Some Diophantine Equations (Linear Diophantine Equations, the Frobenius Coin Problem, Pythagorean Triples) 6.2 ~ Rational Approximation and Transcendence (Farey Sequences, Finite and Infinite Continued Fractions, Rational Approximation, Irrationality and Transcendence) 6.3 ~ Pell's Equation (Motivation and Examples, General Structure, The Super Magic Box) 6.4 ~ An Assortment of Other Diophantine Equations

Tips For Success In This Course
Attend Lecture	Missing lecture is a bad idea! If for any reason you cannot make it to a class, you should review the notes and watch the lecture recording. You are responsible for all material covered in lecture.
Read the Lecture Notes	The lecture notes are a comprehensive source of material for the course. The notes are intended as review material, although many students like to read them as preparation before attending the lecture on the corresponding topics. Please note that the electronic notes are not identical to the material covered in class: this is by design, so as to provide you a slightly different perspective on the material.
Solve Homework Problems	Much of the learning in this course will take place as you solve the homework problems. Like many other activities, problem-solving and proof-writing are things that are learned by doing them, not by hearing someone else tell you about them or reading about them in a book. As such, the homework assignments are an integral part of the course, and are fundamental to learning the material. It is highly recommended that you look over the homework assignments as soon as they are available, and work on them well in advance of the deadline: many problems will take substantial time and effort to solve, and you should expect to spend as much time as you need to finish the assignments.
Attend Office Hours	Office hours are specifically reserved for you to receive individual, one-on-one help from the instructor. Office hours will be the most effective when you have already put in effort to learn the material on your own (including trying to solve the homework problems), and when you come in with a list of specific questions or topics you are struggling with.

Course Schedule
The schedule is subject to change! All sections refer to the course lecture notes.
Week	Schedule
Week of Sep 7 (class starts 9/9)	§6.1.1: Linear Diophantine Equations §6.1.2: The Frobenius Coin Problem No homework this week.
Week of Sep 14	§6.1.3: Pythagorean Triples §6.2.1: Farey Sequences §6.2.2: Continued Fractions §6.2.3: Infinite Continued Fractions Homework #1 due Friday 9/18 via Gradescope.
Week of Sep 21	§6.2.4: Rational Approximation §6.2.5: Irrationality and Transcendence §6.3.1: Pell's Equation Examples §6.3.2: Pell's Equation Properties Homework #2 due Friday 9/25 via Gradescope.
Week of Sep 28	§6.3.3: The Super Magic Box §6.4.1: Assorted Diophantine Equations §6.4.2: The Fermat Equation xⁿ+yⁿ=zⁿ §8.1.1: Ideals of Commutative Rings §8.1.2: Quotient Rings Homework #3 due Friday 10/2 via Gradescope.
Week of Oct 5	§8.1.3: Maximal and Prime Ideals §8.1.4: Arithmetic in Integral Domains §8.1.5: Quadratic Fields and Quadratic Integer Rings §8.1.6: Euclidean Domains §8.1.7: Principal Ideal Domains Homework #4 due Friday 10/9 via Gradescope.
Week of Oct 12 (no class 10/12)	Oral Exam #1 to be scheduled this week. §8.1.8: Unique Factorization Domains §8.1.9: The Chinese Remainder Theorem §8.2.1: Unique Factorization of Elements in O_D Homework #5 due Friday 10/16 via Gradescope.
Week of Oct 19	§8.2.2: Ideals in O_D §8.2.3: Divisibility and Unique Factorization of Ideals in O_D §8.2.4: Calculating Factorizations in O_D §8.3.1: Factorization in Z[i] Homework #6 due Friday 10/23 via Gradescope.
Week of Oct 26	§8.3.2: Factorization in O_√-2 and O_√-3 §8.3.3: More Diophantine Equations §8.3.4: Cubic Reciprocity Homework #7 due Friday 10/30 via Gradescope.
Week of Nov 2	§8.3.4: Cubic Reciprocity §8.3.5: Quartic Reciprocity §9.1.1: Minkowski's Convex-Body Theorems §9.1.2: Sums of Two and Four Squares §9.1.3: Sums of Three Squares Homework #8 due Friday 11/6 via Gradescope.
Week of Nov 9 (no class 11/11)	Oral Exam #2 to be scheduled this week. §9.2.1: The Ideal Class Group §9.2.2: Minkowski's Bound Homework #9 due Friday 11/13 via Gradescope.
Week of Nov 16	§9.3.1: Representations by Quadratic Forms §9.3.2: Equivalence of Quadratic Forms §9.3.3: Composition of Quadratic Forms §9.3.4: Dirichlet's Composition Law Homework #10 due Friday 11/20 via Gradescope.
Week of Nov 23 (no class 11/25-11/27)	§9.3.5: Quadratic Forms and Ideal Class Groups No homework this week.
Week of Nov 30	§10.1.1: The Riemann Zeta Function §10.1.2: Motivation for Dirichlet's Theorem §10.1.3: Dirichlet Series §10.1.4: Group Characters and Dirichlet Characters Homework #11 due Friday 12/4 on Canvas.
Week of Dec 7 (class ends 12/10)	Oral Exam #3 to be scheduled this week. §10.1.5: Dirichlet L-Series and Dirichlet's Theorem §10.2.1: Dedekind Zeta Functions §10.2.2: The Analytic Class Number Formula Homework #12 due Friday 12/11 on Canvas.