Math 3527 (Number Theory 1), Fall 2026
| Course Information | |||||
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| Instructor | Class Times | Office Hours | |||
| Evan Dummit edummit at northeastern dot edu |
MR 11:45am-1:25pm Shillman 415 |
W 4:45pm-5:45pm R 2pm-4pm 571 Lake Hall |
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| For detailed information about the course, please consult the 3527 Course Syllabus. Note: any information given in class or on this webpage supersedes the written syllabus. | |||||
| Problem Session | Session Leader(s) | ||||
| Tuesdays, 3pm-4:30pm, 304 Kariotis | Nur Cataltepe | ||||
| Fridays, 2pm-4pm, 143 Ryder | Minhao Yin, Sally Ambrose | ||||
| We will use Piazza for any course-related discussion: here is the Piazza page. | |||||
| 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. |
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| 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 | |||||||
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| Some Tips on Problem Solving are available as suggestions for the homework assignments. | |||||||
| Assignments to be posted here. | |||||||
| Handouts / Lecture Notes | |||
|---|---|---|---|
| Handout | Topics | ||
| Chapter 1: The Integers (18pp, v4.50, posted 9/7) | 1.1 ~ The Integers, Axiomatically 1.2 ~ Divisibility and the Euclidean Algorithm 1.3 ~ Primes and Unique Factorization 1.4 ~ Rings and Other Number Systems |
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| Exam Information | |||
|---|---|---|---|
| Exam | Date, Time, Location | Topics | Review Material |
| Midterm 1 | Thu, Oct 29th In Class |
Homeworks 1-6 Notes 1.1-3.5 |
Review problems and practice exams to be posted In-class review Mon Oct 26th |
| Midterm 2 | Thu, Dec 3rd In Class |
Homeworks 7-10 Notes 4.1-5.1 |
Review problems and practice exams to be posted In-class review Mon Nov 20th |
| Final ( OPTIONAL!) |
Date TBA Time TBA Location TBA |
The final is COMPREHENSIVE! Homeworks 1-11 Notes Chapters 1-5 |
Review problems and practice exams to be posted Review session TBA |
| On all exams, calculators are permitted though generally they are not needed, and you are allowed a 1-page note sheet (8.5in by 11in, both sides) on which you may write or type anything. | |||
| 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 notes from someone who did attend. You are responsible for all material covered in lecture. | ||
| Read the Lecture Notes (or Textbook) | The lecture notes and the textbook are comprehensive sources 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 Problem Sessions | There are weekly problem sessions run by the course TAs. The goal of the problem sessions are to provide you a location where you can work collaboratively with other students on assignments, and also get TA assistance. | ||
| 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) |
§1.1.1: The Integers, Axiomatically §1.1.2: Basic Arithmetic §1.1.3: Induction No homework this week. |
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| Week of Sep 14 | §1.1.3: Induction §1.2.1: Divisibility and Division with Remainder §1.2.2: Greatest Common Divisors §1.2.3: The Euclidean Algorithm §1.3: Primes and Unique Factorization Homework #1 due Friday 9/18 via Gradescope. |
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| Week of Sep 21 | §1.4.1: Rings and Other Number Systems §1.4.2: Arithmetic in Rings, Units §2.1.1: Modular Congruences §2.1.2: Residue Classes §2.1.3: Modular Arithmetic Homework #2 due Friday 9/25 via Gradescope. |
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| Week of Sep 28 |
§2.1.4: Units in Z/mZ §2.1.5: Zero Divisors in Z/mZ §2.2: Linear Equations Modulo m and The Chinese Remainder Theorem §2.3.1: Orders of Elements Modulo m Homework #3 due Friday 10/2 via Gradescope. |
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| Week of Oct 5 | §2.3.2: Fermat's Little Theorem, Wilson's Theorem §2.3.3: The Euler φ-function and Euler's Theorem §2.3.4: Primitive Roots §2.4: Repeating Decimals Homework #4 due Friday 10/9 via Gradescope. |
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| Week of Oct 12 (no class 10/12) |
§3.1: Primality and Compositeness Testing §3.2: Factorization Algorithms Homework #5 due Friday 10/16 via Gradescope. |
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| Week of Oct 19 | §3.3: Overview of Cryptography §3.4: Rabin Encryption §3.5: RSA Encryption Homework #6 due Friday 10/23 via Gradescope. |
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| Week of Oct 26 | §3.6: Zero-Knowledge Proofs Review for Midterm 1. MIDTERM 1 in class on Thu, Oct 29th |
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| Week of Nov 2 | §4.1.1: Norms and Z[√D] §4.1.2: Integral Domains and Common Divisors §4.1.3: Irreducible and Prime Elements §4.1.4: Euclidean Domains and Division Algorithms §4.1.5: Z[i] and F[x] as Euclidean Domains Homework #7 due Tuesday 11/3 via Gradescope. |
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| Week of Nov 9 | §4.1.6: Unique Factorization in Euclidean Domains §4.2.1: Modular Congruences and Residue Classes §4.2.2: Arithmetic in R/rR §4.2.3: Units and Zero Divisors in R/rR §4.2.4: The Chinese Remainder Theorem §4.2.5: Orders, Euler's Theorem, Fermat's Little Theorem Homework #8 due Tuesday 11/10 via Gradescope. |
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| Week of Nov 16 | §4.3.1: Polynomial Functions, Roots of Polynomials §4.3.2: Finite Fields §4.3.3: Primitive Roots §4.4.1: Residue Classes in Z[i] Homework #9 due Tuesday 11/17 via Gradescope. |
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| Week of Nov 23 (no class 11/25-11/27) | §4.4.2: Factorization in Z[i] §5.1: Quadratic Residues and Legendre Symbols Homework #10 due Tuesday 11/24 via Gradescope. |
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| Week of Nov 30 | §5.2: The Law of Quadratic Reciprocity Review for Midterm 2. MIDTERM 2 in class on Thu, Dec 3rd No homework this week. |
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| Week of Dec 7 (class ends 12/10) |
§5.3: Jacobi Symbols §5.4: Applications of Quadratic Reciprocity §5.5: Generalizations of Quadratic Reciprocity Homework #11 due Tuesday 12/8 via Gradescope. |
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| The OPTIONAL FINAL EXAM will be held on date TBA at time TBA in location TBA | |||