Math 3527 (Number Theory 1), Spring 2026
| Course Information | |||||
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| Instructor | Class Times | Office Hours | |||
| Evan Dummit edummit at northeastern dot edu 571 Lake Hall |
(Sec 1) MWR 1:35pm-2:40pm, 119 Dodge (Sec 2) MWR 10:30am-11:35am, 130 Hurtig |
M noon-1pm MR 3pm-4pm Lake 571 |
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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.) | |||||
| We will use Piazza for any course-related discussion: here is the 3527 Piazza page. | |||||
| Problem Session | Session Leader(s) | ||||
| Tuesdays, 2:30pm-4pm, Ryder 143 | Zach Greenfield | ||||
| Thursdays, 3pm-4:30pm, Ryder 143 | Tony Xiao | ||||
| Fridays, 12:30pm-3:30pm, Ryder 147 | Connor Anderson, Toby Busick-Warner | ||||
| 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 retrival on course topics. Ask questions during class, in office hours, on Piazza, during problem sessions, 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 written assignments. | |||||||
| Homework #1, due Fri Jan 16th. | |||||||
| Homework assignments are to be submitted to Gradescope via the course's Canvas page. To submit an assignment, navigate to "Assignments" and select the appropriate homework assignment. Then attach scans of each page of your assignment (or a pdf) and click Submit. Please submit the pages in order and verify that all pages are included and uploaded correctly. You may resubmit as many times as you like. Assignments are due at 11:59pm eastern time. Late submissions, messy submissions, or otherwise unreadable submissions will be penalized at the grader's discretion. Ensure you mark all problem pages when submitting to Gradescope; failure to do so may result in point penalties. | |||||||
| Handouts / Lecture Notes | |||
|---|---|---|---|
| Handout | Topics | ||
| Chapter 1: The Integers (18pp, v4.00, posted 1/5) | 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, Feb 19th In Class |
Homeworks 1-5 Notes 1.1-3.4 |
Review problems to be posted In-class review Wed Feb 18th |
| Midterm 2 | Mon, Mar 30th In Class |
Homeworks 6-9 Notes 3.5-4.4 |
Review problems to be posted In-class review Thu Mar 26th |
| Final | Date TBA Time TBA Location TBA |
The final is COMPREHENSIVE! Homeworks 1-11 Notes Chapters 1-5 |
Review problems to be posted Review sessions 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 Jan 5 (class starts 1/7) |
§1.1.1: The Integers, Axiomatically §1.1.2: Basic Arithmetic §1.1.3: Induction §1.2.1: Divisibility and Division with Remainder No homework this week. |
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| Week of Jan 12 |
§1.2.2: Greatest Common Divisors §1.2.3: The Euclidean Algorithm §1.3: Primes and Unique Factorization §1.4.1: Rings and Other Number Systems §1.4.2: Arithmetic in Rings, Units Homework #1 due Friday, Jan 16th. |
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| Week of Jan 19 (no class 1/19) |
§2.1.1: Modular Congruences §2.1.2: Residue Classes §2.1.3: Modular Arithmetic Homework #2 due Friday, Jan 23rd. |
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| Week of Jan 26 |
§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, Jan 30th. |
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| Week of Feb 2 |
§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, Feb 6th. |
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| Week of Feb 9 | §3.1: Overview of Cryptography §3.2: Rabin Encryption §3.3: RSA Encryption Homework #5 due Friday, Feb 13th. |
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| Week of Feb 16 (no class 2/16) |
Review for Midterm 1. MIDTERM 1 in class on Thu, Feb 19th No homework this week. |
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| Week of Feb 23 | §3.4: Zero-Knowledge Proofs §3.5: Primality and Compositeness Testing §3.6: Factorization Algorithms Homework #6 due Friday, Feb 27th. |
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| Spring Break (no classes) from Mar 2 to Mar 6 | |||
| Week of Mar 9 | §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 Friday, Mar 13th. |
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| Week of Mar 18 | §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 Homework #8 due Friday, Mar 20th. |
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| Week of Mar 23 | §4.2.5: Orders, Euler's Theorem, Fermat's Little Theorem §4.3.1: Polynomial Functions, Roots of Polynomials §4.3.2: Finite Fields Review for Midterm 2. Homework #9 due Friday, Mar 27th. |
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| Week of Mar 30 | MIDTERM 2 in class on Mon, Mar 30th §4.3.3: Primitive Roots §4.4.1: Residue Classes in Z[i] §4.4.2: Factorization in Z[i] No homework this week. |
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| Week of Apr 6 | §5.1: Quadratic Residues and Legendre Symbols §5.2: The Law of Quadratic Reciprocity §5.3: Jacobi Symbols Homework #10 due Friday, Apr 10th. |
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| Week of Apr 13 (classes end 4/17) |
§5.4: Applications of Quadratic Reciprocity §5.5: Generalizations of Quadratic Reciprocity Review for Final Exam Homework #11 due Friday, Apr 17th. |
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| The FINAL EXAM will be held on date TBA at time TBA in location TBA during finals week (Mon Apr 20 to Sun Apr 26) | |||