Simon Fraser University
Engaging the World

Course Outlines

Spring 2026 - MATH 842 G100

Algebraic Number Theory (4)

Class Number: 5369

Delivery Method: In Person

Overview

  • Course Times + Location:

    Jan 5 – Apr 10, 2026: Tue, Thu, 10:30 a.m.–12:20 p.m.
    Burnaby

Description

CALENDAR DESCRIPTION:

Review of Galois theory, integrality, rings of integers, traces, norms, discriminants, ideals, Dedekind domains, class groups, unit groups, Minkowski theory, ramification, cyclotomic fields, valuations, completions, applications.

COURSE DETAILS:

Algebraic number theory comprises the study of algebraic numbers: numbers that satisfy polynomial equations with rational coefficients. The parallels with usual integer arithmetic are striking, as are the notable differences (as, for instance, failure of unique factorization into prime factors). The subject is fundamental to any further study in number theory or algebraic geometry.

In this course we develop the tools to properly understand unique factorization and its failure. We establish fundamental results such as Dirichlet's Unit theorem and the finiteness of the ideal class group. We highlight the applicability of the algebraic tools we develop to both algebraic numbers and to algebraic curves. Depending on time and interests of the participants, we will also look into various applications and more advanced topics.

Grading

  • Assignments (weighted equally) 25%
  • Quizzes (weighted equally) 25%
  • Final Exam 50%

REQUIREMENTS:

Prerequisite: MATH 440/740

Materials

REQUIRED READING:

Neukirch, Jürgen
Algebraic number theory.
Grundlehren der Mathematischen Wissenschaften, 322. Springer-Verlag, Berlin, 1999. xviii+571 pp.

ISBN: 3-540-65399-6

Stein, William
Algebraic Number Theory, a Computational Approach
Full text available from: https://wstein.org/books/ant/

REQUIRED READING NOTES:

Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

Graduate Studies Notes:

Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

At SFU, you are expected to act honestly and responsibly in all your academic work. Cheating, plagiarism, or any other form of academic dishonesty harms your own learning, undermines the efforts of your classmates who pursue their studies honestly, and goes against the core values of the university.

To learn more about the academic disciplinary process and relevant academic supports, visit: 


RELIGIOUS ACCOMMODATION

Students with a faith background who may need accommodations during the term are encouraged to assess their needs as soon as possible and review the Multifaith religious accommodations website. The page outlines ways they begin working toward an accommodation and ensure solutions can be reached in a timely fashion.