MIT OpenCourseWare

Browse materialsMIT 18.785 · Fall 2021

Number Theory I

Subjects: Algebra · Geometry · Mathematics

Art: Johannes Kepler, Konjukce Saturnu a Jupiteru Originál, 1596 · Public domain

Instructor: Andrew V. Sutherland
Term: Fall 2021
Level: Graduate
What's inside: 1 lecture note · 47 other files · 4 web pages
Materials open: MIT OCW

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About this course

Source: MIT OpenCourseWare 18.785 Number Theory I, Fall 2021, Andrew V. Sutherland — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.

Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.

Before you start

Prerequisites are not listed here. Check MIT's own syllabus for this course.

This course’s cited books, in our reading lists: A Course in Arithmetic · Algebraic Number Theory · An Invitation to Arithmetic Geometry · Commutative Algebra: With a View Toward Algebraic Geometry

How this course was organized

What's here, and what isn't

A lecture sequence of 28 items is confirmed. It stays as organized materials rather than a full course order.

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Materials by section

Grouped by section, as MIT organized them. Not sequenced or ordered.

Lecture Notes

28 files

Assignments

11 problem sets

Other materials from this course

8 files

MIT OpenCourseWare, Andrew V. Sutherland, 18.785 Number Theory I, Fall 2021.

License: CC BY-NC-SA 4.0 · Edition: Fall 2021 · Open the original course on OCW ↗

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Number Theory I

Before you start

What's here, and what isn't

Not included here

Materials by section

Lecture Notes

Assignments

Other materials from this course

Lecture 1: Absolute Values and Discrete Valuations

Lecture 2: Localization and Dedekind Domains

Lecture 3: Properties of Dedekind Domains and Factorization of Ideals

Lecture 4: Étale Algebras, Norm and Trace

Lecture 5: Dedekind Extensions

Lecture 6: Ideal Norms and the Dedekind-Kummer Theorem

Lecture 7: Galois Extensions, Frobenius Elements, and the Artin Map

Lecture 8: Complete Fields and Valuation Rings

Lecture 9: Local Fields and Hensel’s Lemmas

Lecture 10: Extensions of Complete DVRs

Lecture 11: Totally Ramified Extensions and Krasner’s Lemma

Lecture 12: The Different and the Discriminant

Lecture 13: Global Fields and the Product Formula

Lecture 14: The Geometry of Numbers

Lecture 15: Dirichlet’s Unit Theorem

Lecture 16: Riemann’s Zeta Function and the Prime Number Theorem

Lecture 17: The Functional Equation

Lecture 18: Dirichlet L -functions and Primes in Arithmetic Progressions

Lecture 19: The Analytic Class Number Formula

Lecture 20: The Kronecker-Weber Theorem

Lecture 21: Class Field Theory: Ray Class Groups and Ray Class Fields

Lecture 22: The Main Theorems of Global Class Field Theory

Lecture 23: Tate Cohomology

Lecture 24: Artin Reciprocity in the Unramified Case

Lecture 25: The Ring of Adeles and Strong Approximation

Lecture 26: The Idele Group, Profinite Groups, and Infinite Galois Theory

Lecture 27: Local Class Field Theory

Lecture 28: Global Class Field Theory and the Chebotarev Density Theorem