2022 MAST90136 Algebraic Number Theory

I taught MAST90136 Algebraic Number Theory in Semester 1, 2022.

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I plan to follow (rather loosely) Matthew Baker's lecture notes, a copy of which you can download here. This will be supplemented with other material that I will post on this page as we progress along.

Many administrative details about the organisation of the subject can (as always) be found in the subject handbook entry.

Lecture notes

I'll be attaching the handwritten notes I produce during the lectures to the corresponding lecture capture recording. I am also putting together some typed notes that contain some additional material, e.g. exercises. These notes will be growing as the semester progresses. Here is the current version (as of 13 June).

Assignments

The three assignments will be posted both here and on the subject's Canvas page. Your solutions should be submitted via Canvas and Gradescope (and the same mechanism will very likely be used for the final exam).

The tentative due dates for the assignments are: Monday 4 April, Monday 2 May, and Monday 23 May.

Any requests for assignment special consideration should be sent to me, preferably not at the last minute.

Update: the assignment pdfs now include solutions.

Here is the first assignment, due Monday 4 April.

Here is the second assignment, due Monday 2 May.

Here is the third assignment, due Monday 23 May.

Ed discussion board

Please see the subject's Canvas page for access to the discussion board.

Lecture recordings

Please see the subject's Canvas page for access to the lecture recordings.

Other references: algebra

The main prerequisite for the subject is the University of Melbourne's undergraduate algebra sequence consisting of one of the first-year linear algebra subjects, MAST20022 Group Theory and Linear Algebra, and MAST30005 Algebra.

For those of you arriving with a different background, this means a solid understanding of linear algebra and previous exposure to groups, group actions, rings, ideals, modules, fields, field extensions and Galois theory.

There are many excellent abstract algebra texts out there, so feel free to grab one to use as a reference while working on this subject.

For historical reasons, I'm partial to

• Abstract algebra by Dummit and Foote
• Algebra by Lang

Other references: number theory

There are also many excellent algebraic number theory texts out there. Here are some that I might refer to in this subject:

• Number fields by Marcus
• A classical introduction to modern number theory by Ireland and Rosen
• Algebraic theory of numbers by Samuel
• Algebraic number theory by Milne
• A course in computational algebraic number theory by Cohen
• Algebraic number theory, a computational approach by Stein

Note: Many of these references may be accessible via the library system either as electronic resources or (gasp) physical tomes.