Number Fields, Lent 2024

This page contains information for students taking my lectures on Number Fields in Lent 2024. The best way to contact me outside lectures is by email: pv270@dpmms.cam.ac.uk. (I do not monitor Moodle.)

Lecture notes are available here. (Last updated: 8 March 2024.) The notes will be updated in the course of the term. Please check back, and see the changelog below.

Example sheets: example sheet 1, example sheet 2, example sheet 3.

Lecture recordings are available via Panopto. However, I expect that most students will find the notes more useful.

Changelogs

Notes

• Version of 15 January 2024: Contains Sections 1-3, Introduction, Rings of Integers, and their additive structure.
• Version of 1 February: Added Section 4: Unique factorization of ideals. Fixed a typo in Proposition 26.
• Version of 7 February: Added Sections 5 and 6: Norm of ideals and Ideals in field extensions. Added discussion about gcd and lcm of ideals in Section 4.
• Version of 21 February: First complete version. Some typos fixed.
• Version of 8 March: Some typos fixed.

Example sheets

• Version of 8 March: Typos fixed in Sheet 1, Q9; Sheet 2, Q12; Sheet 3, Q14.