Part III notes

This page hosts my (handwritten and very rough) lecture notes for some of the Cambridge (Maths Tripos) Part III courses for the 2019/2020 academic year. All errors are my own. Another well-written reference for the 2019/20 academic year is Qiangru Kuang's typeset lecture notes which can be found hereLink opens in a new window.

Preparatory Workshop notes:

• Rings and Modules I (notes, exercises, handout), 8 Oct 2019
• Algebraic Number Theory (notes, exercises), 10 Oct 2019
• Rings and Modules II (notes), 11 Oct 2019
• Number Theory - Complex Analysis (notes, exercises), 14 Oct 2019
• Algebraic Topology I (notes, handout), 10 Oct 2019
• Algebraic Topology II (notes, handout), 14 Oct 2019

Algebraic Number Theory, Term 1 Michaelmas 2019/2020 (lecturer: Jack ThorneLink opens in a new window)

Official course website: archived linkLink opens in a new window.

Official links: Course NotesLink opens in a new window, Ex Sheet 1Link opens in a new window, Ex Sheet 2Link opens in a new window, Ex Sheet 3Link opens in a new window, Ex Sheet 4Link opens in a new window, Revision SheetLink opens in a new window.

Summary of definitions/theorems and proofs. See also Lecture notesLink opens in a new window by Qiangru Kuang.

• Lecture 1 (notes), 11 Oct 2019
• Lecture 2 (notes), 14 Oct 2019
• Lecture 3 (notes), 16 Oct 2019
• Lecture 4 (notes), 18 Oct 2019
• Lecture 5 (notes), 21 Oct 2019
• Lecture 6 (notes), 23 Oct 2019
• Lecture 7 (notes), 25 Oct 2019
• Examples Class 1 (notes), 25 Oct 2019
• Lecture 8 (notes), 28 Oct 2019
• Lecture 9 (notes), 30 Oct 2019
• Lecture 10 (notes), 01 Nov 2019
• Lecture 11 (notes), 04 Nov 2019
• Lecture 12 (notes), 06 Nov 2019
• Lecture 13 (notes), 08 Nov 2019
• Lecture 14 (notes), 11 Nov 2019
• Lecture 15 (notes), 13 Nov 2019
• Lecture 16 (notes), 15 Nov 2019
• Examples Class 2 (notes), 15 Nov 2019
• Lecture 17 (notes), 18 Nov 2019
• Lecture 18 (notes), 20 Nov 2019
• Lecture 19 (notes), 22 Nov 2019
• Examples Class 3 (notes), 22 Nov 2019
• Lecture 20 (notes), 25 Nov 2019
• Lecture 21 (notes), 27 Nov 2019
• Lecture 22 (notes), 29 Nov 2019
• Lecture 23 (notes), 02 Dec 2019
• Lecture 24 (notes), 04 Dec 2019
• Examples Class 4 (notes), 06 Dec 2019

Elliptic Curves, Term 1 Michaelmas 2019/2020 (lecturer: Tom FisherLink opens in a new window)

Official course website: archived linkLink opens in a new window. See also Lecture notesLink opens in a new window by Qiangru Kuang

Exercise Sheets: Formula Sheet, Ex Sheet 1, Ex Sheet 2, Ex Sheet 3, Ex Sheet 4

Summary of definitions/theorems and proofs.

• Lecture 1 (notes), 11 Oct 2019
• Lecture 2 (notes), 14 Oct 2019
• Lecture 3 (notes), 16 Oct 2019
• Lecture 4 (notes), 18 Oct 2019
• Lecture 5 (notes), 21 Oct 2019
• Lecture 6 (notes), 23 Oct 2019
• Lecture 7 (notes), 25 Oct 2019
• Lecture 8 (notes), 28 Oct 2019
• Lecture 9 (notes), 30 Oct 2019
• Lecture 10 (notes), 01 Nov 2019
• Lecture 11 (notes), 04 Nov 2019
• Lecture 12 (notes), 06 Nov 2019
• Lecture 13 (notes), 08 Nov 2019
• Lecture 14 (notes), 11 Nov 2019
• Lecture 15 (notes), 13 Nov 2019
• Lecture 16 (notes), 15 Nov 2019
• Lecture 17 (notes), 18 Nov 2019
• Lecture 18 (notes), 20 Nov 2019
• Lecture 19 (notes), 22 Nov 2019
• Lecture 20 (notes), 25 Nov 2019
• Lecture 21 (notes), 27 Nov 2019
• Lecture 22 (notes), 29 Nov 2019
• Lecture 23 (notes), 02 Dec 2019
• Lecture 24 (notes), 04 Dec 2019

Algebra, Term 1 Michaelmas 2019/2020 (lecturer: Chris BrookesLink opens in a new window)

Exercise Sheets: Ex Sheet 1, Ex Sheet 2, Ex Sheet 3, Ex Sheet 4

Lecture notesLink opens in a new window by Qiangru Kuang

Summary of definitions/theorems and proofs.

• Lecture 1 (notes), 10 Oct 2019
• Lecture 2 (notes), 12 Oct 2019
• Lecture 3 (notes), 15 Oct 2019
• Lecture 4 (notes), 17 Oct 2019
• Lecture 5 (notes), 19 Oct 2019

Modular forms and L-functions, Term 1 2019/2020 (lecturer: Anthony J. SchollLink opens in a new window)

Official course website: linkLink opens in a new window.

Algebraic Geometry, Term 1 2019/2020 (lecturer: Mark GrossLink opens in a new window)

Lecture notesLink opens in a new window by Qiangru Kuang

Toric Geometry, Term 1 2019/2020 (lecturer: Dhruv RanganathanLink opens in a new window)

Official course website: linkLink opens in a new window.

Algebraic Topology, Term 1 2019/2020 (lecturer: Jacob RasmussenLink opens in a new window)

Official course website: archived linkLink opens in a new window. Introduction handout.

Lecture notesLink opens in a new window by Qiangru Kuang

• Lecture 1 (notes), 11 Oct 2019
• Lecture 2 (notes), 14 Oct 2019
• Lecture 3 (notes), 16 Oct 2019
• Lecture 4 (notes), 18 Oct 2019
• Lecture 5 (notes), 21 Oct 2019
• Lecture 6 (notes), 23 Oct 2019
• Lecture 7 (notes), 25 Oct 2019
• Subdivision Lemma (handout), 25 Oct 2019

Analytic Number Theory, Term 2 2019/2020 (lecturer: Thomas BloomLink opens in a new window)

Official course website: linkLink opens in a new window.

Lecture notes by Qiangru Kuang

Profinite Groups, Term 2 2019/2020 (lecturer: Gareth WilkesLink opens in a new window)

Official course website: linkLink opens in a new window.

Lecture notesLink opens in a new window by Qiangru Kuang

Infinite Games, Term 2 2019/2020 (lecturer: Benedikt LöweLink opens in a new window)

Official course website: linkLink opens in a new window.

• Lecture 1 (notes), 17 Jan 2020.
• Lecture 2 (notes), 20 Jan 2020
• Lecture 3 (notes), 22 Jan 2020
• Lecture 4 (notes), 24 Jan 2020
• Lecture 5 (notes), 27 Jan 2020
• Lecture 6 (notes), 29 Jan 2020
• Lecture 7 (notes), 31 Jan 2020
• Lecture 8 (notes), 03 Feb 2020
• Lecture 9 (notes), 05 Feb 2020
• Lecture 10 (notes), 07 Feb 2020
• Lecture 11 (notes), 10 Feb 2020
• Lecture 12 (notes), 12 Feb 2020

Model Theory, Term 2 2019/2020 (lecturer: Silvia BarbinaLink opens in a new window)

Topics in Discrete Fourier Analysis, Term 2 2019/2020 (lecturer: Tim GowersLink opens in a new window)

Extremal Graph Theory, Term 2 2019/2020 (lecturer: Andrew ThomasonLink opens in a new window)

Some further Part III course notes by others:

• Sebastian PancratzLink opens in a new window (2007/08), Dexter ChauLink opens in a new window (2016/17 and 2017/18), Alexandre DaoudLink opens in a new window (2016/17), Paul MinterLink opens in a new window (2017/18 and 2018/19), Ian LimLink opens in a new window (2018/19), Bhavik MehtaLink opens in a new window (2018/19), Qiangru KuangLink opens in a new window (2019/20), Adam KellyLink opens in a new window (2021/22), David BaiLink opens in a new window (2022/23), Daniel BassettLink opens in a new window (2022/23), Sky WilshawLink opens in a new window (2023/24).