Part III notes
This page hosts some of my handwritten (and very rough) lecture notes for Cambridge Part III (Maths Tripos) courses in the 2019/20 academic year. All errors are my own. Another well-written reference for the 2019/20 academic year is Qiangru Kuang’s notes.
Preparatory workshop
- Rings and Modules I [notes] [exercises] [handout]
- Algebraic Number Theory [notes] [exercises]
- Rings and Modules II [notes]
- Number Theory — Complex Analysis [notes] [exercises]
- Algebraic Topology I [notes] [handout]
- Algebraic Topology II [notes] [handout]
Algebraic Number Theory
Course website: archived. Official material: notes, sheet 1, sheet 2, sheet 3, sheet 4, revision sheet.
My summaries: definitions and theorems, proofs. See also Qiangru Kuang’s notes.
- Lecture 1 [notes]
- Lecture 2 [notes]
- Lecture 3 [notes]
- Lecture 4 [notes]
- Lecture 5 [notes]
- Lecture 6 [notes]
- Lecture 7 [notes]
- Lecture 8 [notes]
Examples classes: Class 1 · Class 2 · Class 3 · Class 4 .
Elliptic Curves
Course website: archived. See also Qiangru Kuang’s notes.
Exercise sheets: formula sheet, sheet 1 (solutions), sheet 2 (solutions), sheet 3 (solutions), sheet 4 (solutions).
My summary: definitions and theorems.
- Lecture 1 [notes]
- Lecture 2 [notes]
- Lecture 3 [notes]
- Lecture 4 [notes]
- Lecture 5 [notes]
- Lecture 6 [notes]
- Lecture 7 [notes]
- Lecture 8 [notes]
Examples classes: Class 1 · Class 2 · Class 3 · Class 4 .
Algebra
Exercise sheets: sheet 1, sheet 2, sheet 3, sheet 4. See also Qiangru Kuang’s notes.
My summary: definitions and theorems.
- Lecture 1 [notes]
- Lecture 2 [notes]
- Lecture 3 [notes]
- Lecture 4 [notes]
- Lecture 5 [notes]
- Lecture 6 [notes]
- Lecture 7 [notes]
- Lecture 8 [notes]
Examples classes: Class 1 · Class 2 · Class 3 · Class 4 .
Modular Forms and L-functions
Course website: link.
My summary: definitions and theorems.
Algebraic Geometry
Toric Geometry
Course website: link.
Algebraic Topology
Course website: archived. Introduction handout. See also Qiangru Kuang’s notes.
- Lecture 1 [notes]
- Lecture 2 [notes]
- Lecture 3 [notes]
- Lecture 4 [notes]
- Lecture 5 [notes]
- Lecture 6 [notes]
- Lecture 7 [notes]
- Subdivision lemma [handout]
Analytic Number Theory
Course website: link. See also Qiangru Kuang’s notes.
My summary: definitions and theorems.
Profinite Groups
Course website: link. See Qiangru Kuang’s notes.
Infinite Games
Course website: link.
- Lecture 1 [notes]
- Lecture 2 [notes]
- Lecture 3 [notes]
- Lecture 4 [notes]
- Lecture 5 [notes]
- Lecture 6 [notes]
- Lecture 7 [notes]
- Lecture 8 [notes]
- Lecture 9 [notes]
- Lecture 10 [notes]
- Lecture 11 [notes]
- Lecture 12 [notes]
Other Lent 2020 courses
- Model Theory (lecturer: Silvia Barbina)
- Topics in Discrete Fourier Analysis (lecturer: Tim Gowers)
- Extremal Graph Theory (lecturer: Andrew Thomason)
Part III notes by others
Sebastian Pancratz (2007/08) · Dexter Chua (2016/17, 2017/18) · Alexandre Daoud (2016/17) · Paul Minter (2017/18, 2018/19) · Ian Lim (2018/19) · Bhavik Mehta (2018/19) · Qiangru Kuang (2019/20) · David Ang (2020/21) · Adam Kelly (2021/22) · David Bai (2022/23) · Daniel Bassett (2022/23) · Sky Wilshaw (2023/24).
