Numbers and Sets
Table of Contents
Part 1A Michaelmas
This is the first term of the Mathematical Tripos you should be taking this with the other first term courses at the same time as Cambridge designed it this way for a good reason.
Course
- Course notes
- Example sheets
- Someone made an entire video series based on the course notes
- Fields medalist supplementary reading and extra sheets
Supplementary reading
The book list in the schedule usually the first few books cover only half the course and the last recommendations cover the rest.
Cambridge schedule recommendations:
- R.B.J.T. Allenby Numbers and Proofs. Butterworth-Heinemann 1997
- R.P. Burn Numbers and Functions: steps into analysis. Cambridge University Press 2000
- H. Davenport The Higher Arithmetic. Cambridge University Press 1999
- A.G. Hamilton Numbers, sets and axioms: the apparatus of mathematics. Cambridge University Press 1983
- C. Schumacher Chapter Zero: Fundamental Notions of Abstract Mathematics. Addison-Wesley 2001
- I. Stewart and D. Tall The Foundations of Mathematics. Oxford University Press 1977
- Couldn't find a copy of this one only the watered down second edition
My strategy
We're doing this by ourselves and shortly taking abstract algebra so we should try and see how much of this we can do in a proof assistant.
- The Mechanics of Proof written by a Cambridge Part III graduate using the Lean proof assistant. Covers 90% of the Cambridge course except infinite sets.
- Logic and Computation Intertwined by Prof Ragde of Waterloo. Learning logic by building a small proof assistant making sense of how Lean/Agda/Coq proof assistants work.
- Algebra Via Problems free English (and Russian) copy on Arkadiy Skopenkov's website or use libgen
- Course notes on infinite sets
"I find that maths proofs are often 80% trivial algebra, and 10% magic tricks that are only relevant to that specific problem, and 10% key ideas that are used again and again." - Tripos graduate Neel Nanda
This is why I'm going to do the Russian algebra problem book because if you're like me your algebra is an incomplete mess. It's almost entirely proofs anyway so fits the nature of this course.
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