Level 7.1 – Numbers and sets

These notes are based on lectures by Zoe Wyatt in the academic 2025-2026. Mistakes are almost surely mine and this is not official nor a recreation of what was in the lectures.

Summary of the course [Expand]

• Lectures 1-6 are about sets, functions, relations, quantifiers and their basic properties. We go through truth tables, indicator functions, and injective and surjective functions.
• Lectures 6-8 introduce the peano axioms and talk about well ordering and induction, and the inclusion-exclusion principle.
• Lectures 9-14 are about basic number theory: Euclids algorithm, prime factorization, Fermat-Euler theorem and RSA encryption.
• Lectures 14-21 are about defining the rational numbers and real numbers, then looking into sequences and series and proving stuff like that e is irrational and that the harmonic series diverges (but very slowly), and that decimal expansions are (usually) unique. We also go through a proof of transcendence of a number.
• Lectures 21-24 are about countable and uncountable sets and the different sizes of infinity.

See my numbers and sets notes here