Foundations of University Mathematics: From Calculation to Proof
1:14:56Natural Numbers, Well-Ordering & Mathematical Induction
1:52:56The Binomial Theorem, Combinatorial Identities & Set Notation
42:36Algebra of Sets, De Morgan's Laws, Truth Tables & Cardinality
1:33:11Binary Relations, Partitions & Equivalence Relations
2:14:26Functions, Injections, Surjections, Bijections & Inverses
45:16Formal Logical Notation, Quantifiers & Constructing Mathematical Proofs
51:59Foundations of University Mathematics: From Calculation to Proof
This introductory session for incoming Oxford mathematics undergraduates reviews essential high-school concepts and outlines the formal rigor and abstract thinking required for university-level mathematics, setting the stage for proof-based courses.
In the run-up to the start of term, our first year students can watch an online introductory course which sets out the type of mathematics they will be studying in their first year as well as recapping much that they have learnt in high-school. We will be showing all the course which concludes with two in-person lectures at the beginning of term.