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
51:59Algebra of Sets, De Morgan's Laws, Truth Tables & Cardinality
This lecture, part of Oxford's introductory course, reviews high-school mathematical concepts while introducing students to the rigor and style of university-level mathematics, focusing on foundational principles and proof strategies essential for advanced study.
The fourth lecture in the Introduction to Mathematics course (Lecture 0 is the first). 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.
The Binomial Theorem, Combinatorial Identities & Set Notation
Next · Lecture 5Binary Relations, Partitions & Equivalence Relations