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
51:59Formal Logical Notation, Quantifiers & Constructing Mathematical Proofs
This lecture, part of Oxford's introductory mathematics sequence, serves as a capstone to foundational concepts, bridging pre-university knowledge with the analytical rigor expected in a first-year undergraduate curriculum.
The seventh lecture in the Introduction to Mathematics course (Lecture 0 is the first) is the last in James Munro's course. These lectures set out the type of mathematics students will be studying in their first year as well as recapping much that they have learnt in high-school.