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
51:59Functions, Injections, Surjections, Bijections & Inverses
This lecture for Oxford first-year undergraduates introduces the pedagogical approach and core topics of university mathematics, bridging high school curricula with advanced concepts and problem-solving methodologies encountered in higher education.
The sixth lecture in the Introduction to Mathematics course (Lecture 0 is the first) is our new first year students' first in-person lecture on the first day of term, the first five lectures having been online in preparation. 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.
Binary Relations, Partitions & Equivalence Relations
Next · Lecture 7Formal Logical Notation, Quantifiers & Constructing Mathematical Proofs