Natural Numbers and Induction
47:48Binomial Theorem and Sets
41:50Algebra of Sets, Truth Tables, and Cardinality
52:50Relations and Equivalence Relations
49:04Functions
53:16Logical Notation and Quantifiers
44:20Constructing Statements and Proofs
46:33Complex Numbers I: Algebraic Foundations, Argand Plane & Polar Form
46:06Complex Numbers II: De Moivre's Theorem & Roots of Unity
50:04Introductory Calculus: First Year Student Lecture
58:03Multiple Integrals in 2D
46:39Multiple Integrals in 2D; Change of Variables and Jacobians
48:06Volume Integrals
52:22Surface Integrals
48:03Natural Numbers and Induction
This lecture introduces first-year students to the foundational concepts of natural numbers and the principle of mathematical induction, emphasizing rigorous proof construction.
This course is taken in the first two weeks of the first year of the Oxford Mathematics degree. It introduces the concepts and ways of mathematical thinking that students need in the years ahead (if you find the writing difficult please use the captions which have been edited).