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
58:03Multivariable Calculus, Lecture 1: Multiple Integrals in 2D
46:39Multivariable Calculus, Lecture 2: Multiple Integrals in 2D; Change of Variables and Jacobians
48:06Multivariable Calculus, Lecture 3: Volume Integrals
52:22Multivariable Calculus, Lecture 4: Surface Integrals
48:03Logical Notation and Quantifiers
This lecture focuses on the precise use of logical notation and quantifiers, essential tools for constructing and analyzing mathematical statements and proofs.
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).
Much of the context will be familiar from high school but the way we think and write about it, and construct arguments and proofs, will be more rigorous.