0 of 72 lectures are ready to read. The rest are listed so you can see where the subject goes; each one switches on as it is finished.
Limits and Continuity0 of 4 ready
- 01What is a limit — approaching a valuecoming soon
- 02Evaluating limits — algebraic techniquescoming soon
- 03Continuity — no jumps or holescoming soon
- 04The epsilon-delta definition of a limitcoming soon
Single Variable Calculus0 of 5 ready
- 01Differentiation revisited — the formal definitioncoming soon
- 02Advanced differentiation techniquescoming soon
- 03Taylor and Maclaurin series — approximating functionscoming soon
- 04Integration techniques — review and advancedcoming soon
- 05Improper integrals — infinite limits and discontinuitiescoming soon
Multivariable Calculus0 of 5 ready
- 01Functions of several variables — visualising surfacescoming soon
- 02Partial derivatives and the gradientcoming soon
- 03Multiple integrals — double and triple integralscoming soon
- 04Vector calculus — div, grad, curlcoming soon
- 05Optimisation in several variablescoming soon
Sequences and Series (Rigorous)0 of 3 ready
- 01Sequences — convergence and divergencecoming soon
- 02Series — convergence testscoming soon
- 03Power series — radius and interval of convergencecoming soon
Vectors and Vector Spaces0 of 3 ready
- 01Vector spaces — abstract definitioncoming soon
- 02Linear independence and basiscoming soon
- 03Linear transformations — maps between spacescoming soon
Matrices0 of 3 ready
- 01Matrix operations — add, multiply, transposecoming soon
- 02Determinants — computing and meaningcoming soon
- 03Matrix inverses — when they exist and how to findcoming soon
Systems of Linear Equations0 of 3 ready
- 01Gaussian elimination — row reductioncoming soon
- 02Solution sets — unique, infinite, nonecoming soon
- 03LU decomposition — factoring for repeated solvingcoming soon
Eigenvalues and Eigenvectors0 of 4 ready
- 01What are eigenvalues and eigenvectorscoming soon
- 02Finding eigenvalues and eigenvectors — the methodcoming soon
- 03Diagonalisation — when and howcoming soon
- 04The spectral theorem — symmetric matricescoming soon
First-Order Differential Equations0 of 4 ready
- 01Separable first-order DEscoming soon
- 02Linear first-order DEs — integrating factorcoming soon
- 03Exact equations and integrating factorscoming soon
- 04Existence and uniqueness — Picard's theoremcoming soon
Second-Order Differential Equations0 of 4 ready
- 01Homogeneous second-order DEs with constant coefficientscoming soon
- 02Non-homogeneous DEs — undetermined coefficientscoming soon
- 03Variation of parameters — a general methodcoming soon
- 04Systems of DEs — matrix methodscoming soon
Logic and Proof0 of 4 ready
- 01Propositional Logic — And, Or, Not, Impliescoming soon
- 02Quantifiers — For All and There Existscoming soon
- 03Proof Methods — Direct, Contrapositive, Contradiction, Inductioncoming soon
- 04Mathematical Induction — Weak and Strongcoming soon
Set Theory0 of 4 ready
- 01Sets — Notation and Basic Operationscoming soon
- 02Functions as Sets — Domain, Codomain, Imagecoming soon
- 03Cardinality — Comparing Infinite Setscoming soon
- 04Relations — Equivalence and Ordercoming soon
Combinatorics0 of 4 ready
- 01Counting Principles — Addition and Multiplicationcoming soon
- 02Permutations and Combinations — Formal Treatmentcoming soon
- 03Generating Functions — A Powerful Counting Toolcoming soon
- 04Pigeonhole Principle and Its Applicationscoming soon
Graph Theory0 of 4 ready
- 01Graphs — Vertices, Edges, and Basic Definitionscoming soon
- 02Trees — Connected Graphs with No Cyclescoming soon
- 03Euler and Hamiltonian Circuitscoming soon
- 04Graph Colouring and Planaritycoming soon
Probability Theory0 of 4 ready
- 01Sample Spaces and Events — Formal Probabilitycoming soon
- 02Independence and Conditional Probabilitycoming soon
- 03Random Variables — Discrete and Continuouscoming soon
- 04Expectation and Variance — Properties and Calculationscoming soon
Key Distributions0 of 4 ready
- 01Discrete Distributions — Binomial, Poisson, Geometriccoming soon
- 02Continuous Distributions — Uniform, Exponential, Normalcoming soon
- 03The Central Limit Theorem — Why the Normal Is Everywherecoming soon
- 04Moment Generating Functionscoming soon
Statistical Inference0 of 4 ready
- 01Point Estimation — Finding Good Estimatorscoming soon
- 02Confidence Intervals — Quantifying Uncertaintycoming soon
- 03Hypothesis Testing — The Formal Frameworkcoming soon
- 04Likelihood Ratio Tests and Goodness of Fitcoming soon
Divisibility and Modular Arithmetic0 of 3 ready
- 01Divisibility — The Basic Theorycoming soon
- 02Modular Arithmetic — Clock Arithmeticcoming soon
- 03Linear Diophantine Equationscoming soon
Prime Numbers and Cryptography0 of 3 ready
- 01Prime Numbers — Distribution and Importancecoming soon
- 02Fermat's Little Theorem and Euler's Theoremcoming soon
- 03RSA Cryptography — The Maths of Public Key Encryptioncoming soon