Tom Rocks Maths Courses

Building the Multiverse Library

Explore complex mathematics behind the Multiverse Library, focusing on branch cuts and multifunctions. Learn about holomorphic branches of complex logarithms and square root functions in this engaging mathematical journey.

• YouTube
• 21 minutes
• Self-Paced
• Free Video

Oxford Linear Algebra - Direct Sum of Vector Spaces

Comprehensive explanation of direct sum of vector spaces with worked examples. Learn formal definitions, alternative representations, and how to verify direct sums through intersection and spanning checks.

• YouTube
• 31 minutes
• Self-Paced
• Free Video

Oxford Linear Algebra - Dimension Formula for Vector Spaces

Explore the dimension formula for vector spaces through worked examples and a complete proof. Learn to calculate dimensions of subspaces and their intersections in R^4.

• YouTube
• 43 minutes
• Self-Paced
• Free Video

Oxford Linear Algebra - Basis, Spanning and Linear Independence

Explore key concepts in linear algebra: basis, spanning, and linear independence. Learn through intuitive examples and formal definitions, with worked problems in vector spaces and Cartesian planes.

• YouTube
• 42 minutes
• Self-Paced
• Free Video

Oxford Calculus - Gradient and Divergence Explained

Comprehensive explanation of gradient vector and divergence in multivariable calculus, including formal definitions, visualizations, examples, and connections to other concepts. Includes free worksheet and app recommendations.

• YouTube
• 28 minutes
• Self-Paced
• Free Video

Oxford Linear Algebra - Subspace Test

Comprehensive explanation of subspace test in vector spaces, including definition, examples, and applications. Includes worked problems and links to additional resources for practice.

• YouTube
• 36 minutes
• Self-Paced
• Free Video

Oxford Linear Algebra - What is a Vector Space?

Explore vector space axioms with concrete examples, including addition and scalar multiplication maps, 8 key axioms, and proofs for 3D coordinate vectors. Gain insights into unique properties of vector spaces.

• YouTube
• 30 minutes
• Self-Paced
• Free Video

Pokémon Catch Rate Formula Explained

Explore the mathematics behind Pokémon's catch rate formula with Oxford mathematician Dr Tom Crawford. Learn how variables like HP, status effects, and ball types influence capture probability.

• YouTube
• 36 minutes
• Self-Paced
• Free Video

Oxford Linear Algebra - Spectral Theorem Proof

Comprehensive proof of the Spectral Theorem for real symmetric matrices, demonstrating real eigenvalues and diagonalization using eigenvector basis. Includes step-by-step explanation and mathematical reasoning.

• YouTube
• 35 minutes
• Self-Paced
• Free Video

Oxford Calculus: How to Solve the Heat Equation

Learn to solve the Heat Equation, a fundamental PDE in calculus, with Oxford mathematician Dr Tom Crawford. Includes practice questions, interactive worksheets, and a free calculator app for comprehensive understanding.

• YouTube
• 35 minutes
• Self-Paced
• Free Video

Oxford Linear Algebra - Eigenvalues and Eigenvectors Explained

Comprehensive tutorial on calculating eigenvalues and eigenvectors of matrices, featuring two worked examples. Covers the eigenvalue equation, characteristic polynomial, and step-by-step solutions for 2x2 and 3x3 matrices.

• YouTube
• 26 minutes
• Self-Paced
• Free Video

Oxford Calculus - Separable Solutions to PDEs

Learn to solve partial differential equations using separable solutions with Oxford mathematician Dr Tom Crawford. Includes examples, practice worksheets, and links to a free calculator app for checking your work.

• YouTube
• 21 minutes
• Self-Paced
• Free Video

Heisenberg's Uncertainty Principle

Derive Heisenberg's Uncertainty Principle in Quantum Mechanics, exploring Schrödinger's Equation, momentum and position operators, and the key proposition leading to this fundamental concept.

• YouTube
• 36 minutes
• Self-Paced
• Free Video

Oxford Calculus - Heat Equation Derivation

Comprehensive derivation of the Heat Equation from physical principles, including Liebniz Rule and Fourier's Law. Extends to 2D and 3D applications with interactive exercises for practice.

• YouTube
• 25 minutes
• Self-Paced
• Free Video

Oxford Linear Algebra - The Easiest Method to Calculate Determinants

Learn the easiest method to calculate determinants using Elementary Row Operations (ERO's). Includes a worked example for a 4x4 matrix and links to practice exercises and video solutions.

• YouTube
• 27 minutes
• Self-Paced
• Free Video