Tom Rocks Maths Courses

Oxford Linear Algebra - Inner Product Space

Explore inner product spaces, bilinear forms, and orthonormal sets in linear algebra. Learn key concepts and proofs with practical examples and exercises to enhance understanding.

• YouTube
• 34 minutes
• On-Demand
• Free Video

Oxford Linear Algebra - Rank Nullity Theorem

Comprehensive exploration of rank and nullity concepts, including definitions, examples, and a step-by-step proof of the Rank Nullity Theorem in linear algebra.

• YouTube
• 29 minutes
• On-Demand
• Free Video

Oxford Linear Algebra - Linear Transformations Explained

Explore linear transformations with Oxford mathematician Dr Tom Crawford, covering definitions, properties, and examples in R3, including matrix multiplication and differentiation.

• YouTube
• 33 minutes
• On-Demand
• Free Video

Oxford Calculus - Fourier Series Derivation

Comprehensive derivation of Fourier Series coefficients, covering orthogonality relations, integration techniques, and uniform convergence. Includes practical examples and a free worksheet for hands-on practice.

• YouTube
• 41 minutes
• On-Demand
• Free Video

Oxford Calculus - Taylor's Theorem Explained with Examples and Derivation

Comprehensive explanation of Taylor's Theorem, including derivation and practical examples. Covers polynomial approximation of functions, Cauchy's Mean Value Theorem, and power series expansion, with interactive exercises and additional resources.

• YouTube
• 26 minutes
• On-Demand
• Free Video

Oxford Linear Algebra - How to Find a Matrix Inverse Using Elementary Row Operations

Learn to calculate matrix inverses using Elementary Row Operations (ERO's) with clear explanations and worked examples for 2x2 and 4x4 matrices, including the case of non-invertible matrices.

• YouTube
• 24 minutes
• On-Demand
• Free Video

Linear Algebra - Elementary Row Operations Explained

Comprehensive tutorial on solving linear equations using matrices and elementary row operations, with worked examples and practice resources for self-study.

• YouTube
• 36 minutes
• On-Demand
• Free Video

AMC 12 Cube Colouring Question

Explore a challenging cube coloring problem and learn how to solve it using mathematical reasoning and combinatorial analysis.

• YouTube
• 31 minutes
• On-Demand
• Free Video

Oxford Calculus - Solving Homogeneous First Order Differential Equations

Learn to solve homogeneous first order differential equations with Oxford mathematician Dr Tom Crawford. Includes worked examples, partial fractions, implicit differentiation, and practice exercises.

• YouTube
• 25 minutes
• On-Demand
• Free Video

Quadratic Formula Derivation and Application to Penalty Kicks and Archery

Derive the quadratic formula and apply it to real-world scenarios in football and archery. Learn 'completing the square' method and solve problems in penalty kicks and projectile motion.

• YouTube
• 31 minutes
• On-Demand
• Free Video

Oxford Calculus - Integrating Factors Explained

Learn to solve first order linear differential equations using integrating factors. Understand the technique's derivation, application, and practice with a provided worksheet and example problems.

• YouTube
• 22 minutes
• On-Demand
• Free Video

Oxford Calculus - Classifying 2D Critical Points Using the Discriminant

Learn to classify 2D critical points using the discriminant method. Explore maximum, minimum, and saddle points with visualizations and step-by-step derivations for multivariable functions.

• YouTube
• 30 minutes
• On-Demand
• Free Video

Mandelbulbs - The Search for a 3D Mandelbrot Fractal

Explore the fascinating world of 3D fractals, from natural examples to complex mathematical constructs like Mandelbulbs, with insights into fractal dimensions and generation techniques.

• YouTube
• 26 minutes
• On-Demand
• Free Video

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
• On-Demand
• 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
• On-Demand
• Free Video