Tom Rocks Maths Courses

Exponential Matrix Integration

Master exponential matrix integration through challenging problems involving determinants, revealing elegant mathematical solutions in advanced linear algebra.

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

Oxbridge Professor Takes High School Statistics Exam - A-Level Further Maths

Discover how an Oxford/Cambridge mathematician tackles A-Level Further Maths statistics, working through real exam questions with expert insights and problem-solving techniques.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

University of Cambridge Mathematics Admissions Interview

Experience a realistic Cambridge mathematics admissions interview with Dr Tom Crawford, revealing the interview process and expectations for prospective undergraduate students.

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

Goalball - The Most Mathematical Sport

Explore the fascinating mathematics behind goalball as Dr Tom Crawford calculates shooting angles and strategic positioning in this unique Paralympic sport.

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

Creating a Superhuman AI Mathematician

Explore cutting-edge research on developing superhuman AI mathematicians with Princeton's Sanjeev Arora, covering computational complexity and AI's potential in mathematical discovery.

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

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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• 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