Insights into Mathematics Courses

Two-Dimensional Surfaces - The Sphere - Algebraic Topology

Explore the two-dimensional sphere's significance in algebraic topology, including its relation to stereographic projection and the inversive plane in Euclidean geometry.

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

Homeomorphism and the Group Structure on a Circle - Algebraic Topology 2 - NJ Wildberger

Explore homeomorphisms, group structures on circles, and projective geometry in this algebraic topology lecture, blending fundamental concepts with novel approaches and historical insights.

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

More Row Reduction With Parameters - Wild Linear Algebra A

Explores advanced row reduction techniques with parameters, focusing on solving linear equations, vector representations, and applications in 2D and 3D spaces. Includes practical examples and exercises.

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

One-Dimensional Objects - Algebraic Topology

Explore one-dimensional objects in algebraic topology, focusing on lines and circles. Learn about their diverse representations and fundamental properties in this introductory lecture.

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

Introduction to Algebraic Topology - Algebraic Topology - NJ Wildberger

Explore the foundations of algebraic topology, its historical roots, and key concepts like homeomorphism and fundamental objects. Tackle challenging problems in this dynamic field of mathematics.

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

Applications of Row Reduction II - Wild Linear Algebra A

Explore row reduction applications in linear transformations, spanning sets, and linear independence. Gain insights into vector spaces and matrix operations through practical examples and in-depth analysis.

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

Equations of Lines and Planes in 3D - Wild Linear Algebra A - NJ Wildberger

Explore parametric and Cartesian equations of lines and planes in 3D space, including novel concepts like describing all 2D lines as a Möbius band and using determinants for 3D analysis.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

Solving a System of Linear Equations - Wild Linear Algebra A

Explore systems of linear equations, matrix forms, row reduction, and echelon forms. Learn key concepts and techniques for solving complex linear algebra problems efficiently.

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

Generalized Dilations and Eigenvalues - Wild Linear Algebra A - NJ Wildberger

Explore coordinate systems, basis changes, and similar matrices in linear algebra. Learn about generalized dilations and the fundamental concept of eigenvalues and eigenvectors.

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

Applications of 3x3 Matrices - Wild Linear Algebra A

Explore 3x3 matrices and their applications in 3D space, covering dilations, reflections, rotations, and projections. Learn key concepts and formulas for linear transformations in three dimensions.

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

Inverting 3x3 Matrices - Wild Linear Algebra A | NJ Wildberger

Comprehensive exploration of 3x3 matrix inversion, covering determinants, adjoints, and inverse properties. Includes theorem derivations, examples, and exercises for practical application.

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

Three Dimensional Affine Geometry - Wild Linear Algebra A - NJ Wildberger

Explore 3D affine geometry through parallel projections, coordinate systems, and the distinctions between points, vectors, lines, and planes. Gain insights into space representation and its mathematical foundations.

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

More Applications of 2x2 Matrices - Wild Linear Algebra A

Explores advanced applications of 2x2 matrices in linear algebra, covering rotations, reflections, composition of transformations, and connections to calculus, with a focus on linear approximations and derivatives.

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

Change of Coordinates and Determinants - Wild Linear Algebra A

Explore change of coordinates, linear equations, vectors, matrices, and determinants in linear algebra. Gain insights into fundamental concepts and their applications through examples and exercises.

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

Area and Volume - Wild Linear Algebra A | NJ Wildberger

Explore area and volume in linear algebra using bi-vectors and tri-vectors. Learn algebraic formulations, geometric proofs, and applications in physics and electromagnetism.

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