Insights into Mathematics Courses

An Introduction to Homology - Algebraic Topology

Explore higher-dimensional topology through homology groups, cycles, and spanning trees. Learn to compute and characterize independent cycles in graphs using algebraic techniques.

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

An Informal Introduction to Abstract Algebra

Informal introduction to abstract algebra, covering fields, rings, and vector spaces. Explores key concepts and examples, from basic number systems to advanced constructions, providing essential background for algebraic topology.

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

Three Dimensional Geometry, ZOME, and the Elusive Tetrahedron

Explore three-dimensional geometry using rational trigonometry and ZOME construction, focusing on tetrahedron trigonometry and new algebraic relations for a deeper understanding of spatial structures.

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

The Stern-Brocot Tree, Matrices and Wedges - Real Numbers and Limits Math Foundations

Explore the Stern-Brocot tree's matrix and geometric representations, including wedges, for a deeper understanding of fractions and their relationships in mathematics.

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

Fractions and the Stern-Brocot Tree - Real Numbers and Limits Math Foundations

Explore the Stern-Brocot tree, a fascinating representation of fractions using a binary tree. Learn its properties, construction, and connections to Ford circles and Farey sequences in this insightful mathematical journey.

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

The Deep Structure of the Rational Numbers - Real Numbers and Limits Math Foundations

Explores the deep structure of rational numbers, focusing on their layered nature within [0,1]. Covers key concepts like Farey sequences and Ford circles, emphasizing rationals' importance in modern mathematics.

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

Problems with Limits and Cauchy Sequences - Real Numbers and Limits Math Foundations

Explores challenges in defining real numbers using Cauchy sequences, discussing convergence concepts and visualizing sequences in the plane. Highlights issues in establishing arithmetic for real numbers.

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

Difficulties With Real Numbers as Infinite Decimals - Real Numbers + Limits Math Foundations

Explores challenges in defining real numbers as infinite decimals from a computational perspective, highlighting technical obstacles in algorithms, arithmetic operations, and number equality recognition.

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

Differential Geometry - Math History - NJ Wildberger

Explore the foundations of differential geometry, from planar curves to Gaussian curvature, and its impact on modern physics. Learn about key concepts and historical contributions in this mathematical field.

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

Complex Numbers and Algebra - Math History - NJ Wildberger

Explore complex numbers' history, applications in cubic equations, and geometric representations. Delve into the Fundamental Theorem of Algebra and its proofs by d'Alembert and Gauss.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

Fractions and P-Adic Numbers - Real Numbers and Limits Math Foundations

Explore 10-adic numbers and repeating reversimals, a playful alternative to decimal arithmetic. Learn addition, multiplication, and conversion of fractions in this number theory adventure.

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

Fractions and Repeating Decimals - Real Numbers and Limits Math Foundations

Explore fractions, repeating decimals, and real numbers. Learn conversion algorithms, arithmetic operations, and gain insights into the foundations of mathematics and rational number theory.

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

The Decline of Rigour in Modern Mathematics - Real Numbers and Limits

Explores the decline of mathematical rigor, discussing Euclid's Elements, proof concepts, and problematic topics in modern mathematics. Examines reasons for this decline and its impact on mathematical foundations.

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

Newton's Method and Algebraic Curves - Real Numbers and Limits Math Foundations

Explore Newton's method for algebraic curves, examining Fermat curves and Bernoulli's Lemniscate. Learn about Taylor expansions, tangent planes, and iterative techniques for approximating curve intersections.

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

Elementary Projective Geometry - Elementary Mathematics Explained

Explore elementary projective geometry, focusing on line geometry and basic concepts like joins, meets, and quadrangles. Learn through hands-on constructions and discover fascinating correspondences in geometry.

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