Insights into Mathematics Courses

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

Pappus and Pascal - Elementary Mathematics Explained

Explore Pappus' and Pascal's theorems in projective geometry, learning key concepts and historical context. Gain insights into reading mathematics and appreciating these fundamental results.

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

Word Problems Using Addition - Elementary Mathematics Explained

Learn to solve word problems using addition with clear explanations and examples. Gain practical skills in elementary mathematics through step-by-step solutions and practice exercises.

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

Rational Trigonometry in Three Dimensions - Universal Hyperbolic Geometry

Extending rational trigonometry to 3D using vectors and dot products. Explores quadrance, spread, and key trigonometric laws. Introduces solid spread and determinants for three vectors.

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

Perpendicularity, Polarity and Duality on a Sphere - Universal Hyperbolic Geometry

Explore perpendicularity, polarity, and duality on a sphere, including polar triangles and point-plane duality. Gain insights into elliptic geometry and the relationships between geometric elements.

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

Rational Trigonometry - An Overview - Universal Hyperbolic Geometry

Introduces rational trigonometry using vectors, replacing distance and angle with quadrance and spread. Covers key concepts, formulas, and laws, offering a purely algebraic approach to trigonometry and geometry.

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

Parametrizing and Projecting a Sphere - Universal Hyperbolic Geometry

Explore stereographic and gnomonic projections of a sphere, including rational parametrization, coordinate systems, and their applications in elliptic geometry.

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

Areas and Volumes for a Sphere - Universal Hyperbolic Geometry

Explore Archimedes' sphere formulas, rational turn angles, and Harriot's theorem. Learn key principles in spherical geometry and discover new ways to conceptualize angles and areas.

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

Spherical and Elliptic Geometries - Universal Hyperbolic Geometry

Explore spherical and elliptic geometries, from ancient Greek astronomy to modern concepts. Learn about longitude, latitude, measurement techniques, and key theorems in non-Euclidean spaces.

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

Spherical and Elliptic Geometries - An Introduction

Explore spherical geometry fundamentals: great circles, antipodal points, triangles, and circles. Learn key concepts and visualize ideas with physical models, connecting to 3D space and Euclidean geometry.

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

Trigonometric Dual Laws and the Parallax Formula - Universal Hyperbolic Geometry

Explore trigonometric dual laws and the Right parallax formula in Universal Hyperbolic Geometry. Learn about Pythagoras' theorem, Cross dual law, and zero quadrance/spread theorems.

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

Newton's Method for Approximating Cube Roots - Real Numbers and Limits Math Foundations

Newton's method for approximating cube roots: explore cubes, cube roots, and techniques to find approximate solutions. Learn about Taylor expansion, tangent lines, and advanced methods like the weighted Babylonian and quadratic Newton approaches.

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

Measurement, Approximation and Interval Arithmetic - Real Numbers and Limits Math Foundations

Explore interval arithmetic, its laws for natural numbers and integers, and the challenges with real number arithmetic. Gain insights into measurement, approximation, and foundational mathematical concepts.

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

Addition in Practice - Elementary Mathematics Explained

Explore addition laws, even/odd numbers, and their geometric representations. Learn associative and commutative properties, and discover practical applications in arithmetic and counting problems.

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