Insights into Mathematics Courses

Analytic Geometry and the Continuum - Math History - NJ Wildberger

Explores Cartesian geometry's development, merging numbers and geometry, and discusses issues with the continuum, irrational numbers, and decimal expansions, including pi's continued fraction approximations.

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

Analytic Geometry and the Continuum - Math History - NJ Wildberger

Explore Cartesian geometry's development, merging numbers and geometry. Delve into conics, cubics, Bezout's theorem, and the continuum, discussing ancient Greek influences and challenges with irrational numbers and pi.

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

First Steps in Hyperbolic Geometry - Universal Hyperbolic Geometry

Explore fundamental concepts of universal hyperbolic geometry, including perpendicularity, quadrance, spread, and key theorems, with a focus on projective study of circles and relativistic geometry.

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

Apollonius and Harmonic Conjugates - Universal Hyperbolic Geometry 2 - NJ Wildberger

Explore harmonic conjugates in geometry, including their relation to circles, conics, and quadrangles. Learn about harmonic ranges, pencils, and vector combinations in this advanced mathematical discussion.

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

Apollonius and Polarity - Universal Hyperbolic Geometry

Explore Apollonius' polarity concept in hyperbolic geometry, focusing on the crucial role of circles and their relationship to points and lines in the projective plane.

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

Universal Hyperbolic Geometry - NJ Wildberger

Discover a revolutionary approach to hyperbolic geometry, simplifying complex concepts using high school algebra and projective geometry, with connections to Einstein's special relativity theory.

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

Polynomial Equations - Math History - NJ Wildberger

Explore the Golden Age of European mathematics, focusing on polynomial equations, algebraic advancements, and key figures like Tartaglia and Cardano. Learn about historical developments in solving complex equations.

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

Number Theory and Algebra in Asia - Math History - NJ Wildberger

Explores number theory, algebra, and astronomy in ancient Chinese, Indian, and Arab mathematics, highlighting key figures and their contributions to mathematical development.

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

Polynomials and Sequence Spaces - Wild Linear Algebra - NJ Wildberger

Explore polynomials as sequences, introducing factorial powers and difference operators. Learn about forward/backward differences, Newton's theorem, and formulas for summing series, with practical examples and exercises.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Infinity in Greek Mathematics - Math History - NJ Wildberger

Explore ancient Greek mathematics, focusing on Eudoxus and Archimedes' groundbreaking work in calculus, geometry, and mechanics. Discover their ingenious formulas and principles that laid the foundation for modern mathematics.

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

Greek Number Theory - Math History - NJ Wildberger

Explore ancient Greek number theory, including primes, perfect numbers, and the Fundamental Theorem of Arithmetic. Learn about Euclidean algorithms, continued fractions, and Pell's equation.

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

Greek Number Theory - Math History - NJ Wildberger

Explore ancient Greek number theory, including squares, primes, and the Fundamental Theorem of Arithmetic. Learn about Euclidean algorithms, continued fractions, and Archimedes' Cattle Problem.

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

Greek Geometry - Math History - NJ Wildberger

Explore ancient Greek geometry, from Euclid's Elements to Apollonius' conics, covering key concepts, constructions, and the Platonic solids in this comprehensive lecture on mathematical history.

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

Bases of Polynomial Spaces - Wild Linear Algebra - NJ Wildberger

Explore polynomial spaces through linear algebra, focusing on bases, translations, and derivatives. Gain insights into calculus concepts from an algebraic perspective, emphasizing practical applications and theoretical foundations.

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

Pythagoras' Theorem - Math History - NJ Wildberger

Explore Pythagoras' theorem's historical significance, Greek mathematical thinking, and its connections to ancient Babylonian mathematics and modern geometry.

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