Insights into Mathematics Courses

Distances to the Sun and Moon - Famous Math Problems

Explore ancient Greek methods for calculating celestial distances, from Thales to Aristarchus. Learn how early astronomers determined Earth's size and the distances to the sun and moon.

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

Newcomb's Paradox - Famous Math Problems

Explore Newcomb's paradox, a mathematical-philosophical puzzle involving free will, determinism, and rationality. Learn about expected value and strategies for decision-making in uncertain scenarios.

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

Archimedes' Squaring of a Parabola - Famous Math Problems

Explore Archimedes' ingenious solution to calculating the area of a parabolic section, a foundational problem in calculus, through geometric insights and elegant proofs.

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

Omar Khayyam and the Binomial Theorem - Famous Math Problems

Explore the history and applications of the Binomial Theorem, from Omar Khayyam to Pascal's triangle, with insights into its expansion, coefficients, and relevance in modern mathematics.

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

Apollonius' Circle Construction Problems - Famous Math Problems

Explore Apollonius' circle construction problems, their historical significance, and related geometric concepts. Learn about circle geometry, constructions, and their relevance in modern mathematics.

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

Change of Basis and Taylor Coefficient Vectors - Wild Linear Algebra A - NJ Wildberger

Explore change of basis, vatrices, and Taylor coefficients in linear algebra. Novel framework connects coordinate vectors to calculus applications, featuring generalized Pascal matrices.

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

Factoring Large Numbers into Primes - Famous Math Problems

Explore prime factorization of large numbers, modular arithmetic, and theorems by Fermat and Euler. Learn techniques to tackle complex mathematical problems and improve number theory skills.

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

Cubic Splines Using Calculus - Wild Linear Algebra

Explore cubic spline interpolation using Taylor coefficient vectors, a novel approach to creating smooth curves through given points without requiring prior calculus knowledge.

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

Cubic Splines - De Casteljau Bezier Curves Using Linear Algebra

Explore de Casteljau Bezier curves and cubic splines using linear algebra, focusing on their elegant formulas and applications in design work from automobiles to modern graphics.

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

The Time Scale of a Human Life - Elementary Mathematics Explained

Explore the measurement of time through human life stages, astronomical cycles, and life spans. Learn to visualize a century-long timeline and understand key milestones in human development.

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

Area Problems Using Multiplication - Elementary Mathematics Explained

Explore area problems using multiplication in the grid plane. Practice addition and multiplication skills while learning about historical connections between multiplication and rectangles.

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

Extending Arithmetic to Infinity - Real Numbers and Limits Math Foundations

Explore extending arithmetic to infinity using rational numbers and projective geometry. Learn about integral points, theorems, and distributive laws in this mathematical journey.

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

Limits and Rational Poly On-Sequences - Real Numbers + Limits Math Foundations | N J Wildberger

Explore rational polynumbers, infinite sequences, and the concept of infinity in mathematics. Learn about factorizations, limiting behaviors, and the delicate nature of associating sequences with rational functions.

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

Challenges With Higher On-Sequences - Real Numbers and Limits Math Foundations

Explores challenges in extending polynumber sequences, discussing exponomials and recursive sequences. Highlights logical issues and the need for clearer definitions in mathematical foundations.

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

Computing Homology Groups - Algebraic Topology - NJ Wildberger

Explore homology groups in algebraic topology, focusing on examples like circles and disks. Learn about connectivity, loops, and higher-dimensional holes in spaces.

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