Insights into Mathematics Courses

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

Hyperbolic Geometry Is Projective Relativistic Geometry - Full Lecture

Explore hyperbolic geometry as projective relativistic geometry, covering key concepts, models, and theorems. Gain insights into quadrance, spread, trigonometry, and unique results like the Jumping Jack theorem.

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

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

Explores interval arithmetic for natural numbers and integers, covering definitions, inequalities, arithmetic operations, and applications in measurement and counting. Lays foundations for mathematical reasoning.

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

Calculus on a Cubic - The Folium of Descartes - Arithmetic and Geometry Math Foundations

Explore the Folium of Descartes through algebraic calculus, examining its parametrization, Taylor expansions, tangents, and unique properties in both 2D and 3D space.

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

An Introduction to Algebraic Curves - Arithmetic and Geometry Math Foundations

Explore the history and concepts of algebraic curves, from ancient Greek spirals to modern polynomial approaches, setting the stage for generalizing algebraic calculus beyond functions.

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

Object-Oriented Versus Expression-Oriented Mathematics - Arithmetic and Geometry Math Foundations

Exploring the shift from object-oriented to expression-oriented mathematics, focusing on the unit circle as a key example and discussing various interpretations and approaches in modern mathematics.

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

Triangle Geometry Old and New - An Introduction to Hyperbolic Triangle Geometry

Explore classical and hyperbolic triangle geometry, covering perpendicularity, midpoints, and bilines. Learn about orthocenters, incenters, circumcenters, and more through visual illustrations without complex formulas.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

Cubics and the Prettiest Theorem in Calculus - Arithmetic and Geometry Math Foundations

Explore cubic polynomials, their calculus, and tangent conics. Learn about Etienne Ghys' theorem, considered one of the most beautiful in calculus, with an elegant proof provided.

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

Lines and Parabolas I - Arithmetic and Geometry Math Foundations

Explore lines and parabolas using algebraic calculus, covering y-intercepts, slopes, x-intercepts, quadratic polynomials, Taylor expansions, derivatives, and tangent lines in elementary mathematics.

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

Translating Polynumbers and the Derivative - Arithmetic and Geometry Math Foundations

Explore polynomials and derivatives algebraically, introducing Taylor polynomials and sub-derivatives. Challenges traditional calculus views, shifting towards Euler and Lagrange's approach to mathematical foundations.

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

Laurent Polynumbers - The New Years Day Lecture - Arithmetic and Geometry Math Foundations

Explore Laurent polynumbers, their arithmetic, and relation to rational polynumbers. Learn about the foundational importance of rational numbers and polynumbers in mathematics.

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

Row and Column Polynumbers - Arithmetic and Geometry Math Foundations

Explore two-dimensional arithmetic with polynumbers, introducing bipolynumbers and their associated polynomials in alpha and beta variables. Learn simplified arithmetic and multiplication techniques.

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