Insights into Mathematics Courses

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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video

Decimal Numbers - Arithmetic and Geometry Math Foundations

Explore decimal numbers, their representation in the Hindu-Arabic system, and conversion between fractions and decimals. Learn about notation, structure, and practical applications in mathematics.

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

The Division Algorithm for Polynumbers - Arithmetic + Geometry Math Foundations | N J Wildberger

Explore the division algorithm for polynumbers, covering integral and rational polynumbers, and different approaches to division. Learn foundational concepts in mathematics with a focus on logical rigor.

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

Menelaus, Ceva and the Laws of Proportion - Universal Hyperbolic Geometry

Explore classical theorems of Menelaus and Ceva in universal hyperbolic geometry, along with new results on triangle proportions and alternate spreads. Learn about ratios, distances, and quadrances in triangular geometry.

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

Isosceles Triangles in Hyperbolic Geometry - Universal Hyperbolic Geometry - NJ Wildberger

Explore isosceles triangles in hyperbolic geometry, including special formulas, midpoint construction, and related theorems. Gain insights through proofs, exercises, and applications of the cross law.

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

Thales' Theorem, Right Triangles + Napier's Rules - Universal Hyperbolic Geometry

Explores Thales' theorem and Napier's rules in universal hyperbolic geometry, focusing on right triangles. Covers key concepts like quadrea, spreads, and proofs, with practical exercises for deeper understanding.

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

The Fundamental Group - Algebraic Topology

Explore the fundamental group in algebraic topology, covering homotopic paths, loop multiplication, and equivalence classes. Understand key concepts for surfaces like disks and circles.

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