Insights into Mathematics Courses

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

Knots and Surfaces I - Algebraic Topology - NJ Wildberger

Explore knot theory's origins, basic concepts, and key invariants in this introductory lecture on algebraic topology, covering Reidemeister moves, crossing numbers, and the Alexander-Conway polynomial.

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

The Two-Holed Torus and 3-Crosscaps Surface - Algebraic Topology - NJ Wildberger

Explore hyperbolic geometric structures of two-holed torus and 3-crosscaps surface through tessellations, hexagons, and the Beltrami Poincare model in this advanced algebraic topology lecture.

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

An Algebraic ZIP Proof of the Classification - Algebraic Topology - NJ Wildberger

Algebraic approach to classifying two-dimensional surfaces using spheres with holes, introducing a notation for manipulating edges between holes on spheres. Explores Conway's ZIP proof in a novel way.

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

Classification of Combinatorial Surfaces - Algebraic Topology - NJ Wildberger

Introduction to the classification of connected compact combinatorial surfaces in algebraic topology, covering key concepts like polygons, vertices, traversing, Euler number, and orientability.

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

More Applications of Winding Numbers - Algebraic Topology - NJ Wildberger

Explore winding numbers, degree of circle functions, and key theorems in algebraic topology. Learn about retractions, fixed points, and Borsuk's Lemma in this advanced mathematics lecture.

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

Non-Orientable Surfaces - The Mobius Band - Algebraic Topology

Explore non-orientable surfaces like the Möbius band, understanding their unique properties and applications in algebraic topology. Learn about crosscaps and key deformations.

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

The Klein Bottle and Projective Plane - Algebraic Topology - NJ Wildberger

Explore the Klein bottle, projective plane, and Platonic solids in this algebraic topology lecture. Learn about Euler's formula and its proof using triangulation and sphere flow.

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

Polyhedra and Euler's Formula - Algebraic Topology

Explore Platonic solids, Euler's formula, and spherical geometry in this engaging lecture on algebraic topology, featuring proofs and insights into fundamental mathematical concepts.

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

Two-Dimensional Objects - The Torus and Genus - Algebraic Topology

Explore surfaces like cylinders and tori, understanding their properties and connections to complex function theory. Learn about genus and how planes cover different surfaces.

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