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.
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.
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.
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.
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.
Simplices and Simplicial Complexes - Algebraic Topology
Explore higher-dimensional geometry through simplices and simplicial complexes. Learn about convex combinations, orientations, and the fundamental concept of homology in algebraic topology.
An Introduction to Homology - Algebraic Topology
Explore higher-dimensional topology through homology groups, cycles, and spanning trees. Learn to compute and characterize independent cycles in graphs using algebraic techniques.
An Informal Introduction to Abstract Algebra
Informal introduction to abstract algebra, covering fields, rings, and vector spaces. Explores key concepts and examples, from basic number systems to advanced constructions, providing essential background for algebraic topology.
Three Dimensional Geometry, ZOME, and the Elusive Tetrahedron
Explore three-dimensional geometry using rational trigonometry and ZOME construction, focusing on tetrahedron trigonometry and new algebraic relations for a deeper understanding of spatial structures.
The Stern-Brocot Tree, Matrices and Wedges - Real Numbers and Limits Math Foundations
Explore the Stern-Brocot tree's matrix and geometric representations, including wedges, for a deeper understanding of fractions and their relationships in mathematics.
Fractions and the Stern-Brocot Tree - Real Numbers and Limits Math Foundations
Explore the Stern-Brocot tree, a fascinating representation of fractions using a binary tree. Learn its properties, construction, and connections to Ford circles and Farey sequences in this insightful mathematical journey.
The Deep Structure of the Rational Numbers - Real Numbers and Limits Math Foundations
Explores the deep structure of rational numbers, focusing on their layered nature within [0,1]. Covers key concepts like Farey sequences and Ford circles, emphasizing rationals' importance in modern mathematics.
Problems with Limits and Cauchy Sequences - Real Numbers and Limits Math Foundations
Explores challenges in defining real numbers using Cauchy sequences, discussing convergence concepts and visualizing sequences in the plane. Highlights issues in establishing arithmetic for real numbers.
Difficulties With Real Numbers as Infinite Decimals - Real Numbers + Limits Math Foundations
Explores challenges in defining real numbers as infinite decimals from a computational perspective, highlighting technical obstacles in algorithms, arithmetic operations, and number equality recognition.
Differential Geometry - Math History - NJ Wildberger
Explore the foundations of differential geometry, from planar curves to Gaussian curvature, and its impact on modern physics. Learn about key concepts and historical contributions in this mathematical field.
Complex Numbers and Algebra - Math History - NJ Wildberger
Explore complex numbers' history, applications in cubic equations, and geometric representations. Delve into the Fundamental Theorem of Algebra and its proofs by d'Alembert and Gauss.
Fractions and P-Adic Numbers - Real Numbers and Limits Math Foundations
Explore 10-adic numbers and repeating reversimals, a playful alternative to decimal arithmetic. Learn addition, multiplication, and conversion of fractions in this number theory adventure.
Fractions and Repeating Decimals - Real Numbers and Limits Math Foundations
Explore fractions, repeating decimals, and real numbers. Learn conversion algorithms, arithmetic operations, and gain insights into the foundations of mathematics and rational number theory.
The Decline of Rigour in Modern Mathematics - Real Numbers and Limits
Explores the decline of mathematical rigor, discussing Euclid's Elements, proof concepts, and problematic topics in modern mathematics. Examines reasons for this decline and its impact on mathematical foundations.
Newton's Method and Algebraic Curves - Real Numbers and Limits Math Foundations
Explore Newton's method for algebraic curves, examining Fermat curves and Bernoulli's Lemniscate. Learn about Taylor expansions, tangent planes, and iterative techniques for approximating curve intersections.
Elementary Projective Geometry - Elementary Mathematics Explained
Explore elementary projective geometry, focusing on line geometry and basic concepts like joins, meets, and quadrangles. Learn through hands-on constructions and discover fascinating correspondences in geometry.