How the Algebra of Boole Simplifies Circuit Analysis - MathFoundations - N J Wildberger
Exploring Boole's algebra for circuit analysis, covering logic gates, negations, and practical examples. Provides a unique approach to understanding and simplifying complex circuits.
The Big Step from Polynumbers to Multinumbers - Math Foundations - N J Wildberger
Explore the transition from polynumbers to multinumbers, expanding arithmetic concepts using multisets. Learn new notations and operations for a more flexible algebraic framework.
Polynumbers and De Casteljau Bezier Curves - Algebraic Calculus and DCB Curves - N J Wildberger
Explore polynumbers and de Casteljau Bezier curves in algebraic calculus. Learn new formulas for planar integration and use GeoGebra to visualize these remarkable curves, with applications in design and animation.
Infinitesimal Calculus with Finite Fields - Famous Math Problems
Explore infinitesimal calculus in finite fields through the semi-cubical parabola over F_7, challenging traditional real number analysis and emphasizing polynumbers and de Casteljau Bezier curves.
Dual Complex Numbers and Leibniz's Differentiation Rules - Famous Math Problems
Explore algebraic infinitesimals, dual complex numbers, and Leibniz's differentiation rules in this advanced mathematics lecture, extending calculus to general and finite fields.
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.
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.
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.
Arithmetic with Negative Multisets and Integral Polynumbers - Math Foundations 232
Explores advanced arithmetic using negative msets and anti-objects, introducing integral polynumbers and Laurent polynomials in a pure algebraic context, revolutionizing traditional algebra understanding.
Tangent Lines and Conics of Polynomials - Math Foundations 71
Explore tangent lines and conics of polynomials using polynumbers. Learn to define tangents, compute approximations, and understand Taylor expansions in this advanced mathematical exploration.
Numbers, Polynumbers, and Arithmetic with Vexels - Part 2
Explore vexels, polynumbers, and Hindu-Arabic arithmetic, transitioning to base-2 for simplified understanding of number systems and their arithmetic operations.
Numbers, Polynumbers and Arithmetic with Vexels - Data Structures Math Foundations 190
Exploring Hindu Arabic numerals through multiset orientation, polynumbers, and vexels. Connects algebra and arithmetic concepts for a deeper understanding of number systems.
Central Polynumber Algebra and Baby Weyl Character Formula - Math Foundations 236
Explores central polynumber algebra and Weyl character formula, focusing on SU(2) and SU(3) representations. Connects to particle physics and quaternions, emphasizing polynumbers over complex exponentials.
Central Polynumbers and SL(2)/SU(2) Characters - Math Foundations 235
Explore a novel algebraic approach to SL(2) and SU(2) representation theory, emphasizing central polynumbers and mset arithmetic, with implications for Lie theory and modern physics.