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#Polynumbers

Showing: 14 courses
Insights into Mathematics

How the Algebra of Boole Simplifies Circuit Analysis - MathFoundations - N J Wildberger

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Exploring Boole's algebra for circuit analysis, covering logic gates, negations, and practical examples. Provides a unique approach to understanding and simplifying complex circuits.
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6 Lesons
25 minutes
On-Demand
Free-Video
Insights into Mathematics

The Big Step from Polynumbers to Multinumbers - Math Foundations - N J Wildberger

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Explore the transition from polynumbers to multinumbers, expanding arithmetic concepts using multisets. Learn new notations and operations for a more flexible algebraic framework.
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16 Lesons
35 minutes
On-Demand
Free-Video
Insights into Mathematics

Polynumbers and De Casteljau Bezier Curves - Algebraic Calculus and DCB Curves - N J Wildberger

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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.
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10 Lesons
54 minutes
On-Demand
Free-Video
Insights into Mathematics

Infinitesimal Calculus with Finite Fields - Famous Math Problems

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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.
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9 Lesons
34 minutes
On-Demand
Free-Video
Insights into Mathematics

Dual Complex Numbers and Leibniz's Differentiation Rules - Famous Math Problems

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Explore algebraic infinitesimals, dual complex numbers, and Leibniz's differentiation rules in this advanced mathematics lecture, extending calculus to general and finite fields.
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7 Lesons
27 minutes
On-Demand
Free-Video
Insights into Mathematics

Translating Polynumbers and the Derivative - Arithmetic and Geometry Math Foundations

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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.
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10 Lesons
37 minutes
On-Demand
Free-Video
Insights into Mathematics

Row and Column Polynumbers - Arithmetic and Geometry Math Foundations

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Explore two-dimensional arithmetic with polynumbers, introducing bipolynumbers and their associated polynomials in alpha and beta variables. Learn simplified arithmetic and multiplication techniques.
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11 Lesons
50 minutes
On-Demand
Free-Video
Insights into Mathematics

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

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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.
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9 Lesons
45 minutes
On-Demand
Free-Video
Insights into Mathematics

Arithmetic with Negative Multisets and Integral Polynumbers - Math Foundations 232

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Explores advanced arithmetic using negative msets and anti-objects, introducing integral polynumbers and Laurent polynomials in a pure algebraic context, revolutionizing traditional algebra understanding.
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8 Lesons
40 minutes
On-Demand
Free-Video
Insights into Mathematics

Tangent Lines and Conics of Polynomials - Math Foundations 71

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Explore tangent lines and conics of polynomials using polynumbers. Learn to define tangents, compute approximations, and understand Taylor expansions in this advanced mathematical exploration.
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8 Lesons
36 minutes
On-Demand
Free-Video
Insights into Mathematics

Numbers, Polynumbers, and Arithmetic with Vexels - Part 2

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Explore vexels, polynumbers, and Hindu-Arabic arithmetic, transitioning to base-2 for simplified understanding of number systems and their arithmetic operations.
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6 Lesons
20 minutes
On-Demand
Free-Video
Insights into Mathematics

Numbers, Polynumbers and Arithmetic with Vexels - Data Structures Math Foundations 190

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Exploring Hindu Arabic numerals through multiset orientation, polynumbers, and vexels. Connects algebra and arithmetic concepts for a deeper understanding of number systems.
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9 Lesons
24 minutes
On-Demand
Free-Video
Insights into Mathematics

Central Polynumber Algebra and Baby Weyl Character Formula - Math Foundations 236

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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.
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1 Lesons
40 minutes
On-Demand
Free-Video
Insights into Mathematics

Central Polynumbers and SL(2)/SU(2) Characters - Math Foundations 235

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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.
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6 Lesons
35 minutes
On-Demand
Free-Video