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#Multisets

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Insights into Mathematics

The Realm of Natural Numbers - Data Structures in Mathematics

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Explore natural numbers through multisets, examining addition, union, and intersection operations. Discover unique properties, including a new distributive law that forms the basis for tropical calculus.
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9 Lesons
25 minutes
On-Demand
Free-Video
Insights into Mathematics

Sets and Other Data Structures - Data Structures in Mathematics

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Explore four fundamental data structures in mathematics: lists, ordered sets, multisets, and sets. Learn their characteristics, applications, and a new notation system for easier recognition and distinction.
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7 Lesons
35 minutes
On-Demand
Free-Video
Insights into Mathematics

The Hindu Arabic Number System Revisited - Data Structures in Mathematics Math Foundations

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Explores three approaches to Hindu Arabic numerals, examining their mathematical foundations and practical applications in arithmetic and number representation.
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9 Lesons
30 minutes
On-Demand
Free-Video
Insights into Mathematics

Higher Data Structures - Data Structures in Mathematics Math Foundations

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Explore advanced mathematical data structures, including nested combinations of lists, ordered sets, multisets, and sets. Learn their applications in combinatorics, graph theory, and other mathematical fields.
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8 Lesons
27 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

Negative Numbers from Antimultisets - Math Foundations 231

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Explore negative numbers through antimultisets, drawing parallels with particle physics concepts. Discover a new arithmetic perspective based on elementary principles.
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10 Lesons
39 minutes
On-Demand
Free-Video
Insights into Mathematics

Four Basic Combinatorial Counting Problems in Data Structures - Math Foundations 162

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Explores four fundamental combinatorial counting problems for lists, ordered sets, sets, and multisets, providing insights into mathematical data structures and their enumeration.
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8 Lesons
28 minutes
On-Demand
Free-Video
Insights into Mathematics

Unique Factorization, Primes and Multisets in Number Theory - Math Foundations 160

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Explore elementary number theory through multisets, examining unique factorization, primes, and integral msets. Learn how prime msets connect to fractions and other number theory concepts.
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6 Lesons
31 minutes
On-Demand
Free-Video
Insights into Mathematics

Linear Spaces and Spans II - MathFoundations 220

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Introduction to integral linear spaces as abstract algebraic objects, exploring their applications in mathematics, chemistry, and physics. Foundational concepts for linear algebra using vexel language for concrete examples.
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1 Lesons
34 minutes
On-Demand
Free-Video
Insights into Mathematics

Linear Spaces and Spans I - Abstract Algebra Math Foundations 219

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Introduction to linear spaces and spans, generalizing natural numbers with addition to form spans of multisets. Explores fundamental concepts in abstract algebra and linear algebra.
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1 Lesons
24 minutes
On-Demand
Free-Video
Insights into Mathematics

The Anti Operation in Mathematics - Data Structures in Math Foundations 212

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Exploring the anti operation in multisets, its symmetry, and applications to vexels and maxels. Expands understanding of mathematical structures and operations.
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1 Lesons
23 minutes
On-Demand
Free-Video
Insights into Mathematics

Numbers as Multipliers and Particle-Antiparticle Duality - Data Structures Math Foundations Lecture 211

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Exploring the concept of anti-mathematical objects and their role in multisets, drawing parallels to particle/antiparticle symmetry in physics. Provides insights for modern algebra foundations.
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1 Lesons
29 minutes
On-Demand
Free-Video
Insights into Mathematics

Numbers as Multipliers and Particle-Antiparticle Duality - Data Structures Math Foundations 210

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Explores numbers as multipliers for sets and introduces particle/antiparticle duality, extending multiplication from natural numbers to integers in mathematical set theory.
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1 Lesons
21 minutes
On-Demand
Free-Video
Insights into Mathematics

A New Trichotomy for Integer Arithmetic - Math Foundations 206

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Novel approach to integer arithmetic using marks, anti-marks, and nothing. Explores symmetry between natural and negative numbers, foundational arithmetic of integers, and the role of multisets in organizing mathematical objects.
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1 Lesons
22 minutes
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Free-Video
Insights into Mathematics

Negative Numbers, Multisets, and Modern Physics in Mathematics - Math Foundations 205

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Exploring a new approach to arithmetic with integers using multisets and insights from modern physics, revolutionizing our understanding of negative numbers and mathematical foundations.
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1 Lesons
22 minutes
On-Demand
Free-Video
Insights into Mathematics

Introducing Box Arithmetic - Math Foundations 237

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Explore a revolutionary approach to arithmetic using multisets and box/anti-box duality, offering new insights into mathematical foundations and their connection to particle physics concepts.
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1 Lesons
23 minutes
On-Demand
Free-Video
Insights into Mathematics

The Curious World of Integral Polynumbers - Math Foundations 233

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Explore integral polynumbers through particle physics concepts, expanding arithmetic to include integers as coefficients and exponents, and viewing polynomials as algebraic objects rather than functions.
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9 Lesons
37 minutes
On-Demand
Free-Video
Derek Banas

C++ Tutorial - Associative Containers and Container Adapters - Lesson 18

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Explore associative containers (set, multiset, map, multimap) and container adapters (stacks, queues, priority queues) in C++. Learn about enums and their applications in programming.
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1 Lesons
21 minutes
On-Demand
Free-Video
JetBrains

Do It Yourself: Collections - Extending Map Data Structures

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Hands-on demo extending Map to create MultiSet and MultiValuedMap. Learn to design new collections, add APIs, and implement safeguards using TDD and JDK data structures.
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1 Lesons
57 minutes
On-Demand
Free-Video
ACM SIGPLAN

Polyregular Functions on Unordered Trees of Bounded Height

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Explore polyregular functions on unordered trees with bounded height, examining first-order interpretations, decidability of equivalence problems, and applications to graph classes with bounded tree-depth.
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1 Lesons
20 minutes
On-Demand
Free-Video
Insights into Mathematics

The Operation of Caret - Exponentiation via Multisets - Math Foundations

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Explore a new arithmetic operation called "caret" (exponentiation) for multisets, extending the ladder of operations beyond addition and multiplication with concrete examples and recursive counting functions.
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16 Lesons
35 minutes
On-Demand
Free-Video
Insights into Mathematics

Multisets and a New Framework for Arithmetic - Data Structures Math Foundations

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Explores multisets to redefine natural numbers, offering fresh insights into fundamental arithmetic operations and laws. Presents a simplified, logical approach to basic mathematics suitable for all levels.
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7 Lesons
30 minutes
On-Demand
Free-Video
Insights into Mathematics

Inclusion-Exclusion via Multisets - Data Structures in Mathematics Math Foundations

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Explore inclusion/exclusion via multisets, expanding to integral multisets with negative multiplicities. Learn a conceptual approach to this fundamental Set Theory theorem and its applications.
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5 Lesons
48 minutes
On-Demand
Free-Video
Insights into Mathematics

An Introduction to the Tropical Calculus - Data Structures in Mathematics

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Explore Tropical calculus, a novel approach to set algebra using unique addition and multiplication concepts derived from union and addition operations.
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6 Lesons
33 minutes
On-Demand
Free-Video
Insights into Mathematics

The Algebra of Natural Number Multisets - Data Structures in Mathematics

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Explore multiset algebra in natural numbers, introducing notation and operations. Discover potential extensions to negative and rational multiplicities, with implications for modern algebra.
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5 Lesons
23 minutes
On-Demand
Free-Video
Insights into Mathematics

Multiset Arithmetic via Trees - Math Foundations 230

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Explore multiset arithmetic using rooted trees, offering a visual representation for counting functions and new arithmetic operations. Gain insights into this alternative approach with concrete examples and useful notations.
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6 Lesons
32 minutes
On-Demand
Free-Video
GDC

Indexing and Iterating Design Space Permutations

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Explore mathematical techniques for indexing and iterating design space permutations, focusing on perfect hash functions for efficient game state conversion and representation.
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20 Lesons
28 minutes
On-Demand
Free-Video