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#Natural Numbers

Showing: 30 courses
MITCBMM

A Number Sense as an Emergent Property of the Manipulation Brain

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Explore how number sense emerges from brain manipulation, examining experiments, perceptions, and the role of supervised learning in developing numerical understanding.
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28 Lesons
47 minutes
On-Demand
Free-Video
The Organic Chemistry Tutor

Real Numbers

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Comprehensive overview of real numbers, covering rational and irrational numbers, integers, and decimals. Includes practice problems and examples for better understanding.
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5 Lesons
25 minutes
On-Demand
Free-Video
Insights into Mathematics

A Multiset Approach to Arithmetic - Math Foundations

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Explore a new framework for arithmetic using multisets, introducing natural numbers, polynumbers, and multinumbers. Learn innovative definitions and operations that offer profound insights into mathematical structures.
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13 Lesons
39 minutes
On-Demand
Free-Video
Insights into Mathematics

How to Set Up Fractions IV - The Relation Between Fractions and Other Number Systems

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Explore number systems, focusing on rational numbers and their relationships. Challenges traditional views on real numbers, emphasizing the distinction between counting and measuring in mathematics.
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6 Lesons
30 minutes
On-Demand
Free-Video
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

Absolute Versus Relative Measurements in Geometry - Rational Geometry Math Foundations

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Explore the distinction between absolute and relative measurements in geometry, focusing on proportions and ratios. Learn about ancient Greek approaches and their relevance to modern mathematics.
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8 Lesons
31 minutes
On-Demand
Free-Video
Insights into Mathematics

Divisibility of Big Numbers - Data Structures in Mathematics Math Foundations

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Explore divisibility of large numbers, modular arithmetic, and long division techniques. Learn key concepts and practical applications in number theory and mathematical foundations.
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9 Lesons
27 minutes
On-Demand
Free-Video
Insights into Mathematics

Arithmetical Expressions as Natural Numbers - Data Structures in Mathematics Math Foundations

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Explores the complexities of representing large numbers through arithmetical expressions, discussing limitations, logical issues, and the challenges of creating a coherent system for such representations.
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10 Lesons
27 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

Naming and Ordering Numbers for Students - Data Structures in Mathematics Math Foundations

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Explores naming, ordering, and using natural numbers, focusing on their fundamental nature as expressions of marks. Discusses counting, cardinal vs ordinal usage, and the successor operation.
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7 Lesons
25 minutes
On-Demand
Free-Video
Insights into Mathematics

The Essential Dichotomy Underlying Mathematics - Data Structures Math Foundations

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Explore the fundamental dichotomy underlying mathematics, challenging traditional views on natural numbers and geometry to uncover the core essence of mathematical thinking.
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7 Lesons
21 minutes
On-Demand
Free-Video
Insights into Mathematics

The Sporadic Nature of Big Numbers - Data Structures in Mathematics

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Explores how arithmetic breaks down with large numbers, revealing most "numbers" are invisible to us. Challenges conventional number theory and questions the nature of natural numbers.
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9 Lesons
32 minutes
On-Demand
Free-Video
Insights into Mathematics

The Chaotic Complexity of Natural Numbers - Data Structures in Mathematics

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Exploring the complex nature of arithmetic with large numbers, focusing on exponential and triangular complexity, and examining the role of powers in mathematical computations.
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7 Lesons
38 minutes
On-Demand
Free-Video
Insights into Mathematics

Maxel Algebra I - Data Structures in Mathematics Math Foundations

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Explore maxel algebra, a new matrix theory focusing on idempotent diagonal maxels and sets of natural numbers. Learn about multiplication, identity maxels, and key propositions in this mathematical foundation.
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10 Lesons
35 minutes
On-Demand
Free-Video
Insights into Mathematics

Measurement, Approximation and Interval Arithmetic - Real Numbers and Limits Math Foundations

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Explore interval arithmetic, its laws for natural numbers and integers, and the challenges with real number arithmetic. Gain insights into measurement, approximation, and foundational mathematical concepts.
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10 Lesons
42 minutes
On-Demand
Free-Video
Insights into Mathematics

Measurement, Approximation and Interval Arithmetic - Real Numbers and Limits Math Foundations

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Explores interval arithmetic for natural numbers and integers, covering definitions, inequalities, arithmetic operations, and applications in measurement and counting. Lays foundations for mathematical reasoning.
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10 Lesons
46 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

Infinity in Greek Mathematics - Math History - NJ Wildberger

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Explore ancient Greek mathematics, focusing on Eudoxus and Archimedes' groundbreaking work in calculus, geometry, and mechanics. Discover their ingenious formulas and principles that laid the foundation for modern mathematics.
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12 Lesons
54 minutes
On-Demand
Free-Video
Michael Penn

The Division Algorithm - Number Theory

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Explore the division algorithm in number theory, covering natural numbers, division with remainder, and related concepts through clear explanations and exercises.
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7 Lesons
27 minutes
On-Demand
Free-Video
Numberphile

TREE vs Graham's Number - Numberphile

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Explore the mind-bending concept of TREE vs Graham's Number, delving into successor functions, ordinal infinity, and the vastness of mathematical concepts beyond comprehension.
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8 Lesons
24 minutes
On-Demand
Free-Video
Insights into Mathematics

Reconsidering Natural Numbers and Arithmetical Expressions - Math Foundations 185

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Exploring the foundations of arithmetic, redefining natural numbers, and challenging traditional notions of prime numbers and infinity in mathematics.
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7 Lesons
32 minutes
On-Demand
Free-Video
Insights into Mathematics

Euler's Product for the Zeta Function via Box Arithmetic - Part 2

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Explores connections between Box Arithmetic and Number Theory, focusing on Euler's product formula for the Zeta function and its variants, including the sum of reciprocal squares of natural numbers.
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1 Lesons
31 minutes
On-Demand
Free-Video
Isaac Newton Institute for Mathematical Sciences

Higher Algebra and Arithmetic - Rothschild Lecture

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Explore higher algebra's impact on arithmetic, examining how counting processes influence number theory and cohomology, with applications in geometry and zeta functions.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Schmid College, Chapman University

Revised GCH or Would Cantor Have Understood - A Contemporary Perspective on the Continuum Hypothesis

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Explore the Continuum Hypothesis and its philosophical implications in set theory. Examine contemporary perspectives on Cantor's famous postulate and its generalized form.
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1 Lesons
1 hour 39 minutes
On-Demand
Free-Video
Schmid College, Chapman University

Remarks about Cantor's Theorem

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Explore Cantor's Theorem and its implications for infinite cardinalities. Examine the historical context, compare proofs, and discover applications to paradoxical mathematical situations.
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1 Lesons
1 hour 13 minutes
On-Demand
Free-Video
USC Probability and Statistics Seminar

On the Origin of the Boltzmann Distribution

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Explore the unique characterization of the Boltzmann distribution in statistical mechanics, focusing on its independence property for uncoupled systems.
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1 Lesons
56 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

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
GOTO Conferences

A Taste of Type Theory

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Explore the foundations of type theory in programming, from algebraic data types to dependent types, with insights on mathematical connections and future developments in the field.
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11 Lesons
54 minutes
On-Demand
Free-Video
Dr Trefor Bazett

Mathematical Conventions and Disagreements in Basic Mathematical Concepts

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Explore fascinating mathematical debates and disagreements among experts on fundamental concepts like 0^0, natural numbers, continuous functions, and the Axiom of Choice.
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10 Lesons
15 minutes
On-Demand
Free-Video