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Blog
Essays and short explorations on mathematics, statistics, games and business.
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Alternative Histories of Integration: Part 1
This content explores the evolution of integration in mathematics, highlighting alternative approaches to classical methods like Riemann and Lebesgue integration. It discusses…
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Can We Transform Complicated Functions To Integrable Functions?
The essence of mathematical progress lies in transforming complex functions into simpler forms for integration. This concept drives advancements in analysis and…
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Eigenfunctions: The Functional Version of Eigenvectors
The concept of eigenvalues and eigenvectors extends beyond matrices to include eigenfunctions in calculus and functional analysis. These special functions, which remain…
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Every Matrix Is Actually a Linear Function
Matrices, often seen as number grids, are actually functions that transform input vectors into output vectors, crucial for understanding linear algebra and…
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The Principle of Least Action: The Single Rule Behind Physics
The principle of stationary action posits that physical systems follow paths where the action remains unchanged under small variations. This principle unites…
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Can You Predict an Election by Watching Yourself? A Statistical and Game-Theoretic Exploration
The article examines how individual political shifts might reflect broader electoral trends among independent voters, highlighting concepts from economics, psychology, and game…
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Why Hardline Diplomacy Often Leads to Disaster: A Game Theory Perspective
The article discusses how game theory illuminates the dynamics of hardline diplomacy, revealing that rational actions can lead to mutual escalation and…
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How Google Used Eigenvalues and Eigenvectors to Rank the Entire Internet
Eigenvalues and eigenvectors, initially seen as abstract concepts, play a critical role in Google’s PageRank algorithm, transforming the internet into a matrix.…
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Universe 25: What Happens When a Society Has Everything Except Purpose?
John B. Calhoun’s Universe 25 experiment revealed that even with abundant resources, social structures are vital for society’s sustainability, highlighting how social…
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The Prisoner’s Dilemma: How Cooperation Emerges Among Rational Self-Interested Individuals
Introduction Why do nations avoid war when they possess the weapons to destroy one another? Why do animals help each other despite…