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Mathematical Concepts
The mathematics underneath the analysis: measure, linear algebra, probability and the ideas that make models work.
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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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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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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…