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Correlation (Statistics) --- Information theory

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Communication --- Information theory

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Statistical mechanics. --- Entropy (Information theory). --- Probabilities. --- Statistical physics.

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This book traces a remarkable path of mathematical connections through seemingly disparate topics. Frustrations with a 1940's electro-mechanical computer at a premier research laboratory begin this story. Subsequent mathematical methods of encoding messages to ensure correctness when transmitted over noisy channels lead to discoveries of extremely efficient lattice packings of equal-radius balls, especially in 24-dimensional space. In turn, this highly symmetric lattice, with each point neighboring exactly 196,560 other points, suggested the possible presence of new simple groups as groups of symmetries. Indeed, new groups were found and are now part of the "Enormous Theorem" - the classification of all simple groups whose entire proof runs some 10,000+ pages. And these connections, along with the fascinating history and the proof of the simplicity of one of those "sporatic" simple groups, are presented at an undergraduate mathematical level.

Error-correcting codes (Information theory) --- Finite simple groups. --- Simple groups, Finite --- Finite groups --- Linear algebraic groups --- Codes, Error-correcting (Information theory) --- Error-detecting codes (Information theory) --- Forbidden-combination check (Information theory) --- Self-checking codes (Information theory) --- Artificial intelligence --- Automatic control --- Coding theory --- Information theory --- Finite simple groups

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Error-correcting codes (Information theory) --- Finite simple groups --- Codes correcteurs d'erreurs (Théorie de l'information) --- Groupes simples finis --- Simple groups, Finite --- Linear algebraic groups --- Codes, Error-correcting (Information theory) --- Error-detecting codes (Information theory) --- Forbidden-combination check (Information theory) --- Self-checking codes (Information theory) --- Finite simple groups. --- Codes correcteurs d'erreurs (Théorie de l'information) --- 51 --- Finite groups --- Artificial intelligence --- Automatic control --- Coding theory --- Information theory --- 51 Mathematics --- Mathematics --- Mathematical control systems --- Error-correcting codes (Information theory).