Pattern Recognition and the Whitehead Minimization Problem
Exploratory data analysis in abstract algebra: mathematical structure discovery through experiment.
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In the book, "Experimentation in Mathematics," authors J.Borwein and D.Bailey write: "One of the greatest ironies of the information technology evolution is that while the computer was conceived and born in the field of pure mathematics, through the genius of giants such as John von Neumann and Alan Turing, until recently this marvelous technology had only a minor impact within the field that gave it birth." One of the main objectives of this research is to show that computers can be successfully used for analysis of mathematical problems. Our philosophy here that if an irregular or non-random...
In the book, "Experimentation in Mathematics," authors J.Borwein and D.Bailey write: "One of the greatest ironies of the information technology evolution is that while the computer was conceived and born in the field of pure mathematics, through the genius of giants such as John von Neumann and Alan Turing, until recently this marvelous technology had only a minor impact within the field that gave it birth." One of the main objectives of this research is to show that computers can be successfully used for analysis of mathematical problems. Our philosophy here that if an irregular or non-random behavior has been observed during an experiment then there must be a pure mathematical reason behind this phenomenon, which can be uncovered by a proper statistical analysis. Using methods of pattern recognition and exploratory data analysis we formulate conjectures and design nearly optimal heuristic algorithms for solving the Whitehead Minimization Problem. Several years later after this work was completed, the conjectures formulated in the book were proven by renowned mathematicians and a deterministic polynomial algorithm for the Whitehead-Minimization Problems was discovered.
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