From Great Discoveries in Number Theory to Applications
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Beschreibung
This book provides an overview of many interesting properties of natural numbers, demonstrating their applications in areas such as cryptography, geometry, astronomy, mechanics, computer science, and recreational mathematics. In particular, it presents the main ideas of error-detecting and error-correcting codes, digital signatures, hashing functions, generators of pseudorandom numbers, and the RSA method based on large prime numbers. A diverse array of topics is covered, from the properties and applications of prime numbers, some surprising connections between number theory and graph theory, pseudoprimes, Fibonacci and Lucas numbers, and the construction of Magic and Latin squares, to the mathematics behind Prague’s astronomical clock. Introducing a general mathematical audience to some of the basic ideas and algebraic methods connected with various types of natural numbers, the book will provide invaluable reading for amateurs and professionals alike.
This book provides an overview of many interesting properties of natural numbers, demonstrating their applications in areas such as cryptography, geometry, astronomy, mechanics, computer science, and recreational mathematics. In particular, it presents the main ideas of error-detecting and error-correcting codes, digital signatures, hashing functions, generators of pseudorandom numbers, and the RSA method based on large prime numbers. A diverse array of topics is covered, from the properties and applications of prime numbers, some surprising connections between number theory and graph theory, pseudoprimes, Fibonacci and Lucas numbers, and the construction of Magic and Latin squares, to the mathematics behind Prague’s astronomical clock. Introducing a general mathematical audience to some of the basic ideas and algebraic methods connected with various types of natural numbers, the book will provide invaluable reading for amateurs and professionals alike.
Presents not only theoretical results, but gives real-life technical applications of number theory Illustrates the close connection between number theory, graph theory, the theory of groups, and geometry Suitable not only for scientists, but also for non-professionals who want to feel the joy of mathematics
Autor*in
Michal Křížek
Themen in »From Great Discoveries in Number Theory to Applications«
Natural Numbers Primes Finite Graphs Pseudoprimes Figural Numbers Triangular Numbers Coding Cryptography Kepler Tessellations Fractal
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“This is a nicely written book that can be read with profit by undergraduates with a background in elementary number theory, and it may serve as bedtime reading for the experts.” (Franz Lemmermeyer, zbMATH 1486.11001, 2022)
“It also has more applications than is usual in either kind of book. Apart from that it is very conventional and has the theorems and proofs that you would expect. … The book does cover a number of newer discoveries … .” (Allen Stenger, MAA Reviews, December 27, 2021)
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