Overview
- 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
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Table of contents (13 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
“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)
Authors and Affiliations
About the authors
Lawrence Somer is a professor emeritus at the Catholic University of America in Washington, D.C. He is a member of the Editorial board of the journal Fibonacci Quarterly. His research interests are in number theory, combinatorics, graph theory, group theory, algebra and geometry.
Alena Šolcová is an associate professor at the Faculty of Information Technology of the Czech Technical University in Prague. She has been the President of the Union of Czech Mathematicians and Physicists since 2018 and is a member of the Editorial board of the Czechoslovak Journal for Physics. She is an active member of the Czech Mathematical Society and the Czech Society for Cybernetics and Informatics (expert group for logic, probability and reasoning). Her research interests include mathematical logic, number theory, some numerical methods and the history of mathematics, informatics and astronomy. Asteroid No. 58 622 was named “Alenašolcová” in her honor by the International Astronomical Union.
Bibliographic Information
Book Title: From Great Discoveries in Number Theory to Applications
Authors: Michal Křížek, Lawrence Somer, Alena Šolcová
DOI: https://doi.org/10.1007/978-3-030-83899-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-83898-0Published: 22 September 2021
Softcover ISBN: 978-3-030-83901-7Published: 23 September 2022
eBook ISBN: 978-3-030-83899-7Published: 21 September 2021
Edition Number: 1
Number of Pages: XV, 337
Number of Illustrations: 67 b/w illustrations, 15 illustrations in colour
Topics: Number Theory, Applications of Mathematics, Graph Theory