From Great Discoveries in Number Theory to Applications

1. Auflage 2021
ISBN: 978-3-030-83898-0
Verlag: Springer International Publishing

Buch, Englisch, 337 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 764 g

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.

Zielgruppe

Popular/general

Autoren/Hrsg.

K¿í¿ek, Michal

Krížek, Michal

¿Olcová, Alena

Somer, Lawrence

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Operations Research Graphentheorie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

Foreword.- 1. Divisibility and Congruence.- 2. Prime and Composite Numbers.- 3. Properties of Prime Numbers.- 4. Special Types of Primes.- 5. On a Connection of Number Theory with Graph Theory.- 6. Pseudoprimes.- 7. Fibonacci and Lucas Numbers.- 8. Further Special Types of Integers.- 9. Magic and Latin Squares.- 10. The Mathematics Behind Prague's Horologe.- 11. Applications of Primes.- 12. Further Applications of Number Theory.- Tables.- References.

Über Autor(innen)

Michal Krížek is professor and head of the Numerical Analysis Department of the Institute of Mathematics of the Czech Academy of Sciences. For many years he was Editor-in-chief of the Czech journal Advances of Mathematics, Physics and Astronomy, and the journal Applications of Mathematics. He is a member of the Czech Learned Society and is the author of ten monographs. His research interests include number theory, numerical analysis, the finite element method for solving partial differential equations, mathematical physics, linear algebra, and mathematical and functional analysis. 
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.