Read more
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.
List of contents
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.
About the author
Michal K¿ížek 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.
Report
"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)
