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17 Lectures on Fermat Numbers: From Number Theory to Geometry (CMS Books in Mathematics)

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17 Lectures on Fermat Numbers: From Number Theory to Geometry (CMS Books in Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

French mathematician Pierre de Fermat became most well known for his pioneering work in the area of number theory. His work with numbers has been attracting the attention of amateur and professional mathematicians for over 350 years. This book was written in honor of the 400th anniversary of his birth and is based on a series of lectures given by the authors. The purpose of this book is to provide readers with an overview of the many properties of Fermat numbers and to demonstrate their numerous appearances and applications in areas such as number theory, probability theory, geometry, and signal processing. This book introduces a general mathematical audience to basic mathematical ideas and algebraic methods connected with the Fermat numbers and will provide invaluable reading for the amateur and professional alike. Michal Krizek is a senior researcher at the Mathematical Institute of the Academy of Sciences of the Czech Republic and Associate Professor in the Department of Mathematics and Physics at Charles University in Prague. Florian Luca is a researcher at the Mathematical Institute of the UNAM in Morelia, Mexico. Lawrence Somer is a Professor of Mathematics at The Catholic University of America in Washington, D. C.

Synopsis:

The pioneering work of Pierre de Fermat has attracted the attention of mathematicians for over 350 years. This book provides an overview of the many properties of Fermat numbers and demonstrates their applications in areas such as number theory, probability theory, geometry, and signal processing. It is an ideal introduction to the basic mathematical ideas and algebraic methods connected with the Fermat numbers.

Synopsis:

The pioneering work of French mathematician Pierre de Fermat has attracted the attention of mathematicians for over 350 years. This book was written in honor of the 400th anniversary of his birth, providing readers with an overview of the many properties of Fermat numbers and demonstrating their applications in areas such as number theory, probability theory, geometry, and signal processing. This book introduces a general mathematical audience to basic mathematical ideas and algebraic methods connected with the Fermat numbers.

Table of Contents

Foreword by Alena Solcová * Table of Contents * Preface * Glossary of Symbols * Introduction * Fundamentals of Number Theory * Basic Properties of Fermat Numbers * The Most Beautiful Theorems on Fermat Numbers * Primality of Fermat Numbers * Divisibility of Fermat Numbers * Factors of Fermat Numbers * Connection With the Pascal Triangle * Miscellaneous Results * The Irrationality of the Sum of Some Reciprocals * Fermat Primes and a Diophantine Equation * Fermat's Little Theorem, Pseudoprimes, and Super-Pseudoprimes * Generalizations of Fermat Numbers * Open Problems * Fermat Number Transform and Other Applications * The Proof of Gauss's Theorem * Euclidean Constructions of the Regular Heptadecagon * Appendix A, B, C * References * Web Site Sources * Name Index * Subject Index

Product Details

ISBN:
9781441929525
Author:
Krizek, Michal
Publisher:
Springer
Author:
Solcova, A.
Author:
Somer, Lawrence
Author:
Luca, Florian
Location:
New York, NY
Subject:
Number Theory
Subject:
Fermat
Subject:
Fermat numbers
Subject:
History of Mathematics
Subject:
History of Mathematical Sciences
Subject:
Geometry
Subject:
Mathematics-Number Theory
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Copyright:
Edition Description:
1st Edition. Softcover version of original hardcover edition 2002
Series:
CMS Books in Mathematics
Publication Date:
20110701
Binding:
TRADE PAPER
Language:
English
Pages:
281
Dimensions:
235 x 155 mm

Related Subjects

History and Social Science » Sociology » General
Science and Mathematics » Mathematics » Geometry » Algebraic Geometry
Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry
Science and Mathematics » Mathematics » History
Science and Mathematics » Mathematics » Number Theory

17 Lectures on Fermat Numbers: From Number Theory to Geometry (CMS Books in Mathematics) New Trade Paper
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Product details 281 pages Springer - English 9781441929525 Reviews:
"Synopsis" by , The pioneering work of Pierre de Fermat has attracted the attention of mathematicians for over 350 years. This book provides an overview of the many properties of Fermat numbers and demonstrates their applications in areas such as number theory, probability theory, geometry, and signal processing. It is an ideal introduction to the basic mathematical ideas and algebraic methods connected with the Fermat numbers.
"Synopsis" by , The pioneering work of French mathematician Pierre de Fermat has attracted the attention of mathematicians for over 350 years. This book was written in honor of the 400th anniversary of his birth, providing readers with an overview of the many properties of Fermat numbers and demonstrating their applications in areas such as number theory, probability theory, geometry, and signal processing. This book introduces a general mathematical audience to basic mathematical ideas and algebraic methods connected with the Fermat numbers.
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