Integers And Theory Of Numbers
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Integers and Theory of Numbers
Author: Abraham Adolf Fraenkel
language: en
Publisher: Courier Corporation
Release Date: 2004-01-01
A concise work on important topics in number theory, this classic text was devised by a prominent mathematician to explain the essentials of mathematics in a manner accessible to high school and college students as well as to other readers. Clear-cut explanations cover natural numbers as cardinals, with discussions of positional notation and the ordering of numbers according to magnitude; natural numbers as ordinals, including Peano's axioms and the relation of ordinals to cardinals; the theory of numbers, encompassing prime numbers and their distribution, partitions of the circle, Fermat's simple and last theorems, perfect numbers, amicable numbers, and algebraic and ideal numbers; and rational numbers, with considerations of positive fractions, negative integers, and the field of rationals. 1955 ed.
Excursions in Number Theory
Author: Charles Stanley Ogilvy
language: en
Publisher: Courier Corporation
Release Date: 1988-01-01
Challenging, accessible mathematical adventures involving prime numbers, number patterns, irrationals and iterations, calculating prodigies, and more. No special training is needed, just high school mathematics and an inquisitive mind. "A splendidly written, well selected and presented collection. I recommend the book unreservedly to all readers." — Martin Gardner.
Number Theory for Computing
Author: Song Y. Yan
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-11-11
Modern cryptography depends heavily on number theory, with primality test ing, factoring, discrete logarithms (indices), and elliptic curves being perhaps the most prominent subject areas. Since my own graduate study had empha sized probability theory, statistics, and real analysis, when I started work ing in cryptography around 1970, I found myself swimming in an unknown, murky sea. I thus know from personal experience how inaccessible number theory can be to the uninitiated. Thank you for your efforts to case the transition for a new generation of cryptographers. Thank you also for helping Ralph Merkle receive the credit he deserves. Diffie, Rivest, Shamir, Adleman and I had the good luck to get expedited review of our papers, so that they appeared before Merkle's seminal contribu tion. Your noting his early submission date and referring to what has come to be called "Diffie-Hellman key exchange" as it should, "Diffie-Hellman-Merkle key exchange", is greatly appreciated. It has been gratifying to see how cryptography and number theory have helped each other over the last twenty-five years. :'-Jumber theory has been the source of numerous clever ideas for implementing cryptographic systems and protocols while cryptography has been helpful in getting funding for this area which has sometimes been called "the queen of mathematics" because of its seeming lack of real world applications. Little did they know! Stanford, 30 July 2001 Martin E. Hellman Preface to the Second Edition Number theory is an experimental science.