Kategoria BISAC: Mathematics >> Number Theory

Elementary Number Theory takes an accessible approach to teaching students about the role of number theory in pure mathematics and its important applications to cryptography and other areas.

The first chapter of the book explains how to do proofs and includes a brief discussion of lemmas, propositions, theorems, and corollaries. The core of the text covers linear Diophantine equations; unique factorization; congruences; Fermat s, Euler s, and Wilson s theorems; order and primitive roots; and quadratic reciprocity. The authors also discuss numerous...

This volume of papers presented at the conference in honor of Calixto P. Calderon by his friends, colleagues, and students is intended to make the mathematical community aware of his important scholarly and research contributions in contemporary Harmonic Analysis and Mathematical Models applied to Biology and Medicine, and to stimulate further research in the future in this area of pure and applied mathematics.

Neal Koblitz is a co-inventor of one of the two most popular forms of encryption and digital signature, and his autobiographical memoirs are collected in this volume. Besides his own personal career in mathematics and cryptography, Koblitz details his travels to the Soviet Union, Latin America, Vietnam and elsewhere; political activism; and academic controversies relating to math education, the C. P. Snow "two-culture" problem, and mistreatment of women in academia. These engaging stories fully capture the experiences of a student and later a scientist caught up in the tumultuous events of...

In the first four chapters the authors cover material for competitions at high school level. The level advances with the chapters. The topics explored include polynomials, functional equations, sequences and an elementary treatment of complex numbers. The final chapters provide a comprehensive list of problems posed at national and international contests in...

When Leonhard Euler first arrived at the Russian Academy of Sciences, at the age of 20, his career was supported and promoted by the Academy's secretary, the Prussian jurist and amateur mathematician Christian Goldbach (1690-1764). Their encounter would grow into a lifelong friendship, as evinced by nearly 200 letters sent over 35 years.

This exchange - Euler's most substantial long-term correspondence - has now been edited for the first time with an English translation, ample commentary and documentary indices. These present an overview of 18th-century number theory, its sources and...

The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth century. This volume is a continuation and an in-depth study, stressing the non-commutative nature of the first two volumes of Algebras, Rings and Modules by M. Hazewinkel, N. Gubareni, and V. V. Kirichenko. It is largely independent of the other...

- ...beautiful and well worth the reading ... with many exercises and a good bibliography, this book will fascinate both students and teachers.- Mathematics Teacher

Fibonacci and Lucas Numbers with Applications, Volume I, Second Edition provides a user-friendly and historical approach to the many fascinating properties of Fibonacci and Lucas numbers, which have intrigued amateurs and professionals for centuries. Offering an in-depth study of the topic, this book includes exciting applications that provide many...

In this book, Leo Corry tells the story behind the idea of number from the early days of the Pythagoreans, up until the turn of the twentieth century. He presents an overview of how numbers were handled and conceived in classical Greek mathematics, in the mathematics of Islam, in European mathematics of the middle ages and the Renaissance, during the scientific revolution, all the way through...

The interest earned on a bank account, the arrangement of seeds in a sunflower, and the shape of the Gateway Arch in St. Louis are all intimately connected with the mysterious number e. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with only a modest mathematical background, this biography brings out the central importance of e to mathematics and illuminates a golden era in the age of science.

The role of human rights in United States policy toward Latin America is the subject of this study. It covers the early sixties to 1980, a period when humanitarian values came to play an important role in determining United States foreign policy. The author is concerned both with explaining why these values came to impinge on government decision making and how internal bureaucratic processes affected the specific content of United States policy.

Originally published in 1981.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available...