Number Theory category: 319 books

Analysis, assessment, and data management are core competencies for operation research analysts. This volume addresses a number of issues and developed methods for improving those skills. It is an outgrowth of a conference held in April 2013 at the Hellenic Military Academy, and brings together a...

This volume contains a collection of research and survey papers written by some of the most eminent mathematicians in the international community and is dedicated to Helmut Maier, whose own research has been groundbreaking and deeply influential to the field. Specific emphasis is given to topics regarding...

The sequence of the primes is something of a mystery in number theory‚ if not in all of mathematics. Hardly any topic has ever fascinated mathe¬maticians more. Euler once said‚ “Mathematicians have tried in vain‚ to this day‚ to discover some order in the sequence of prime numbers‚ and...

Basic treatment, incorporating language of abstract algebra and a history of the discipline. Topics include unique factorization and the GCD, quadratic residues, number-theoretic functions and the distribution of primes, sums of squares, quadratic equations and quadratic fields, diophantine approximation,...

This is the fifth conference in a bi-annual series, following conferences in Besancon, Limoges, Irsee and Toronto. The meeting aims to bring together different strands of research in and closely related to the area of Iwasawa theory. During the week before the conference in a kind of summer school...

Focusing on an approach of solving rigorous problems and learning how to prove, this volume is concentrated on two specific content themes, elementary number theory and algebraic polynomials. The benefit to readers who are moving from calculus to more abstract mathematics is to acquire the ability...

This unique volume presents a fruitful and beautiful mathematical world hidden in Caianiello's neuronic equations, which describe the instantaneous behavior of a model of a brain or thinking machine. The detailed analysis from a viewpoint of “dynamical systems”, even in a single neuron case, enables...

Important results surrounding the proof of Goldbach's ternary conjecture are presented in this book. Beginning with an historical perspective along with an overview of essential lemmas and theorems, this monograph moves on to a detailed proof of Vinogradov's theorem. The principles of the Hardy-Littlewood...

This is the first work on Discrepancy Theory to show the present variety of points of view and applications covering the areas Classical and Geometric Discrepancy Theory, Combinatorial Discrepancy Theory and  Applications and Constructions. It consists of several chapters, written by experts in their...

The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This volume stresses this interplay as it develops the basic theory, thereby providing an opportunity for advanced undergraduates to appreciate the unity of modern mathematics. At the same time,...

In 1842 the Belgian mathematician Eugène Charles Catalan asked whether 8 and 9 are the only consecutive pure powers of non-zero integers. 160 years after, the question was answered affirmatively by the Swiss mathematician of Romanian origin Preda Mihăilescu. In other words, 32 – 23 = 1 is the...

Pell and Pell–Lucas numbers, like the well-known Fibonacci and Catalan numbers, continue to intrigue the mathematical world with their beauty and applicability. They offer opportunities for experimentation, exploration, conjecture, and problem-solving techniques, connecting the fields of analysis,...

Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a typical example, have deep arithmetic significance. Prior to this book, the fastest known...

Designed as a self-contained account of a number of key algorithmic problems and their solutions for linear algebraic groups, this book combines in one single text both an introduction to the basic theory of linear algebraic groups and a substantial collection of useful algorithms. Computation...