Number theory

Proofs 101: An Introduction to Formal Mathematics serves as an introduction to proofs for mathematics majors who have completed the calculus sequence (at least Calculus I and II) and a first course in linear algebra.

The book provides an introduction to modern abstract algebra and its applications.

The book provides an introduction to modern abstract algebra and its applications.

Congruences are ubiquitous in computer science, engineering, mathematics, and related areas.

Congruences are ubiquitous in computer science, engineering, mathematics, and related areas.

This textbook thoroughly outlines combinatorial algorithms for generation, enumeration, and search.

This book is devoted to algebraic models and their applications.

This textbook thoroughly outlines combinatorial algorithms for generation, enumeration, and search.

This book covers the application of algebraic inequalities for reliability improvement and for uncertainty and risk reduction.

This book covers the application of algebraic inequalities for reliability improvement and for uncertainty and risk reduction.

This volume, based on fourteen papers from the Millennial Conference on Number Theory, represents surveys of topics in number theory and provides an outlook into the future of number theory research.

Originally published in 1994, The Incommensurability Thesis is a critical study of the Incommensurability Thesis of Thomas Kuhn and Paul Feyerabend.

Originally published in 1994, The Incommensurability Thesis is a critical study of the Incommensurability Thesis of Thomas Kuhn and Paul Feyerabend.

Geodesic and Horocyclic Trajectories presents an introduction to the topological dynamics of two classical flows associated with surfaces of curvature -1, namely the geodesic and horocycle flows.

This text approaches integration via measure theory as opposed to measure theory via integration, an approach which makes it easier to grasp the subject.

Multiple Dirichlet Series, L-functions and Automorphic Forms gives the latest advances in the rapidly developing subject of Multiple Dirichlet Series, an area with origins in the theory of automorphic forms that exhibits surprising and deep connections to crystal graphs and mathematical physics.

From the original hard cover edition:In the modern age of almost universal computer usage, practically every individual in a technologically developed society has routine access to the most up-to-date cryptographic technology that exists, the so-called RSA public-key cryptosystem.

This book comprises five parts.

This second edition of Mathematical Olympiad Treasures contains a stimulating collection of problems in geometry and trigonometry, algebra, number theory, and combinatorics.

This original monograph investigates several unsolved problems that currently exist in coding theory.

For the past several decades the theory of automorphic forms has become a major focal point of development in number theory and algebraic geometry, with applications in many diverse areas, including combinatorics and mathematical physics.

Over the course of the last century, the systematic exploration of the relationship between Fourier analysis and other branches of mathematics has lead to important advances in geometry, number theory, and analysis, stimulated in part by Hurwitz's proof of the isoperimetric inequality using Fourier series.

One of the great successes of twentieth century mathematics has been the remarkable qualitative understanding of rational and integral points on curves, gleaned in part through the theorems of Mordell, Weil, Siegel, and Faltings.

The first edition of this book presented the theory of linear algebraic groups over an algebraically closed field.

Many of the important and creative developments in modern mathematics resulted from attempts to solve questions that originate in number theory.

It is impossible to imagine modern mathematics without complex numbers.

Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics.

Many partial differential equations (PDEs) that arise in physics can be viewed as infinite-dimensional Hamiltonian systems.

Why Olympiads?

Eisenstein series are an essential ingredient in the spectral theory of automorphic forms and an important tool in the theory of L-functions.

Conformal groups play a key role in geometry and spin structures.

Number theory, an ongoing rich area of mathematical exploration, is noted for its theoretical depth, with connections and applications to other fields from representation theory, to physics, cryptography, and more.

This book is an outgrowth of the special term "e;Harmonic Analysis, Representation Theory, and Integral Geometry,"e; held at the Max Planck Institute for Mathematics and the Hausdorff Research Institute for Mathematics in Bonn during the summer of 2007.

Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established.

This volume contains the first two out of four chapters which are intended to survey a large part of the theory of theta functions.

Number Theory or arithmetic, as some prefer to call it, is the oldest, purest, liveliest, most elementary yet sophisticated field of mathematics.

This book contains 104 of the best problems used in the training and testing of the U.

Algebra, Arithmetic, and Geometry: In Honor of Yu.

This book is an introduction to the study of Diophantine equations.

Number theory is fascinating.

One of the most creative mathematicians of our times, Vladimir Drinfeld received the Fields Medal in 1990 for his groundbreaking contributions to the Langlands program and to the theory of quantum groups.

The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory.

Complex numbers can be viewed in several ways: as an element in a field, as a point in the plane, and as a two-dimensional vector.