Algebraic Geometry and Number Theory

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An Introduction to Number Theory with Cryptography, Second Edition

James Kraft, Lawrence Washington
January 31, 2018

Building on the success of the first edition, An Introduction to Number Theory with Cryptography, Second Edition, increases coverage of the popular and important topic of cryptography, integrating it with traditional topics in number theory. The authors have written the text in an engaging style...

Actions and Invariants of Algebraic Groups, Second Edition

Walter Ricardo Ferrer Santos, Alvaro Rittatore
December 20, 2017

Actions and Invariants of Algebraic Groups, Second Edition presents a self-contained introduction to geometric invariant theory starting from the basic theory of affine algebraic groups and proceeding towards more sophisticated dimensions." Building on the first edition, this book provides an...

Algebraic Numbers and Algebraic Functions

P.M. Cohn
November 29, 2017

This book is an introduction to the theory of algebraic numbers and algebraic functions of one variable. The basic development is the same for both using E Artin's legant approach, via valuations. Number Theory is pursued as far as the unit theorem and the finiteness of the class number. In...

An Invitation to the Rogers-Ramanujan Identities

Andrew V. Sills
October 12, 2017

The Rogers--Ramanujan identities are a pair of infinite series—infinite product identities that were first discovered in 1894. Over the past several decades these identities, and identities of similar type, have found applications in number theory, combinatorics, Lie algebra and vertex operator...

Beyond First Order Model Theory

Jose Iovino
August 15, 2017

Model theory is one of the central branches of mathematical logic. The field has evolved rapidly in the last few decades. This book is an introduction to current trends in model theory, and contains a collection of articles authored by top researchers in the field. It is intended as a reference for...

Computation with Linear Algebraic Groups

Willem Adriaan de Graaf
August 11, 2017

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 with...

Advanced Number Theory with Applications

Richard A. Mollin
June 07, 2017

Exploring one of the most dynamic areas of mathematics, Advanced Number Theory with Applications covers a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory. Written by a recognized leader in algebra and number theory, the book includes a page...

Noncommutative Deformation Theory

Eivind Eriksen, Olav Arnfinn Laudal, Arvid Siqveland
April 25, 2017

Noncommutative Deformation Theory is aimed at mathematicians and physicists studying the local structure of moduli spaces in algebraic geometry. This book introduces a general theory of noncommutative deformations, with applications to the study of moduli spaces of representations of associative...

Buildings and Schubert Schemes

Carlos Contou-Carrere
November 01, 2016

The first part of this book introduces the Schubert Cells and varieties of the general linear group Gl (k^(r+1)) over a field k according to Ehresmann geometric way. Smooth resolutions for these varieties are constructed in terms of Flag Configurations in k^(r+1) given by linear graphs called...

Introduction to Abelian Model Structures and Gorenstein Homological Dimensions

Marco A. P. Bullones
August 17, 2016

Introduction to Abelian Model Structures and Gorenstein Homological Dimensions provides a starting point to study the relationship between homological and homotopical algebra, a very active branch of mathematics. The book shows how to obtain new model structures in homological algebra by...

Algebraic Operads: An Algorithmic Companion

Murray R. Bremner, Vladimir Dotsenko
April 05, 2016

Algebraic Operads: An Algorithmic Companion presents a systematic treatment of Gröbner bases in several contexts. The book builds up to the theory of Gröbner bases for operads due to the second author and Khoroshkin as well as various applications of the corresponding diamond lemmas in algebra....

Algebras, Rings and Modules: Non-commutative Algebras and Rings

Michiel Hazewinkel, Nadiya M. Gubareni
January 26, 2016

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,...