### Beyond First Order Model Theory

The traditional logical language of model theory is first-order logic. This language was proposed in the late 19th by G. Frege, and throughout the 20th century, it remained at the center of the development of model theory. Model theory is one of the central branches of mathematical logic and the…

Hardback – 2017-07-05

Chapman and Hall/CRC### Computation with Linear Algebraic Groups

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…

Hardback – 2017-04-19

Chapman and Hall/CRC*Chapman & Hall/CRC Monographs and Research Notes in Mathematics*### Noncommutative Deformation Theory

Deformation theory is used as a tool for studying the structure of moduli schemes in geometry by many mathematicians and physicists. Mainly, the structure of the obstruction groups and their vanishing is used for smoothness properties, but there is a need to find the structure of the singularities…

Hardback – 2017-04-18

Chapman and Hall/CRC*Chapman & Hall/CRC Monographs and Research Notes in Mathematics*### Actions and Invariants of Algebraic Groups, Second Edition

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…

Hardback – 2016-12-20

Chapman and Hall/CRC*Chapman & Hall/CRC Monographs and Research Notes in Mathematics*### Buildings and Schubert Schemes

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…

Hardback – 2016-11-01

CRC Press### Introduction to Abelian Model Structures and Gorenstein Homological Dimensions

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…

Hardback – 2016-08-17

Chapman and Hall/CRC*Chapman & Hall/CRC Monographs and Research Notes in Mathematics*### Algebraic Operads

#### An Algorithmic Companion

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.…

Hardback – 2016-04-05

Chapman and Hall/CRC### Algebras, Rings and Modules

#### Non-commutative Algebras and Rings

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,…

Hardback – 2016-01-26

CRC Press### Introduction to Number Theory, 2nd Edition

Introduction to Number Theory is a classroom-tested, student-friendly text that covers a diverse array of number theory topics, from the ancient Euclidean algorithm for finding the greatest common divisor of two integers to recent developments such as cryptography, the theory of elliptic curves,…

Hardback – 2015-12-01

Chapman and Hall/CRC*Textbooks in Mathematics*### Mathematical Foundations of Public Key Cryptography

In Mathematical Foundations of Public Key Cryptography, the authors integrate the results of more than 20 years of research and teaching experience to help students bridge the gap between math theory and crypto practice. The book provides a theoretical structure of fundamental number theory and…

Hardback – 2015-10-21

CRC Press### Algebraic Number Theory and Fermat's Last Theorem, Fourth Edition

Updated to reflect current research, Algebraic Number Theory and Fermat’s Last Theorem, Fourth Edition introduces fundamental ideas of algebraic numbers and explores one of the most intriguing stories in the history of mathematics—the quest for a proof of Fermat’s Last Theorem. The authors use this…

Hardback – 2015-10-13

Chapman and Hall/CRC### Semialgebraic Statistics and Latent Tree Models

Semialgebraic Statistics and Latent Tree Models explains how to analyze statistical models with hidden (latent) variables. It takes a systematic, geometric approach to studying the semialgebraic structure of latent tree models. The first part of the book gives a general introduction to key…

Hardback – 2015-08-21

Chapman and Hall/CRC*Chapman & Hall/CRC Monographs on Statistics & Applied Probability*