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Mathematics
Abstract Algebra


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Featured Titles in Mathematics - Abstract Algebra
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Lecture Notes in Computer Science #1672: Projective Modules and Complete Intersections
Lecture Notes in Computer Science #1672: Projective Modules and Complete Intersections
by Satya Mandal
Publisher Comments
In these notes on "Projective Modules and Complete Intersections" an account on the recent developments in research on this subject is presented. The author's preference for the technique of Patching isotopic isomorphisms due to Quillen, formalized by... (read more)

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Asymptotic Cyclic Cohomology, Vol. XXIII
Asymptotic Cyclic Cohomology, Vol. XXIII
by Michael Puschnigg
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The aim of cyclic cohomology theories is the approximation of K-theory by cohomology theories defined by natural chain complexes. The basic example is the approximation of topological K-theory by de Rham cohomology via the classical Chern character. A... (read more)

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The Linear Algebra a Beginning Graduate Student Ought to Know
The Linear Algebra a Beginning Graduate Student Ought to Know
by Jonathan S. Golan
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Linear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics, both pure and applied, as well as to computer science, to the physical, biological, and social sciences, and to engineering. It... (read more)

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Inverse Galois Theory (Springer Monographs in Mathematics)
Inverse Galois Theory (Springer Monographs in Mathematics)
by Gunter Malle
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Inverse Galois Theory is concerned with the question of which finite groups occur as Galois Groups over a given field. In particular, this includes the question of the structure and the representations of the absolute Galois group of K and also the... (read more)

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Graduate Texts in Mathematics #91: The Geometry of Discrete Groups
Graduate Texts in Mathematics #91: The Geometry of Discrete Groups
by Alan F. Beardon
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This text is about the geometric theory of discrete groups and the associated tesselations of the underlying space. The theory of Möbius transformations in n-dimensional Euclidean space is developed. These transformations are discussed as isometries of... (read more)

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Integral Closure
Integral Closure
by Wolmer Vsconcelos
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This book gives an account of theoretical and algorithmic developments on the integral closure of algebraic structures. It gives a comprehensive treatment of Rees algebras and multiplicity theory while pointing to applications in many other problem areas.... (read more)

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Exploratory Galois Theory
Exploratory Galois Theory
by John Swallow
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Combining a concrete perspective with an exploration-based approach, this analysis develops Galois theory at an entirely undergraduate level. The text grounds the presentation in the concept of algebraic numbers with complex approximations and only... (read more)

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Pure and Applied Mathematics: A Wiley Series of Texts, Monog #106: Galois Theory
Pure and Applied Mathematics: A Wiley Series of Texts, Monog #106: Galois Theory
by David A. Cox
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Praise for the First Edition ". . .will certainly fascinate anyone interested in abstract algebra: a remarkable book!"—Monatshefte fur Mathematik Galois theory is one of the most established topics in mathematics, with historical roots that led to... (read more)

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Encyclopedia of Mathematics and Its Applications #141: Hadamard Expansions and Hyperasymptotic Evaluation: An Extension of the Method of Steepest Descents
Encyclopedia of Mathematics and Its Applications #141: Hadamard Expansions and Hyperasymptotic Evaluation: An Extension of the Method of Steepest Descents
by R. B. Paris
Publisher Comments
The author describes the recently developed theory of Hadamard expansions applied to the high-precision (hyperasymptotic) evaluation of Laplace and Laplace-type integrals. This brand new method builds on the well-known asymptotic method of steepest... (read more)

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Springer Series in Statistics #199: Markov Bases in Algebraic Statistics
Springer Series in Statistics #199: Markov Bases in Algebraic Statistics
by Satoshi Aoki
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Algebraic statistics is a rapidly developing field, where ideas from statistics and algebra meet and stimulate new research directions. One of the origins of algebraic statistics is the work by Diaconis and Sturmfels in 1998 on the use of Gr\"obner bases... (read more)

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Lecture Notes in Mathematics #2032: Algebraic Topology of Finite Topological Spaces and Applications
Lecture Notes in Mathematics #2032: Algebraic Topology of Finite Topological Spaces and Applications
by Jonathan Barmak
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This volume deals with the theory of finite topological spaces and its relationship with the homotopy and simple homotopy theory of polyhedra. The interaction between their intrinsic combinatorial and topological structures makes finite spaces a useful... (read more)

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Graduate Texts in Mathematics #4: A Course in Homological Algebra
Graduate Texts in Mathematics #4: A Course in Homological Algebra
by Peter J. Hilton
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Homological algebra has found a large number of applications in many fields ranging from finite and infinite group theory to representation theory, number theory, algebraic topology and sheaf theory. In the new edition of this broad introduction to the... (read more)

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Selected papers and other writings
Selected papers and other writings
by Irving Kaplansky
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Irving Kaplansky is one of the top mathematicians of this continent of this century. He was the Director from the MSRI 1984-1992. He has made many contributions to many fields of mathematics and they are very valuable. In this volume, 22 of his research... (read more)

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Flat covers of modules
Flat covers of modules
by Jinzhong Xu
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Since the injective envelope and projective cover were defined by Eckmann and Bas in the 1960s, they have had great influence on the development of homological algebra, ring theory and module theory. In the 1980s, Enochs introduced the flat cover and... (read more)

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An Introduction to Abstract Algebra with Notes to the Future Teacher:
An Introduction to Abstract Algebra with Notes to the Future Teacher:
by Olympia Nicodemi
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This traditional treatment of abstract algebra is designed for the particular needs of the mathematics teacher. Readers must have access to a Computer Algebra System (C. A. S.) such as Maple, or at minimum a calculator such as the TI 89 with C. A. S... (read more)

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A Classical Introduction to Galois Theory
A Classical Introduction to Galois Theory
by Stephen C. Newman
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Explore the foundations and modern applications of Galois theory Galois theory is widely regarded as one of the most elegant areas of mathematics. A Classical Introduction to Galois Theory develops the topic from a historical perspective, with an... (read more)

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Classifying Spaces & Classifying Topoi, Vol. VII
Classifying Spaces & Classifying Topoi, Vol. VII
by Ieke Moerdijk
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This monograph presents a new, systematic treatment of the relation between classifying topoi and classifying spaces of topological categories. Using a new generalized geometric realization which applies to topoi, a weak homotopy equival- ence is... (read more)

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Abstract Algebra (Brooks/Cole Series in Advanced Mathematics)
Abstract Algebra (Brooks/Cole Series in Advanced Mathematics)
by Ronald Solomon
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In the same way the subject evolved historically, Ronald Solomon lets the abstract concepts emerge gradually from less abstract problems about geometry, polynomials, numbers, and more. Solomon also strongly emphasizes the connections between algebra and... (read more)

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Advances in Mathematics #7: Ordered Sets
Advances in Mathematics #7: Ordered Sets
by Egbert Harzheim
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The textbook literature on ordered sets is still rather limited. A lot of material is presented in this book that appears now for the first time in a textbook. Order theory works with combinatorial and set-theoretical methods, depending on whether the... (read more)

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Progress in Mathematics #297: Metric and Differential Geometry: The Jeff Cheeger Anniversary Volume
Progress in Mathematics #297: Metric and Differential Geometry: The Jeff Cheeger Anniversary Volume
by Xianzhe Dai
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Metric and Differential Geometry grew out... (read more)

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