Mathematics
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Topics in Geometric Group Theory (Chicago Lectures in Mathematics)
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Topics in Geometric Group Theory (Chicago Lectures in Mathematics)
by Pierre De La Harpe

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Groups as abstract structures were first recognized by mathematicians in the nineteenth century. Groups are, of course, sets given with appropriate "multiplications," and they are often given together with actions on interesting geometric objects. But...
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The Structure of Spherical Buildings
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The Structure of Spherical Buildings
by Richard M Weiss

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This book provides a clear and authoritative introduction to the theory of buildings, a topic of central importance to mathematicians interested in the geometric aspects of group theory. Its detailed presentation makes it suitable for graduate students...
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Lecture Notes in Mathematics, #1754: The Geometry of Jordan and Lie Structures
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Lecture Notes in Mathematics, #1754: The Geometry of Jordan and Lie Structures
by Wolfgang Bertram

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The geometry of Jordan and Lie structures tries to answer the following question: what is the integrated, or geometric, version of real Jordan algebras, - triple systems and - pairs? Lie theory shows the way one has to go: Lie groups and symmetric spaces...
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Graduate Texts in Mathematics #235: Compact Lie Groups
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Graduate Texts in Mathematics #235: Compact Lie Groups
by Mark R Sepanski

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Blending algebra, analysis, and topology, the study of compact Lie groups is one of the most beautiful areas of mathematics and a key stepping stone to the theory of general Lie groups. Assuming no prior knowledge of Lie groups, this book covers the...
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Indra's Pearls: The Vision of Felix Klein
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Indra's Pearls: The Vision of Felix Klein
by David Mumford and Caroline Series and Davis Wright

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Highly illustrated realization of infinitely reflected images related to fractals, chaos and symmetry....
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Graduate Texts in Mathematics Series #0042: Linear Representations of Finite Groups
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Graduate Texts in Mathematics Series #0042: Linear Representations of Finite Groups
by Jean Pierre Serre

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This book consists of three parts, rather different in level and purpose. The first part was originally written for quantum chemists. It describes the correspondence, due to Frobenius, between linear representations and characters. This is a fundamental...
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Fuchsian Groups (Chicago Lectures in Mathematics)
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Fuchsian Groups (Chicago Lectures in Mathematics)
by Svetlana Katok

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This introductory text provides a thoroughly modern treatment of Fuchsian groups that addresses both the classical material and recent developments in the field. A basic example of lattices in semisimple groups, Fuchsian groups have extensive connections...
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Representations & Characters of Grou 2ND Edition
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Representations & Characters of Grou 2ND Edition
by G D James

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'This book provides a modern introduction to the representation theory of finite groups.'...
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Abelian Groups and Representations of Finite Partially Ordered Sets (CMS Advanced Books in Mathematics)
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Abelian Groups and Representations of Finite Partially Ordered Sets (CMS Advanced Books in Mathematics)
by David M Arnold

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"A recurring theme in a traditional introductory graduate algebra course is the existence and consequences of relationships between different algebraic structures. This is also the theme of this book, an exposition of connections between representations...
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Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other Mathematical Toys
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Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other Mathematical Toys
by David Joyner

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"A tour through the algebra of several 'permutation puzzles'... If you like puzzles, this is a somewhat fun book. If you like algebra, this is a fun book. If you like puzzles and algebra, this is a really fun book." -- MAA...
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London Mathematical Society Student Texts #0021: Representations of Finite Groups of Lie Type
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London Mathematical Society Student Texts #0021: Representations of Finite Groups of Lie Type
by Francois Digne

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The authors aim to treat the basic theory of representations of finite groups of Lie type, such as linear, unitary, orthogonal and symplectic groups. They emphasize the Curtis-Alvis duality map and Mackey's theorem and the results that can be deduced...
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Completely Regular Semigroups (Canadian Mathematical Society Monographs & Advanced Texts)
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Completely Regular Semigroups (Canadian Mathematical Society Monographs & Advanced Texts)
by Mario Petrich

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Present a systematic treatment of completely regular semigroups, from introductory to research level, comprised of preliminaries on lattices, semigroups, varieties, and complete regularity; congruences and relations on the congruence lattice; and...
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Field Theory
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Field Theory
by Steven Roman

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Intended for graduate courses or for independent study, this book presents the basic theory of fields. The first part begins with a discussion of polynomials over a ring, the division algorithm, irreducibility, field extensions, and embeddings. The...
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Representation Theory of Finite Groups &
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Representation Theory of Finite Groups &
by Charles W Curtis

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In this study of concrete realizations of the axiomatic systems of abstract algebra, Curtis and Reiner noted the increased emphasis in the 1950s on integral representations of groups and rings, which had been motivated by questions engendered by...
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Valuations Orderings & Milnor K Theory
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Valuations Orderings & Milnor K Theory
by Ido Efrat

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This comprehensive examination of the theory of valued and ordered fields describes their classical aspects, such as their arithmetic, topology, and Galois theory. It also includes material on the newly developed study of generalized Milnor K-rings...
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Linearity, Symmetry, and Prediction in the Hydrogen Atom (Undergraduate Texts in Mathematics)
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Linearity, Symmetry, and Prediction in the Hydrogen Atom (Undergraduate Texts in Mathematics)
by Stephanie F. Singer

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The predictive power of mathematics in quantum phenomena is one of the great intellectual successes of the 20th century. This textbook, aimed at undergraduate or graduate level students (depending on the college or university), concentrates on how to...
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Categories of Commutative Algebras
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Categories of Commutative Algebras
by Yves Diers

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This book studies the universal constructions and properties in categories of commutative algebras, bringing out the specific properties that make commutative algebra and algebraic geometry work. Two universal constructions are presented and used here...
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Problems in Group Theory
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Problems in Group Theory
by John D Dixon

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Text deals with subgroups, permutation groups, automorphisms and finitely generated abelian groups, normal series, commutators and derived series, solvable and nilpotent groups, the group ring and monomial representations, Frattini subgroup...
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London Mathematical Society Lecture Note #251: Grobner Bases and Applications
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London Mathematical Society Lecture Note #251: Grobner Bases and Applications
by Burchberger Winkler

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The theory of Gröbner bases, invented by Bruno Buchberger, is a general method by which many fundamental problems in various branches of mathematics and engineering can be solved by structurally simple algorithms. The method is now available in all...
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Annals of Mathematics Studies #83: Automorphic Forms on Adele Groups
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Annals of Mathematics Studies #83: Automorphic Forms on Adele Groups
by Stephen S. Gelbart

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The subject matter of these Notes is the interplay between the theory of automorphic forms and group representations. One goal is to interpret some recent developments in this area, most significantly the theory of Jacquet-Langlands, working out...
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