American Mathematical Society

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Latest release: December 31, 1946
Series
22
Books
A Semicentennial History of the American Mathematical Society, 1888-1938: With Biographies and Bibliographies of the Past Presidents
Book 1·Dec 1938
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$68.00
This volume outlines the history of the AMS in its first fifty years. To download free chapters of this book, click here.
The Logarithmic Potential: Discontinuous Dirichlet and Neumann Problems: Discontinuous Dirichlet and Neumann Problems
Book 6·Dec 1927
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$42.00
This book studies fundamental properties of the logarithmic potential and their connections to the theory of Fourier series, to potential theory, and to function theory. The material centers around a study of Poisson's integral in two dimensions and of the corresponding Stieltjes integral. The results are then extended to the integrals in terms of Green's functions for general regions. There are some thirty exercises scattered throughout the text. These are designed in part to familiarize the reader with the concepts introduced, and in part to complement the theory. The reader should know something of potential theory, functions of a complex variable, and Lebesgue integrals. The book is based on lectures given by the author in 1924-1925 at the Rice Institute and at the University of Chicago.
The Representation Problem for Frechet Surfaces
Book 8·Jan 1951
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$28.00
Non-Riemannian Geometry: Volume 8
Book 8·Jan 1927
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$52.00
Algebraic Geometry and Theta Functions
Book 10·Dec 1929
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$69.00
This book is the result of extending and deepening all questions from algebraic geometry that are connected to the central problem of this book: the determination of the tritangent planes of a space curve of order six and genus four, which the author treated in his Colloquium Lecture in 1928 at Amherst. The first two chapters recall fundamental ideas of algebraic geometry and theta functions in such fashion as will be most helpful in later applications. In order to clearly present the state of the central problem, the author first presents the better-known cases of genus two (Chapter III) and genus three (Chapter IV). The case of genus four is discussed in the last chapter. The exposition is concise with a rich variety of details and references.
The Calculus of Variations in the Large: Volume 18
Book 18·Dec 1934
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$76.00
Morse theory is a study of deep connections between analysis and topology. In its classical form, it provides a relationship between the critical points of certain smooth functions on a manifold and the topology of the manifold. It has been used by geometers, topologists, physicists, and others as a remarkably effective tool to study manifolds. In the 1980s and 1990s, Morse theory was extended to infinite dimensions with great success. This book is Morse's own exposition of his ideas. It has been called one of the most important and influential mathematical works of the twentieth century. Calculus of Variations in the Large is certainly one of the essential references on Morse theory.
Foundations of Algebraic Geometry: Volume 29
Book 29·Dec 1946
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$47.00
This classic is one of the cornerstones of modern algebraic geometry. At the same time, it is entirely self-contained, assuming no knowledge whatsoever of algebraic geometry, and no knowledge of modern algebra beyond the simplest facts about abstract fields and their extensions, and the bare rudiments of the theory of ideals.
Noncommutative Geometry, Quantum Fields and Motives
Book 55
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$102.00
Eisenstein Series and Automorphic $L$-Functions
Book 58·Jan 2010
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$62.00
This book presents a treatment of the theory of $L$-functions developed by means of the theory of Eisenstein series and their Fourier coefficients, a theory which is usually referred to as the Langlands-Shahidi method. The information gathered from this method, when combined with the converse theorems of Cogdell and Piatetski-Shapiro, has been quite sufficient in establishing a number of new cases of Langlands functoriality conjecture; at present, some of these cases cannot be obtained by any other method. These results have led to far-reaching new estimates for Hecke eigenvalues of Maass forms, as well as definitive solutions to certain problems in analytic and algebraic number theory. This book gives a detailed treatment of important parts of this theory, including a rather complete proof of Casselman-Shalika's formula for unramified Whittaker functions as well as a general treatment of the theory of intertwining operators. It also covers in some detail the global aspects of the method as well as some of its applications to group representations and harmonic analysis. This book is addressed to graduate students and researchers who are interested in the Langlands program in automorphic forms and its connections with number theory.
C^*-Bundles and Compact Transformation Groups
Book 269·Jan 1982
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$18.00
The Oscillator Duality Correspondence for the Pair $O(2,2)$, $SP(2,{\mathbb R})$
Book 403·Jan 1989
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$27.00
We calculate this correspondence and show that the unitary representation of O(2, 2), are mapped to unitary representations of Sp(2, [bold]R).
Actions of Linearly Reductive Groups on Affine PI -Algebras
Book 414·Jan 1989
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$26.00
This very interesting monograph straddles two well-studied areas--invariant theory of commutative rings, and the theory of a fixed (noncommutative) ring under a finite group of automorphisms. The author develops a new theory--the fixed subring of a polynomial identity algebra under a linear algebraic group of automorphisms.
Ueda Theory: Theorems and Problems: Theorems and Problems
Book 415·Jan 1989
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$28.00
Higher Spinor Classes
Book 528·Jan 1994
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$42.00
This work defines the higher spinor classes of an orthogonal representation of a Galois group. These classes are higher-degree analogues of the Fröhlich spinor class, which quantify the difference between the Stiefel-Whitney classes of an orthogonal representation and the Hasse-Witt classes of the associated form. Jardine establishes various basic properties, including vanishing in odd degrees and an induction formula for quadratic field extensions. The methods used include the homotopy theory of simplicial presheaves and the action of the Steenrod algebra on mod 2 étale cohomology.
Homotopy Theory of Diagrams
Book 736·Jan 2002
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$63.00
In this paper the authors develop homotopy theoretical methods for studying diagrams. In particular they explain how to construct homotopy colimits and limits in an arbitrary model category. The key concept introduced is that of a model approximation. A model approximation of a category $\mathcal{C}$ with a given class of weak equivalences is a model category $\mathcal{M}$ together with a pair of adjoint functors $\mathcal{M} \rightleftarrows \mathcal{C}$ which satisfy certain properties. The key result says that if $\mathcal{C}$ admits a model approximation then so does the functor category $Fun(I, \mathcal{C})$.
Ergodic Theory of Equivariant Diffeomorphisms: Markov Partitions and Stable Ergodicity: Markov Partitions and Stable Ergodicity
Book 803·Jan 2004
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$67.00
On the assumption that the $\Gamma$-orbits all have dimension equal to that of $\Gamma$, this title shows that there is a naturally defined $F$- and $\Gamma$-invariant measure $\nu$ of maximal entropy on $\Lambda$ (it is not assumed that the action of $\Gamma$ is free).
Mutually Catalytic Super Branching Random Walks: Large Finite Systems and Renormalization Analysis: Large Finite Systems and Renormalization Analysis
Book 809·Jan 2004
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$67.00
Studies the evolution of the large finite spatial systems in size-dependent time scales and compare them with the behavior of the infinite systems, which amounts to establishing the so-called finite system scheme. This title introduces the concept of a continuum limit in the hierarchical mean field limit.
Infinite Dimensional Complex Symplectic Spaces
Book 810·Jan 2004
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$64.00
Complex symplectic spaces are non-trivial generalizations of the real symplectic spaces of classical analytical dynamics. This title presents a self-contained investigation of general complex symplectic spaces, and their Lagrangian subspaces, regardless of the finite or infinite dimensionality.
The Calculus of One-Sided $M$-Ideals and Multipliers in Operator Spaces
Book 842·Jan 2006
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$73.00
The theory of one-sided $M$-ideals and multipliers of operator spaces is simultaneously a generalization of classical $M$-ideals, ideals in operator algebras, and aspects of the theory of Hilbert $C*$-modules and their maps. Here we give a systematic exposition of this theory. The main part of this memoir consists of a 'calculus' for one-sided $M$-ideals and multipliers, i.e. a collection of the properties of one-sided $M$-ideals and multipliers with respect to the basic constructions met in functional analysis. This is intended to be a reference tool for 'noncommutative functional analysts' who may encounter a one-sided $M$-ideal or multiplier in their work.
Relatively Hyperbolic Groups: Intrinsic Geometry, Algebraic Properties, and Algorithmic Problems: Intrinsic Geometry, Algebraic Properties, and Algorithmic Problems
Book 843·Jan 2006
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$73.00
In this the authors obtain an isoperimetric characterization of relatively hyperbolicity of a groups with respect to a collection of subgroups. This allows them to apply classical combinatorial methods related to van Kampen diagrams to obtain relative analogues of some well-known algebraic and geometric properties of ordinary hyperbolic groups. There is also an introduction and study of the notion of a relatively quasi-convex subgroup of a relatively hyperbolic group and solve somenatural algorithmic problems.