Edited by Frank W. J. Olver , Daniel W. Lozier , Ronald F. Boisvert , Charles W. Clark

Modern developments in theoretical and applied science depend on knowledge of the properties of mathematical functions, from elementary trigonometric functions to the multitude of special functions. 

Reinhard Schertz

This is a self-contained account of the state of the art in classical complex multiplication that includes recent results on rings of integers and applications to cryptography using elliptic curves. The author is exhaustive in his treatment, giving a thorough development of the theory of elliptic functions, modular functions and quadratic number fields and providing a concise summary of the results from class field theory. 

Ergodic Theory Methods

Feliks Przytycki , Mariusz Urbanski

This is a one-stop introduction to the methods of ergodic theory applied to holomorphic iteration. The authors begin with introductory chapters presenting the necessary tools from ergodic theory thermodynamical formalism, and then focus on recent developments in the field of 1-dimensional holomorphic iterations and underlying fractal sets, from the point of view of geometric measure theory and rigidity. 

An Example-Based Approach

John Maindonald , W. John Braun

Discover what you can do with R! Introducing the R system, covering standard regression methods, then tackling more advanced topics, this book guides users through the practical, powerful tools that the R system provides.  

Edited by Françoise Delon , Ulrich Kohlenbach , Penelope Maddy , Frank Stephan

The Annual European Meeting of the Association for Symbolic Logic, also known as the Logic Colloquium, is among the most prestigious annual meetings in the field. The current volume, Logic Colloquium 2007, with contributions from plenary speakers and selected special session speakers, contains both expository and research papers by some of the best logicians in the world. 

Elizabeth Louise Mansfield

This book explains recent results in the theory of moving frames that concern the symbolic manipulation of invariants of Lie group actions. In particular, theorems concerning the calculation of generators of algebras of differential invariants, and the relations they satisfy, are discussed in detail.  

Javier Majadas , Antonio G. Rodicio

Written to complement standard texts on commutative algebra, this short book gives complete and relatively easy proofs of important results, including the standard results involving localisation of formal smoothness (M. André) and localisation of complete intersections (L. Avramov), some important results of D. Popescu and André on regular homomorphisms, and some results from A. Grothendieck's EGA on smooth homomorphisms.  

Rick Durrett

The notion of six degrees of separation - that any two people on the planet can be connected by a short chain of people - inspired Strogatz and Watts to define the small world random graph, where each site is connected to close neighbours, but also has long range connections.
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Daniel Zelterman

This textbook for a second course in basic statistics for undergraduates or first-year graduate students introduces linear regression models and describes other linear models including Poisson regression, logistic regression, proportional hazards regression, and nonparametric regression.  

Linear and Nonlinear Models

S. Albeverio , A. Yu Khrennikov , V. M. Shelkovich

This is the first book devoted to the theory of p-adic wavelets and pseudo-differential equations in the framework of distribution theory. This relatively recent theory has become increasingly important in the last decade with exciting applications in a variety of fields, including biology, image analysis, psychology, and information science. 

Steven Kalikow , Randall McCutcheon

This informal introduction provides a fresh perspective on isomorphism theory, which is the branch of ergodic theory that explores the conditions under which two measure preserving systems are essentially equivalent. It contains a primer in basic measure theory, proofs of fundamental ergodic theorems, and material on entropy, martingales, Bernoulli processes, and various varieties of mixing. 

Manuel Lerman

This book presents a unifying framework for using priority arguments to prove theorems in computability. Priority arguments provide the most powerful theorem-proving technique in the field, but most of the applications of this technique are ad hoc, masking the unifying principles used in the proofs.  

Essays for his Centennial

Edited by Solomon Feferman , Charles Parsons , Stephen G. Simpson

Kurt Gödel (1906–1978) did groundbreaking work that transformed logic and other important aspects of our understanding of mathematics, especially his proof of the incompleteness of formalized arithmetic. This book on different aspects of his work and on subjects in which his ideas have contemporary resonance includes papers from a May 2006 symposium celebrating Gödel’s centennial as well as papers from a 2004 symposium.  

Edited by Nils Lid Hjort , Chris Holmes , Peter Müller , Stephen G. Walker

Bayesian nonparametrics works – theoretically, computationally. The theory provides highly flexible models whose complexity grows appropriately with the amount of data. Computational issues, though challenging, are no longer intractable. 

Joseph Neisendorfer

The most modern and thorough treatment of unstable homotopy theory available. The focus is on those methods from algebraic topology which are needed in the presentation of results, proven by Cohen, Moore, and the author, on the exponents of homotopy groups.  

Edited by Frederick P. Gardiner , Gabino González-Diez , Christos Kourouniotis

Riemann surfaces is a thriving area of mathematics with applications to hyperbolic geometry, complex analysis, fractal geometry, conformal dynamics, discrete groups, geometric group theory, algebraic curves and their moduli, various kinds of deformation theory, coding, thermodynamic formalism, and topology of three-dimensional manifolds. 

Peter Mörters , Yuval Peres

This eagerly awaited textbook covers everything the graduate student in probability wants to know about Brownian motion, as well as the latest research in the area. Starting with the construction of Brownian motion, the book then proceeds to sample path properties like continuity and nowhere differentiability.