Series: Algorithms and Computation in Mathematics , Vol. 22
2008, Approx. 300 p., Hardcover
ISBN: 978-3-540-73724-7
Due: October 23, 2007
About this textbook
The central problem considered in this book is the determination of rational parametrizability of an algebraic curve, and, in the positive case, the computation of a good rational parametrization. This amounts to determining the genus of a curve, i.e. its complete singularity structure, computing regular points of the curve in small coordinate fields, and constructing linear systems of curves with prescribed intersection multiplicities. Various optimality criteria for rational parametrizations of algebraic curves are discussed.
This book is mainly intended for graduate students and researchers in constructive algebraic curve geometry.
Written for:
Students and lecturers in mathematics and computer science
Keywords:
algebraic curves
computer algebra
geometric computation
rational parametrization
Series: Lecture Notes in Mathematics , Vol. 1916
2008, Approx. 175 p., Softcover
ISBN: 978-3-540-73704-9
Due: November 6, 2007
About this book
Entropy and entropy production have recently become mathematical tools for kinetic and hydrodynamic limits, when deriving the macroscopic behaviour of systems from the interaction dynamics of their many microscopic elementary constituents at the atomic or molecular level.
During a special semester on Hydrodynamic Limits at the Centre Emile Borel in Paris, 2001 two of the research courses were held by C. Villani and F. Rezakhanlou. Both illustrate the major role of entropy and entropy production in a mutual and complementary manner and have been written up and updated for joint publication. Villani describes the mathematical theory of convergence to equilibrium for the Boltzmann equation and its relation to various problems and fields, including information theory, logarithmic Sobolev inequalities and fluid mechanics. Rezakhanlou discusses four conjectures for the kinetic behaviour of the hard sphere models and formulates four stochastic variations of this model, also reviewing known results for these.
Table of contents
Preface.- C. Villani: Entropy Production and Convergence to Equilibrium.- F. Rezakhanlou: Kinetic Limits for Interacting Particle Systems.
Series: Lecture Notes in Mathematics
Subseries: Mathematical Biosciences Subseries , Vol. 1922
2008, Approx. 240 p., Softcover
ISBN: 978-3-540-74328-6
Due: October 23, 2007
About this book
The book offers an easy introduction to fast growing research areas in evolution of species, population genetics, ecological models, and population dynamics. The first two chapters review the concept and methodologies of phylogenetic trees; computational schemes and illustrations are given, including applications such as tracing the origin of SARS and influenza. The third chapter introduces the reader to ecological models, including predator-prey models. This chapter includes and introduction to reaction-diffusion equations, which are used to analyze the ecological models. The next chapter reviews a broad range of ongoing research in population dynamics, including evolution of dispersal models; it also features interesting mathematical theorems and lists open problems. The final chapter deals with gene frequencies under the action of migration and selection. The book is addressed to readers at the level of grad students and researchers. A background in PDEs is provided.
Table of contents
Inference of Phylogenetic Trees (Laura Salter Kubatko).- Large-Scale Phylogenetic Analysis of Emerging Infectious Diseases (Daniel Janies and Diego Pol).- Reaction-Diffusion Equations and Ecological Modeling (Chris Cosner).- The Dynamics of Migration-Selection Models (Thomas Nagylaki and Yuan Lou).- Some Challenging Mathematical Problems in Evolution of Dispersal and Population Dynamics (Yuan Lou).
Series: Lecture Notes in Mathematics , Vol. 1925
2008, XII, 200 p., Softcover
ISBN: 978-3-540-74701-7
Due: November 2007
About this book
Zeta functions have been a powerful tool in mathematics over the last two centuries. This book considers a new class of non-commutative zeta functions which encode the structure of the subgroup lattice in infinite groups. The book explores the analytic behaviour of these functions together with an investigation of functional equations. Many important examples of zeta functions are calculated and recorded providing an important data base of explicit examples and methods for calculation.
Table of contents
Introduction.- Nilpotent Groups: Explicit Examples.- Soluble Lie Rings.- Local Functional Equations.- Natural Boundaries I: Theory.- Natural boundaries II: Algebraic groups.- Natural boundaries III: Nilpotent groups.- Large polynomials.- Factorisation of polynomials associated to classical groups.- References.- Index.
Series: Problem Books in Mathematics
2008, Hardcover
ISBN: 978-0-387-74521-3
Due: July 2008
About this book
In 1977 the Mathematics Department at the University of California, Berkeley, instituted a written examination as one of the first major requirements toward the Ph.D. degree in Mathematics. Its purpose was to determine whether first-year students in the Ph.D. program had successfully mastered basic mathematics in order to continue in the program with the likelihood of success. Since its inception, the exam has become a major hurdle to overcome in the pursuit of the degree. The purpose of this book is to publicize the material and aid in the preparation for the examination during the undergraduate years. The book is a compilation of over 1,250 problems which have appeared on the preliminary exams in Berkeley over the last twenty-five years. It is an invaluable source of problems and solutions for every mathematics student who plans to enter a Ph.D. program. Students who work through this book will develop problem-solving skills in areas such as real analysis, multivariable calculus, differential equations, metric spaces, complex analysis, algebra, and linear algebra. The problems are organized by subject and ordered in an increasing level of difficulty. Tags with the exact exam year provide the opportunity to rehearse complete examinations. The appendix includes instructions on accessing electronic versions of the exams as well as a syllabus and statistics of passing scores.
This new edition has been updated with the most recent exams, including exams given during the Fall 2003 semester. There are numerous new problems and solutions which were not included in previous editions.
Table of contents