Introduction to Quantitative Basque Center for Applied ... · net; and the building of the Three “M’s” Maple, Mathematica and Matlab. We intend to persuade that Mathematica

Mathematics springer.com/NEWSonline

36

H. Albrecher, University of Lausanne, Switzerland; A. Binder, MathConsult GmbH, Linz, Austria; V. Lautscham, University of Lausanne, Switzerland; P. Mayer, Technische Universität Graz, Austria

Introduction to Quantitative Methods for Financial MarketsFeatures 7 First volume of a new series 7 Self-contained and compact introduction to financial math-ematics and quantitative modeling of financial markets 7 Covers a broad area, from a basic introduction to financial markets, products and concepts, via model development, up to the cali-bration of models to market data and implementa-tion of pricing algorithms 7 Leads the reader from standard derivatives to quite advanced recent exotic products 7 Practical aspects and benefits of implementation techniques are discussed and illustrated using Mathematica and UnRisk (soft-ware available to readers) 7 Ready for classroom use or self-study 7 Provides many illustrative examples and exercises, some with solutions

Contents I Interest Rates.- II Financial Products.- III The No-Arbitrage Principle.- IV European and American Options.- The Binomial Option Pricing Model.- VI The Black-Scholes Model.- VII The Black-Scholes Formula.- VIII Stock-Price Mod-els.- IX Interest Rate Models and the Valuation of Interest Rate Derivatives.- X Numerical Tools.- XI Simulation Methods.- XII Calibrating Models – Inverse Problems.- XIII Case Studies: Exotic Derivatives.- XIV Portfolio-Optimization.- XV Introduction to Credit Risk Models.

Fields of interestsGame Theory, Economics, Social and Behav. Sciences; Game Theory/Mathematical Methods; Quantitative Finance

Target groupsUpper undergraduate

Discount groupProfessional Non-Medical

Due October 2012

Originally published in German under the title Einführung in die Finanzmathematik in the Mathematik Kompakt series

2013 2012. X, 196 p. (Compact Textbooks in Mathematics) Softcover7 approx. $59.95ISBN 978-3-0348-0518-6

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L. Ambrosio, Scuola Normale Superiore di Pisa, Italy; A. Bressan, PennState University, University Park, PA, USA; D. Helbing, ETH Zürich, Switzerland; A. Klar, Technische Universität Kaiserslautern, Germany; E. Zuazua, Basque Center for Applied Mathematics, Bilbao, Spain

Modelling and Optimisation of Flows on NetworksCetraro, Italy 2009, Editors: Benedetto Piccoli, Michel Rascle

Scientific editors: B. Piccoli, Rutgers University, Camden, NJ, USA; M. Rascle, University of Nice Sophia Antipolis, Nice, France

Feature 7 Rich notes on most recent advances on traffic flow on networks, including control and opti-mization. Tutorials on conservation laws,,wave equations and optimal transport theory Diverse applications such as vehicular traffic, supply chains and others

Contents A User’s Guide to Optimal Transport.- Hyper-bolic Conservation Laws: an Illustrated Tuto-rial.- Derivation of Non-Local Macroscopic Traffic Equations and Consistent Traffic Pressures from Microscopic Car-Following Models.- On the Controversy around Daganzo’s Requiem for and Aw-Rascle’s Resurrection of Second-Order Traffic Flow Models.- Theoretical vs. Empirical Classification and Prediction of Congested Traffic States.- Self-Organized Network Flows.- Opera-tion Regimes and Slower-is-Faster-Effect in the Control of Traffic Intersections.- Modeling and Optimization of Scalar Flows on Networks.- The Wave Equation: Control and Numerics

Fields of interestsPartial Differential Equations; Mathematical Mod-eling and Industrial Mathematics; Analysis

Target groupsResearch


Due October 2012

2013. XVI, 540 p. 141 illus., 32 in color. (Lecture Notes in Mathematics / C.I.M.E. Foundation Subseries, Volume 2062) Softcover7 $119.00ISBN 978-3-642-32159-7

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M. Bachar, King Saud University, Riyadh, Saudi Arabia; J. Batzel, University of Graz, Austria; S. Ditlevsen, University of Copenhagen, Denmark (Eds)

Stochastic Biomathematical Modelswith Applications to Neuronal Modeling

Stochastic biomathematical models are becoming increasingly important as new light is shed on the role of noise in living systems. In certain biological systems, stochastic effects may even enhance a signal, thus providing a biological motivation for the noise observed in living systems.

Feature 7 Written by current leading experts in the field Focus on interdisciplinary (physiological and biological) applications of stochastic methods Representation of key theoretical ideas but also clear and motivated examples of application and implementation issues

Contents 1 Introduction to stochastic models in biology.- 2 One-dimensional homogeneous diffusions.- 3 A brief introduction to large deviations theory.- 4 Some numerical methods for rare events simula-tion and analysis.- 5 Stochastic Integrate and Fire models: a review on mathematical methods and their applications.- 6 Stochastic partial differential equations in Neurobiology: linear and nonlinear models for spiking neurons.- 7 Deterministic and stochastic FitzHugh-Nagumo systems.- 8 Stochas-tic modeling of spreading cortical depression

Fields of interestsProbability Theory and Stochastic Processes; Mathematical Modeling and Industrial Mathemat-ics; Statistics for Life Sciences, Medicine, Health Sciences



Due October 2012

2013. X, 216 p. 34 illus., 13 in color. (Lecture Notes in Mathematics / Mathematical Biosciences Subseries, Volume 2058) Softcover7 $89.95ISBN 978-3-642-32156-6

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www.springer.com/978-3-0348-0518-6



News 8/2012 Mathematics

37

J. M. Borwein, M. P. Skerritt, The University of Newcastle, Callaghan, NSW, Australia

An Introduction to Modern Mathematical ComputingWith Mathematica®

Thirty years ago mathematical, as opposed to applied numerical, computation was difficult to perform and so relatively little used. Three threads changed that: the emergence of the personal computer; the discovery of fiber-optics and the consequent development of the modern inter-net; and the building of the Three “M’s” Maple, Mathematica and Matlab. We intend to persuade that Mathematica and other similar tools are worth knowing, assuming only that one wishes to be a mathematician, a mathematics educator, a computer scientist, an engineer or scientist, or anyone else who wishes/needs to use mathematics better. We also hope to explain how to become an „experimental mathematician“ while learning to be better at proving things.

Features 7 Places primary importance on the mathemat-ics, rather than being a 'how to' manual for mak-ing computations 7 Integrates numerous worked examples and introduces all key programming constructions 7 Includes exercises, sample tests, and a careful selection of 'explorations' suitable for either independent studies or for term projects

Contents Preface.- Conventions and Notation.- 1. Num-ber Theory.- 2. Calculus.- 3. Linear Algebra.- 4. Visualisation and Geometry: a Postscript.- Sample Quizzes.- Index.- References.-

Fields of interestsComputational Mathematics and Numerical Analysis; Mathematical Software; Simulation and Modeling



Due August 2012

2013. XVI, 224 p. 95 illus., 91 in color. (Springer Undergraduate Texts in Mathematics and Technology) Hardcover7 $59.95ISBN 978-1-4614-4252-3

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E. Brieskorn, Eitorf, Germany; H. Knörrer, ETH Zürich, Switzerland

Plane Algebraic CurvesTranslated by John Stillwell

Translated by: J. Stillwell, University of San Francisco, CA, USA

In a detailed and comprehensive introduction to the theory of plane algebraic curves, the au-thors examine this classical area of mathematics that both figured prominently in ancient Greek studies and remains a source of inspiration and topic of research to this day. Arising from notes for a course given at the University of Bonn in Germany, “Plane Algebraic Curves” reflects the authorʼs concern for the student audience through emphasis upon motivation, development of imagi-nation, and understanding of basic ideas.

Features 7 Lively introduction and overview of the field 7 Anchors the subject in history, science and technology 7 Clearly explains the tools from local analytic geometry and from algebraic and differential topology 7 Presents a wealth of attractive geometric illustrations

Contents I. History of algebraic curves.- 1. Origin and generation of curves.- 2. Synthetic and analytic geometry.- 3. The development of projective ge-ometry.- II. Investigation of curves by elementary algebraic methods.- 4. Polynomials.- 5. Defini-tion and elementary properties of plane algebraic curves.- 6. The intersection of plane curves.- 7. Some simple types of curves.- III. Investigation of curves by resolution of singularities.- 8. Local investigations.- 9. Global investigations.- Bibliog-raphy.- Index.

Fields of interestsAlgebraic Geometry; Commutative Rings and Algebras; Algebraic Topology



Due August 2012

Originally published 1981 as Ebene algebraische Kurven by Birkhäuser Boston

2012. X, 724 p. 356 illus. (Modern Birkhäuser Classics) Softcover7 $99.00ISBN 978-3-0348-0492-9

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X. Cheng, Chongqing University of Technology, China; Z. Shen, Indiana University Purdue University Indianapolis, IN, US

Finsler GeometryAn Approach via Randers Spaces

„Finsler Geometry: An Approach via Randers Spaces“ exclusively deals with a special class of Finsler metrics -- Randers metrics, which are defined as the sum of a Riemannian metric and a 1-form. Randers metrics derive from the research on General Relativity Theory and have been ap-plied in many areas of the natural sciences. They can also be naturally deduced as the solution of the Zermelo navigation problem. The book provides readers not only with essential findings on Randers metrics but also the core ideas and methods which are useful in Finsler geometry. It will be of significant interest to researchers and practitioners working in Finsler geometry, even in differential geometry or related natural fields.

Features 7 Deals with a special class of Finsler metrics -- Randers metrics 7 Presents core ideas and methods which are useful in Finsler geom-etry 7 Provides many interesting and important examples and results obtained by the authors and other mathematicians during the past decade

Contents Randers Spaces.- Randers Metrics and Geodesics.- Randers Metrics of Isotropic S-Curvature.- Rie-mann Curvature and Ricci Curvature.- Projective Geometry of Randers Spaces.- Randers Metrics with Special Riemann Curvature Proper-ties.- Randers Metrics of Weakly Isotropic Flag Curvature.-Projectively Flat Randers Metrics.- Conformal Geometry of Randers Metrics.- Dually Flat Randers Metrics

Fields of interestsDifferential Geometry; Geometry; Mathematical Methods in Physics



Due September 2012

Jointly published with Science Press Ltd

Distribution rights in China: Science Press Ltd

2012. Approx. 200 p. 5 illus. Hardcover7 $109.00ISBN 978-3-642-24887-0

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38

A. Chinchuluun, National University of Mongolia, Ulaanbaatar, Mongolia; P. M. Pardalos, University of Florida, Gainesville, FL, USA; R. Enkhbat, National University of Mongolia, Ulaanbaatar, Mongolia; E. N. Pistikopoulos, Imperial College, London, UK (Eds)

Optimization, Simulation, and ControlContents Preface.- 1. On the Composition of Convex Enve-lopes for Quadrilinear Terms (P. Belotti, S. Cafieri, J. Lee, L. Liberti, A. Miller).- 2. An Oriented Distance Function Application to Gap Functions for Vector Variational Inequalities (L. Altangerel, G. Wanka).-3. Optimal Inscribing of Two Balls into Polyhedral Set (R. Enkhbat, B. Barsbold).-4. Mathematical Programs with Equilibrium Con-straints: A Brief Survey of Methods and optimality conditions (I. Tseveendorj).-5. Linear program-ming with interval data: a Two-Level Program-ming Approach (C. Kao, S. Liu).-6 Quantifying Retardation in Simulation Based Optimization (A. Griewank, A. Hamdi, E. Ozkaya).-7. Evolution-ary Algorithm for Generalized Nash Equilibrium Problems (M. Majig, R. Enkhbat, M. Fuku-shima).-8. Scalar and Vector Optimization with Composed Objective Functions and Constraints (N. Lorenze, G. Wanka).-9. A PTAS for Weak Minimum Routing Cost Connected Dominating Set of Unit Disk Graph (Q. Liu, Z. Zhang, Y. Hong, W. Wu, D. Du).-10. Power Control in Wireless Ad-Hoc Networks: Stability and Convergence Under Uncertainties (T. Charalambous).-11. The Changing Role of Optimization in Urban Planning (J. Keirstead, N. Shah).-12. Parametric Optimiza-tion Approach to the Solow Growth Theory (R. Enkhbat, D. Bayanjargal ). [...]

Fields of interestsOptimization; Systems Theory, Control; Math-ematical Modeling and Industrial Mathematics



Due November 2012

2013. X, 338 p. 75 illus., 25 in color. (Springer Optimization and Its Applications, Volume 76) Hardcover7 $129.00ISBN 978-1-4614-5130-3

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D. Colton, University of Delaware, Newark, DE, USA; R. Kress, University of Göttingen, Germany

Inverse Acoustic and Electromagnetic Scattering TheoryThe inverse scattering problem is central to many areas of science and technology such as radar and sonar, medical imaging, geophysical exploration and nondestructive testing. This book is devoted to the mathematical and numerical analysis of the inverse scattering problem for acoustic and electromagnetic waves. In this third edition, new sections have been added on the linear sampling and factorization methods for solving the inverse scattering problem as well as expanded treatments of iteration methods and uniqueness theorems for the inverse obstacle problem. These additions have in turn required an expanded presentation of both transmission eigenvalues and boundary integral equations in Sobolev spaces. As in the previous editions, emphasis has been given to simplicity over generality thus providing the reader with an accessible introduction to the field of inverse scat-tering theory.

Features 7 New sections included 7 Chapters up-dated throughout 7 This book has become the standard reference book in the field of inverse scattering theory

Contents Introduction.- The Helmholtz Equation.- Direct Acoustic Obstacle Scattering.- III-Posed Prob-lems.- Inverse Acoustic Obstacle Scattering.- The Maxwell Equations.- Inverse Electromagnetic Ob-stacle Scattering.- Acoustic Waves in an Inhomo-geneous Medium.- Electromagnetic Waves in an Inhomogeneous Medium.- The Inverse Medium Problem.-References.- Index

Fields of interestsPartial Differential Equations; Integral Equations; Visualization



Due October 2012

3rd ed. 2012. X, 417 p. 8 illus., 4 in color. (Applied Mathematical Sciences, Volume 93) Hardcover7 $129.00ISBN 978-1-4614-4941-6

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N. J. Cutland, A. Roux, University of York, UK

Derivative Pricing in Discrete TimeDerivatives are financial entities whose value is derived from the value of other more concrete assets such as stocks and commodities. They are an important ingredient of modern financial markets. This book provides an introduction to the mathematical modelling of real world financial markets and the rational pricing of derivatives, which is part of the theory that not only underpins modern financial practice but is a thriving area of mathematical research. The central theme is the question of how to find a fair price for a derivative; defined to be a price at which it is not possible for any trader to make a risk free profit by trading in the derivative.

Features 7 Accessible to students of a quantitative subject such as such as economics or physics as well as undergraduates in the final years of a mathemat-ics degree 7 Includes a complete treatment of no-arbitrage pricing for both European and American derivatives in incomplete markets as well as Black-Scholes theory 7 Although focus-ing on the theory of derivative pricing in models with discrete time, the book also provides an understanding of the more advanced theory of continuous-time models

Contents Derivative Pricing and Hedging.- A Simple Market Model.- Single-Period Models.- Multi-Period Models: No-Arbitrage Pricing.- Multi-Period Models: Risk-Neutral Pricing.- The Cox-Ross-Rubinstein model.- American Options.- Advanced Topics.

Fields of interestsQuantitative Finance; Probability Theory and Sto-chastic Processes; Finance/Investment/Banking



Due October 2012

2013. XVI, 320 p. 34 illus. With online files/update. (Springer Undergraduate Mathematics Series) Softcover7 approx. $49.95ISBN 978-1-4471-4407-6

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39

M. M. Deza, Ecole Normale Superieure (ENS), Paris, France and and JAIST, Ishikawa, Japan; E. Deza, Moscow State Pedagogical University, Moscow, Russia

Encyclopedia of DistancesFeatures 7 Offers a unique overview of the theme "dis-tance" in mathematics and science 7 Done in a cross-disciplinary fashion 7 Comprehensive

Contents Part I. Mathematics of Distances.- 1 General Definitions.- 2 Topological Spaces.- 3 Generaliza-tion of Metric Spaces.- 4 Metric Transforms.- 5 Metrics on Normed Structures.- Part II. Geom-etry and Distances.- 6 Distances in Geometry.- 7 Riemannian and Hermitian Metrics.- 8 Distances on Surfaces and Knots.- 9 Distances on Convex Bodies, Cones and Simplicial Complexes.- Part III. Distances in Classical Mathematics.- 10 Distances in Algebra.- 11 Distances on Strings and Permuta-tions.- 12 Distances on Numbers, Polynominals and Matrices.- 13 Distances in Functional Analy-sis.- 14 Distances in Probability Theory.- Part IV. Distances in Applied Mathematics.- 15 Distances in Graph theory.- 16 Distances in Coding Theory.- 17 Distances and Similarities in Data Analysis.- 18 Distances in Mathematical Engineering.- Part V. Computer-Related Distances.- 19 Distances on Real and Digital Planes.- 20 Voronoi Diagram Distances.- 21 Image and Audio Distances.- 22 Distances in Internet and Similar Networks.- Part VI. Distances in Natural Sciences.- 23 Distances in Biology.- 24 Distances in Physics and Chemistry.- 25 Distances in Geography, Geophysics and As-tronomy.- 26 Distances in Cosmology and Theory of Relativity.- Part VII. Real-World Distances.- 27 Length Measures and Scales.- 28 Distances in Ap-plied Social Sciences.- 29 Other Distances.

Fields of interestsGeometry; Differential Geometry; Topology



Due November 2012

2nd ed. 2013. Approx. 650 p. Hardcover7 approx. $149.00ISBN 978-3-642-30957-1

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A. d‘Onofrio, Istituto Europeo di Oncologia, Milan, Italy; P. Cerrai, Università di Pisa, Italy; A. Gandolfi, CNR, Rome, Italy (Eds)

New Challenges for Cancer Systems BiomedicineContents A. Csikasz-Nagy, M. Cavaliere, S. Sedwards_Com-bining Game Theory and Graph Theory to Model Interactions between Cells in the Tumour Micro-environment.- A. Silva, R. Gatenby_Growth as the Root of all Evil in Carcinomas: Synergy between pH Buffering and Anti-Angiogenesis prevents Emergence of Hallmarks of Cancer.- R.V. Solé_Phase Transitions in Cancer.- M.A.J. Chaplain, M. Sturrock, A.J. Terry_Spatio-Temporal Modelling of Intracellular Signalling Pathways: Transcription Factors, Negative Feedback Systems and Oscil-lations.- D. Fey, D.R. Croucher, W. Kolch, B.N. Kholodenko_Understanding Cell Fate Decisions by Identifying Crucial System Dynamics.- P. Milazzo, A. Del Corso, A. Maggiolo-Schettini, U. Mura, R. Barbuti_Modelling Biochemical Path-ways with the Calculus of Looping Sequences.- L. Tortolina, N. Castagnino, C. De Ambrosi, A. Barla, A. Verri, G. Zoppoli, L. Bagnasco, D. Piras, F. Patrone, A. Ballestrero, S. Parodi_Dynamic Simulations of Pathways Downstream of TGF, Wnt and EGF-Family Growth Factors, in Colorectal Cancer, including Mutations and Treatments with Onco-Protein Inhibitors.- E. Beretta, V. Capasso, N. Morozova_Some Results on the Population Behavior of Cancer Stem Cells.- A. Fasano_Glu-cose Metabolism in Multicellular Spheroids, ATP Production and Effects of Acidity.- X. Gao, J.T. McDonald, L. Hlatky, H. Enderling_Cell-Cell Interactions in Solid Tumors - the Role of Cancer Stem Cells.- M. Scianna, L. Preziosi_Hybrid Cellular Potts Model for Solid Tumor Growth.- F. Castiglione, P.-L. Lollini, S. Motta, A. Paladini, F. Pappalardo, M. [...]

Fields of interestsPhysiological, Cellular and Medical Topics; Cancer Research; Biophysics and Biological Physics



Due October 2012

2013. Approx. 350 p. 11 illus. (SIMAI Springer Series) Hardcover7 approx. $119.00ISBN 978-88-470-2570-7

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D.‑Z. Du, University of Texas, Dallas, TX, USA; P.‑J. Wan, Illinois Institute of Technology, Chicago, IL, USA

Connected Dominating Set: Theory and ApplicationsThe connected dominating set has been a classic subject studied in graph theory since 1975. Since the 1990s, it has been found to have important applications in communication networks, espe-cially in wireless networks, as a virtual backbone. Motivated from those applications, many papers have been published in the literature during last 15 years. Now, the connected dominating set has become a hot research topic in computer science.

Features 7 This unique book may be used as a refer-ence and/or supplementary text in a graduate seminar 7 The expository content and complete list of references in each chapter bring the reader quickly to the forefront of research 7 Wide applications of connected dominating sets attract readers not only from optimization and theoretical computer science, but also from computer com-munication networks and industrial engineering

Contents -Preface.-1. Introduction.-2. CDS in General Graph-3. CDS in Unit Disk Graph.-4. CDS in Unit Ball Graphs and Growth Bounded Graphs.- 5. Weighted CDS in Unit Disk Graph.-6. Cover-age.-7. Routing-Cost Constrained CDS.-8. CDS in Disk-Containment Graphs.-9. CDS in Disk-Intersection Graphs.-10. Geometric Hitting Set and Disk Cover.-11. Minimum-Latency Schedul-ing.-12 CDS in Planar Graphs.-Bibliography

Fields of interestsOperations Research, Management Science; Algorithm Analysis and Problem Complexity; Combinatorics

Target groupsGraduate


Due October 2012

2013. XIV, 236 p. 72 illus., 6 in color. (Springer Optimization and Its Applications, Volume 77) Hardcover7 approx. $69.95ISBN 978-1-4614-5241-6

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40

B. I. Dundas, The Norwegian University of Science and Technology, Trondhiem, Norway; T. G. Goodwillie, Brown University, Providence, RI, USA; R. McCarthy, University of Illinois, Urbana, IL, USA

The Local Structure of Algebraic K-TheoryAlgebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic geometry. As is commonly encountered, this powerful mathemati-cal object is very hard to calculate. Apart from Quillen‘s calculations of finite fields and Suslin‘s calculation of algebraically closed fields, few com-plete calculations were available before the discov-ery of homological invariants offered by motivic cohomology and topological cyclic homology.

Features 7 Covers the connection between algebraic K-theory and Bökstedt, Hsiang and Madsen's topological cyclic homology, and gives a proof of the fact that the difference between the theories are ‘locally constant’ 7 Provides an inroad to the necessary background in algebraic K-theory and highly structured homotopy theory; col-lecting all necessary tools into one common framework 7 Contains the proof of the integral Goodwillie ICM 1990 conjecture and explains the mathematical prerequisites needed to do this

Contents Algebraic K-theory.- Gamma-spaces and S-algebras.- Reductions.- Topological Hochschild Homology.- The Trace K → THH.- Topological Cyclic Homology.- The Comparison of K-theory and TC.

Fields of interestsK-Theory; Algebraic Topology; Category Theory, Homological Algebra



Due October 2012

2013. XVIII, 422 p. 2 illus. (Algebra and Applications, 18) Hardcover7 $129.00ISBN 978-1-4471-4392-5

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G. Dzemyda, O. Kurasova, J. Žilinskas, Vilnius University, Lithuania

Multidimensional Data VisualizationMethods and Applications

This book highlights recent developments in mul-tidimensional data visualization, presenting both new methods and modifications on classic techniques. Throughout the book, various appli-cations of multidimensional data visualization are presented including its uses in social sciences (economy, education, politics, psychology), envi-ronmetrics, and medicine (ophthalmology, sport medicine, pharmacology, sleep medicine). The book provides recent research results in optimiza-tion-based visualization.

Features 7 Presents an overview of multidimensional data visualization 7 Provides backgroud to construc-tion, analysis, and implementation of optimization algorithms for visualization of multidimensional data 7 Shows benefits of artificial neural net-works and their integrated use with other methods for visualization of multidimensional data 7 Presents various applications of multidimen-sional data visualization: from social sciences to medicine

Contents Preface.- 1. Multidimensional Data and the Concept of Visualization.- 2. Strategies for Multi-dimensional Data Visualization.- 3. Optimization-Based Visualization.- 4. Combining Multidimen-sional Scaling with Artificial Neural Networks.- 5. Applications of Visualizations.- A. Test Data Sets.- References.- Index.

Fields of interestsOptimization; Simulation and Modeling; Visual-ization



Due October 2012

2013. XII, 250 p. 120 illus., 38 in color. (Springer Optimization and Its Applications, Volume 75) Hardcover7 $109.00ISBN 978-1-4419-0235-1

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M. Fontana, Università degli Studi „Roma Tre“, Rome, Italy; E. Houston, T. Lucas, University of North Carolina, Charlotte, NC, USA

Factoring Ideals in Integral DomainsThis volume provides a wide-ranging survey of, and many new results on, various important types of ideal factorization actively investigated by sev-eral authors in recent years. Examples of domains studied include (1) those with weak factorization, in which each nonzero, nondivisorial ideal can be factored as the product of its divisorial closure and a product of maximal ideals and (2) those with pseudo-Dedekind factorization, in which each nonzero, noninvertible ideal can be factored as the product of an invertible ideal with a product of pairwise comaximal prime ideals. Prüfer domains play a central role in our study, but many non-Prüfer examples are considered as well.

Feature 7 Latest developments in the theory of ideal factorizations - not included in any other recent books Particularly useful to young researchers in commutative algebra Emphasizes historical devel-opment of the subject

Fields of interestsAlgebra; Commutative Rings and Algebras; Alge-braic Geometry



Due October 2012

2013. X, 158 p. (Lecture Notes of the Unione Matematica Italiana, Volume 14) Softcover7 $49.95ISBN 978-3-642-31711-8

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41

S. Hong, Korea University, Seoul, Korea; J. Kalliongis, Saint Louis University, MO, USA; D. McCullough, University of Oklahoma, Norman, OK, USA; J. H. Rubinstein, University of Melbourne, VIC, Australia

Diffeomorphisms of Elliptic 3-ManifoldsThis work concerns the diffeomorphism groups of 3-manifolds, in particular of elliptic 3-mani-folds. These are the closed 3-manifolds that admit a Riemannian metric of constant positive curvature, now known to be exactly the closed 3-manifolds that have a finite fundamental group. The (Generalized) Smale Conjecture asserts that for any elliptic 3-manifold M, the inclusion from the isometry group of M to its diffeomorphism group is a homotopy equivalence. The original Smale Conjecture, for the 3-sphere, was proven by J. Cerf and A. Hatcher, and N. Ivanov proved the generalized conjecture for many of the elliptic 3-manifolds that contain a geometrically incom-pressible Klein bottle. The main results establish the Smale Conjecture for all elliptic 3-manifolds containing geometrically incompressible Klein bottles, and for all lens spaces L(m,q) with m at least 3. Additional results imply that for a Haken Seifert-fibered 3 manifold V, the space of Seifert fiberings has contractible components, and apart from a small list of known exceptions, is contract-ible. Considerable foundational and background

Contents 1 Elliptic 3-manifolds and the Smale Conjecture.- 2 Diffeomorphisms and Embeddings of Mani-folds.- 3 The Method of Cerf and Palais.- 4 Elliptic 3-manifolds Containing One-sided Klein Bottles.- 5 Lens Spaces

Fields of interestManifolds and Cell Complexes (incl. Diff.Topol-ogy)



Due September 2012

2012. X, 153 p. 22 illus. (Lecture Notes in Mathematics, Volume 2055) Softcover7 $49.95ISBN 978-3-642-31563-3

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W.‑H. Hui, K. Xu, The Hong Kong University of Science & Technology, China

Computational Fluid Dynamics Based on the Unified Coordinates„Computational Fluid Dynamics Based on the Unified Coordinates“ reviews the relative advan-tages and drawbacks of Eulerian and Lagrangian coordinates as well as the Arbitrary Lagrangian-Eulerian (ALE) and various moving mesh meth-ods in Computational Fluid Dynamics (CFD) for one- and multi-dimensional flows.

Features 7 Introduces Lagrangian system and presents its mathematical properties 7 Distinguishes the advantages and disadvantages of Lagrangian and Eulerian systems 7 Provides a foundation for the development of a unified method with arbitrary mesh velocity

Contents Derivation of Conservation Law Equations.- Re-view of Eulerian Computation for One-dimen-sional Flow.- One-Dimensional Flow Computa-tion Using the Unified Coordinates.- Comments on Current Methods for Multi-Dimensional Flow Computation.- The Unified Coordinates Formulation of CFD.- Properties of the Unified Coordinates.- Lagrangian Gas Dynamics.- Steady 2-D and 3-D Supersonic Flow.- Unsteady 2-D and 3-D Flow Computation.- Viscous Flow Computa-tion.- Applications of the Unified Coordinates to Kinetic Theory.

Fields of interestsComputational Mathematics and Numerical Analysis; Numerical and Computational Physics; Numeric Computing



Due September 2012

Jointly published with Science Press Ltd

Distribution rights in China: Science Press Ltd

2012. 300 p. 79 illus. Hardcover7 $129.00ISBN 978-3-642-25895-4

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J. Jost, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

Partial Differential EquationsThis book offers an ideal graduate-level introduc-tion to the theory of partial differential equations. The first part of the book describes the basic mathematical problems and structures associated with elliptic, parabolic, and hyperbolic partial dif-ferential equations, and explores the connections between these fundamental types.

Features 7 New edition extensively revised and up-dated 7 Features a systematic discussion of the relations between different types of partial differential equations 7 Presents new Harnack type techniques

Contents Preface.- Introduction: What are Partial Differ-ential Equations?.- 1 The Laplace equation as the Prototype of an Elliptic Partial Differential Equa-tion of Second Order.- 2 The Maximum Principle.- 3 Existence Techniques I: Methods Based on the Maximum Principle.- 4 Existence Techniques II: Parabolic Methods. The Heat Equation.- 5 Reaction-Diffusion Equations and Systems.- 6 Hyperbolic Equations.- 7 The Heat Equation, Semigroups, and Brownian Motion.- 8 Rela-tionships between Different Partial Differential Equations.- 9 The Dirichlet Principle. Variational Methods for the Solutions of PDEs (Existence Techniques III).- 10 Sobolev Spaces and L^2 Regularity theory.- 11 Strong solutions.- 12 The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV).- 13The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash.- Appendix: Banach and Hil-bert spaces. The L^p-Spaces.- References.- Index of Notation.- Index.

Fields of interestsPartial Differential Equations; Theoretical, Math-ematical and Computational Physics



Due November 2012

3rd ed. 2013. XIV, 396 p. 10 illus. (Graduate Texts in Mathematics, Volume 214) Hardcover7 $79.95ISBN 978-1-4614-4808-2

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42

E. Kranakis, Carleton University, Ottawa, ON, Canada (Ed)

Advances in Network Analysis and its ApplicationsContents FINANCIAL NETWORKS: 1. Mathematical modeling of systemic risk: H. Amini, A. Minca.- 2. Systemic risk in banking networks without Monte Carlo simulation: J. P. Gleeson, T. R. Hurd, S. Melnik, A. Hackett.- 3. Systemic Valuation of Banks — Interbank Equilibrium and Contagion: G. Hałaj.- 4. An Open Problem: J. B. Walsh.- II SE-CURITY NETWORKS: 5. Dynamic Trust Man-agement: Network Profiling for High Assurance Resilience: M. Burmester , W. O. Redwood.- 6. Security Issues in Link State Routing Protocols for MANETs: G.Cervera, M.Barbeau, J. Garcia-Alfaro, E.Kranakis.-7. TCHo: a Code-based Cryptosys-tem: A. Duc , S. Vaudenay.- 8. Formal Method for (k)-Neighborhood Discovery Protocols: R.Jamet, P.Lafourcade.- 9. A Tutorial on White-box AES: J. A. Muir.- 10. Efficient 1-Round Almost-Perfect Secure Message Transmission Protocols with Flexible Connectivity: R. Safavi-Naini, M. Ashra-ful Alam Tuhin.- III SOCIAL NETWORKS: 11. Mathematical modelling to evaluate measures and control the spread of illicit drug use: A. Bakhtiari, A. Rutherford.- 12. Complex Networks and Social Networks: A. Bonato, A. Tian.- 13. NAVEL Gaz-ing: Studying a Networked Scholarly Organiza-tion: D. Dimitrova, A. Gruzd, Z.Hayat, G. Ying Mo, D.Mok, Th. Robbins, B.Wellman, X. Zhuo.- 14. How Al Qaeda can use order theory to evade or defeat U.S. Forces: J.D.Farley.- 15. The ABCs of Designing Social Networks for Health Behaviour Change: The VivoSpace Social Network: N. Kamal, S. Fels, M. Blackstock, K. Ho.- 16. Evolution of an Open Source Community Network: N. Saraf, A. Seary, D. Chandrasekaran, P.Monge. [...]

Fields of interestsComplex Systems; Computer Communication Networks; Electrical Engineering



Due October 2012

2012. XIV, 214 p. 95 illus., 39 in color. (Mathematics in Industry, Volume 18) Hardcover7 $129.00ISBN 978-3-642-30903-8

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H. P. Langtangen, Simula Research Laboratory, Lysaker, Norway

A Primer on Scientific Programming with PythonThe book serves as a first introduction to comput-er programming of scientific applications, using the high-level Python language. The exposition is example- and problem-oriented, where the ap-plications are taken from mathematics, numerical calculus, statistics, physics, biology, and finance.

Features 7 Example-oriented text with all applications taken from science and engineering 7 Aimed at newcomers to programming and Python, but proved to be useful for professionals too 7 All examples are accompanied by complete program codes, which can be modified to the reader's needs 7 Covers both Matlab-style "simple" programming and object-oriented program-ming 7 Demonstrates how Python can be an alternative to Matlab in scientific computing

Contents Preface.- Computing with Formulas.- Loops and Lists.- Functions and Branching.- Input Data and Error Handling.- Array Computing and Curve Plotting.- Files, Strings and Dictionaries.- Intro-duction to Classes.- Random Numbers and Simple Games.- Object-Oriented Programming.- Se-quences and Difference Equations.- Introduction to Discrete Calculus.- Introduction to Differential Equations.- A Complete Differential Equation Project.- Programming of Differential Equations.- Debugging.- Migrating Python to Compiled Code.- Technical Topics.- Bibliography.- Index.

Fields of interestsComputational Science and Engineering; Pro-gramming Techniques; Software Engineering/Programming and Operating Systems



Due July 2012

3rd ed. 2012. XXXII, 798 p. 79 illus., 30 in color. (Texts in Computational Science and Engineering, Volume 6) Hardcover7 $79.95ISBN 978-3-642-30292-3

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M. Merz, University of Hamburg, Germany; M. V. Wüthrich, ETH Zürich, Switzerland

Financial Modeling, Actuarial Valuation and Solvency in InsuranceRisk management for financial institutions is one of the main questions the financial industry has to deal with. The present volume is a mathematically rigorous text on solvency modeling.

Features 7 Addressed to practitioners in the financial and actuarial industry as well as more academic researchers 7 Takes into account all current solvency developments of the financial indus-try 7 Core text for enterprise risk management in Chartered Enterprise Risk Analyst (CERA) training and qualification

Contents Introduction.- Part I. Financial Valuation Prin-ciples.- 1. State price deflators and stochastic discounting.- 2. Gaussian spot rate models.- 3. Non-Gaussian spot rate models.- 4. Stochastic forward rate modeling.- 5.Dynamic Nelson-Siegel and Svensson framework.- 6. Pricing of financial assets.- Part II. Actuarial Valuation and Solvency.- 7. Actuarial and financial modeling.- 8. Valuation portfolio.- 9. Protected valuation portfolio.- 10. Solvency.- 11. Selected topics and examples.- Part III. Appendix.- A. Auxiliary considerations.- Bib-liography.- Index.

Fields of interestsQuantitative Finance; Actuarial Sciences; Statistics for Business/Economics/Mathematical Finance/Insurance

Target groupsProfessional/practitioner


Due October 2012

2012. XVI, 445 p. (Springer Finance) Hardcover7 approx. $99.00ISBN 978-3-642-31391-2

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43

R. C. Mittelhammer, Washington State University, Pullman, WA, USA

Mathematical Statistics for Economics and BusinessMathematical Statistics for Economics and Busi-ness, Second Edition, provides a comprehensive introduction to the principles of mathematical statistics which underpin statistical analyses in the fields of economics, business, and econometrics. The selection of topics in this textbook is designed to provide students with a conceptual foundation that will facilitate a substantial understanding of statistical applications in these subjects.

Features 7 Fully-revised second edition of bestselling statistics textbook with more than 3,400 copies sold 7 Features 25% new material consisting of updated end-of-chapter problems and solutions, more streamlined notations and explanations, as well as new examples 7 Provides a comprehen-sive introduction to the principles of mathematical statistics in the context of economics, business, and econometrics

Contents Elements of Probability Theory.- Random Vari-ables, Densities, and Cumulative Distribution Functions.- Expectations and Moments of Ran-dom Variables.- Parametric Families of Density Functions.- Basic Asymptotics.- Sampling, Sample Moments, Sampling Distributions, and Simula-tion.- Point Estimation Theory.- Point Estimation Methods.- Hypothesis Testing Theory.- Hypoth-esis Testing Methods and Confidence Regions.- Appendix.

Fields of interestsProbability Theory and Stochastic Processes; Sta-tistics, general; Statistics for Business/Economics/Mathematical Finance/Insurance



Due November 2012

2nd ed. 2013. X, 840 p. 50 illus. Hardcover7 $99.00ISBN 978-1-4614-5021-4

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A. Mucherino, Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique (CERFACS), Toulouse, France; C. Lavor, State University of Campinas, Brazil; L. Liberti, École Polytechnique, Palaiseau, France; N. Maculan, Federal University of Rio de Janeiro, Brazil (Eds)

Distance GeometryWith Applications to Molecular Conformation and Sensor Networks

Contents Preface.- 1. Universal Rigidity of Bar Frame-works in General Position (A. Alfakih).- 2. Mixed Volume and Distance Geometry Techniques for Counting Euclidean Embeddings of Rigid Graphs (I. Emiris, E. Tsigaridas, A. Varvitsiotis).- 3. (The discretizable molecular distance Geometry Problem Seems Easier on Proteins (L. Liberti, C. Lavor, A. Mucherino).- 4. Spheres Unions and Intersections and Some of Their Applications in Molecular Modeling (M. Petitjean).- 5. Is the Distance Geometry Problem in NP? (N. Beeker, S. Gaubert, C. Glusa, L. Liberti).- 6. Solving Spatial Constraints with Generalized Distance Geometry (L. Yang).- 7. A Topological Interpretation of the Walk Distances (P. Chebotarev, M. Deza).- 8. Distance Geometry Methods for Protein Structure Determination (Z. Voller, Z. Wu).- 9. Solving the discretizable molecular distance geometry problem by multiple realization trees (P. Nucci, L. Nogueira, C. Lavor).- 10.-ASAP - An Eigenvector Synchronization Algorithm for the Graph Realiza-tion Problem (M. Cucuringu).- 11. Global Opti-mization for Atomic Cluster Distance Geometry Problems (M. Locatelli, F. Schoen).- 12. Solving molecular distance geometry problems using a continuous optimization approach (R. Lima, J.M. Martinez).- 13. DC Programming Approaches for Distance Geometry Problems (H. Thi, T. Dinh). [...]

Fields of interestsGeometry; Operations Research, Management Science; Visualization



Due November 2012

2013. XXIV, 410 p. 160 illus., 10 in color. Hardcover7 $129.00ISBN 978-1-4614-5127-3

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R. Murty, Queen‘s University, Kingston, ON, Canada; K. Murty, University of Toronto, ON, Canada

The Mathematical Legacy of Srinivasa RamanujanSrinivasa Ramanujan was a mathematician bril-liant beyond comparison who inspired many great mathematicians. There is extensive literature available on the work of Ramanujan. But what is missing in the literature is an analysis that would place his mathematics in context and interpret it in terms of modern developments. The 12 lectures by Hardy, delivered in 1936, served this purpose at the time they were given.

Features 7 Gives a panoramic view of the main contribu-tions of Srinivasa Ramanujan 7 Presents a major theme of Ramanujan's work in non-technical language 7 Provides an excellent introduction to Ramanujan's life and work

Contents Preface.- Chapter 1. The Legacy of Srinivasa Ramanujan.- Chapter 2. The Ramanujan tau function.- Chapter 3. Ramanujan’s conjecture and l-adic representations.- Chapter 4. The Ramanujan conjecture from GL(2) to GL(n).- Chapter 5. The circle method.- Chapter 6. Ramanujan and tran-scendence.- Chapter 7. Arithmetic of the partition function.- Chapter 8. Some nonlinear identities for divisor functions.- Chapter 9. Mock theta functions and mock modular forms.- Chapter 10. Prime numbers and highly composite numbers.- Chapter 11. Probabilistic number theory.- Chapter 12. The Sato-Tate conjecture for the Ramanujan tau-function.- Bibliography.- Index.

Fields of interestsNumber Theory; History of Mathematical Sci-ences; Combinatorics



Due November 2012

2013. Approx. 200 p. Hardcover7 approx. $119.00ISBN 978-81-322-0769-6

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44

J. Pach, École Polytechnique Fédérale de Lausanne, Switzerland (Ed)

Thirty Essays on Geometric Graph TheoryContents Introduction.- 1) B. Ábrego - S. Fernández-Merchant - G. Salazar: The rectilinear crossing number of K_n: closing in (or are we?).- 2) E. Ackerman: The maximum number of tangen-cies among convex regions with a triangle-free intersection graph.- 3) G. Aloupis - B. Ballinger - S. Collette - S. Langerman - A. Pór - D.R.Wood: Blocking coloured point sets.- 4) M. Al-Jubeh - G. Barequet - M. Ishaque - D. Souvaine - Cs. D. Tóth - A. Winslow: Constrained tri-connected planar straight line graphs.- 5) S. Buzaglo - R. Pinchasi - G. Rote: Topological hypergraphs.- 6) J. Cano Vila - L. F. Barba - J. Urrutia - T. Sakai: On edge-disjoint empty triangles of point sets.- 7) J. Cibulka - J. Kynčl - V. Mészáros - R. Stolař - P. Valtr: Universal sets for straight-line embeddings of bicolored graphs.- 8) G. Di Battista - F. Frati: Drawing trees, outerplanar graphs, series-parallel graphs, and planar graphs in small area.- 9) W. Didimo - G. Liotta: The crossing angle resolution in graph drawing.- 10) A. Dumitrescu: Mover problems.- 11) S. Felsner: Rectangle and square representations of planar graphs.- 12) R. Fulek - N. Saeedi - D. Sariöz: Convex obstacle numbers of outerplanar graphs and bipartite permutation graphs.- 13) R. Fulek - M. Pelsmajer - M. Schaefer - D. Štefankovič: Hanani-Tutte, monotone draw-ings, and level-planarity.- 14) R. Fulek - A. Suk: On disjoint crossing families in geometric graphs.- 15) M. Hoffmann - A. Schulz - M. Sharir - A. Shef-fer - Cs. D. Tóth - E. Welzl: Counting plane graphs: flippability and its applications.- 16) F. Hurtado - Cs. D. Tóth: Geometric graph augmentation: a generic perspective.- 17) M. Kano - K. [...]

Fields of interestsDiscrete Mathematics; Geometry; Combinatorics



Due November 2012

2013. XVI, 504 p. 251 illus., 47 in color. Hardcover7 $149.00ISBN 978-1-4614-0109-4

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J. Pachl, The Fields Institute for Research in Mathematical Sciences, Toronto, ON, Canada

Uniform Spaces and Measures This book addresses the need for an accessible comprehensive exposition of the theory of uni-form measures; the need that became more critical when recently uniform measures reemerged in new results in abstract harmonic analysis. Until now, results about uniform measures have been scattered through many papers written by a num-ber of authors, some unpublished, written using a variety of definitions and notations.

Features 7 Presents a self-contained development of selected topics in the theory of uniform spaces using pseudometrics rather than the more common approach via entourages 7 Contains exercises and research problems and can be used as supplementary text in graduate and advanced undergraduate courses 7 Details the history of core concepts and links to key references to help the reader understand connections to related areas and explore other sources

Contents Preface.- 1. Prerequisites.- 2. Uniformities and Topologies.- 3. Induce Uniform Structures.- 4. Uniform Structures on Semigroups.- 5. Some No-table Classes of Uniform Spaces.- 6. Measures on Complete Metric Spaces.- 7. Uniform Measures.- 8. Uniform Measures as Measures.- 9. Instances of Uniform Measures.- 10. Direct Product and Convolution.- 11. Free Union Measures.- 12. Approximation of Probability Distributions.- 13. Measurable Functionals.- Excercise Hints.- Index of terms.- Index of symbols.- Cited authors.- Ref-erences.

Fields of interestsFunctional Analysis; Fourier Analysis; Functions of a Complex Variable



Due October 2012

2013. XIV, 204 p. (Fields Institute Monographs, Volume 30) Hardcover7 $109.00ISBN 978-1-4614-5057-3

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J. Prüss, Martin-Luther- Universität Halle-Wittenberg, Halle, Germany

Evolutionary Integral Equations and ApplicationsThis book deals with evolutionary systems whose equation of state can be formulated as a linear Volterra equation in a Banach space. The main feature of the kernels involved is that they consist of unbounded linear operators. The aim is a coher-ent presentation of the state of art of the theory including detailed proofs and its applications to problems from mathematical physics, such as vis-coelasticity, heat conduction, and electrodynamics with memory. The importance of evolutionary integral equations ‒ which form a larger class than do evolution equations ‒ stems from such applica-tions and therefore special emphasis is placed on these.

Features 7 Presents a general approach to linear evo-lutionary systems 7 Clearly written and of lasting value 7 A substantial part of the results presented originate from the author

Contents Preface.- Introduction.- Preliminaries.- I Equa-tions of Scalar Type.- 1 Resolvents.- 2 Analytic Resolvents.- 3 Parabolic Equations.- 4 Subordi-nation.- 5 Linear Viscoelasticity.- II Nonscalar Equations.- 6 Hyperbolic Equations of Nonscalar Type.- 7 Nonscalar Parabolic Equations.- 8 Para-bolic Problems in Lp-Spaces.- 9 Viscoelasticity and Electrodynamics with Memory.- III Equations on the Line.- 10 Integrability of Resolvents.- 11 Limiting Equations.- 12 Admissibility of Function Spaces.- 13 Further Applications and Comple-ments.- Bibliography.- Index.

Fields of interestsIntegral Equations; Ordinary Differential Equa-tions; Operator Theory



Due August 2012

Originally published as volume 87 in the Monographs in Mathematics series

2nd ed. 1993 1993. XXVI, 368 p. 8 illus. (Modern Birkhäuser Classics) Softcover7 $79.95ISBN 978-3-0348-0498-1

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45

T. Roubíček, Charles University, Praha, Czech Republic

Nonlinear Partial Differential Equations with ApplicationsThis book primarily concerns quasilinear and semilinear elliptic and parabolic partial differ-ential equations, inequalities, and systems. The exposition leads general theory based on abstract (pseudo) monotone or accretive operators as fast as possible towards the analysis of concrete dif-ferential equations, which have specific applica-tions in continuum (thermo-) mechanics of solids and fluids, electrically (semi-) conductive media, modelling of biological systems, or in mechanical engineering.

Features 7 Considerably extended second edition of a well-written monograph on modern theory of PDEs 7 Presents theory and applications in a concise, clear, elegant and rigorous way 7 Use-ful also to engineers, physicists, biologists and other scientists interested in nonlinear differential models

Contents Preface.- Preface to the 2nd edition.- 1 Prelimi-nary general material.- I Steady-state prob-lems.- 2 Pseudomonotone or weakly continuous mappings.- 3 Accretive mappings.- 4 Potential problems: smooth case.- 5 Nonsmooth problems; variational inequalities.- 6. Systems of equations: particular examples.- II Evolution problems.- 7 Special auxiliary tools.- 8 Evolution by pseudo-monotone or weakly continuous mappings.- 9 Evolution governed by accretive mappings.- 10 Evolution governed by certain set-valued map-pings.- 11 Doubly-nonlinear problems.- 12 Systems of equations: particular examples.- Refer-ences.- Index.

Fields of interestsDifference and Functional Equations; Partial Dif-ferential Equations; Computational Mathematics and Numerical Analysis


Due September 2012

Original edition published by Wiley, 1997

2nd ed. 2012. XX, 476 p. (International Series of Numerical Mathematics, Volume 153) Hardcover7 approx. $89.95ISBN 978-3-0348-0512-4

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C. Sabbah, CNRS, Palaiseau, France

Introduction to Stokes StructuresThis research monograph provides a geometric description of holonomic differential systems in one or more variables. Stokes matrices form the extended monodromy data for a linear differential equation of one complex variable near an irregular singular point. The present volume presents the approach in terms of Stokes filtrations. For linear differential equations on a Riemann surface, it also develops the related notion of a Stokes-perverse sheaf. This point of view is generalized to holonomic systems of linear differential equations in the complex domain, and a general Riemann-Hilbert correspondence is proved for vector bundles with meromorphic connections on a com-plex manifold. Applications to the distributions solutions to such systems are also discussed, and various operations on Stokes-filtered local systems are analyzed.

Feature 7 A first part on the classical theory of linear differential equations in the complex domain re-visited from a geometric view point. Original and new study of the Stokes phenomenon in higher dimension. Application to classical problems in distribution theory.

Fields of interestsAlgebraic Geometry; Ordinary Differential Equa-tions; Approximations and Expansions



Due October 2012

2013. X, 278 p. 14 illus., 1 in color. (Lecture Notes in Mathematics, Volume 2060) Softcover7 $59.95ISBN 978-3-642-31694-4

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I. R. Shafarevich, Russian Academy of Sciences, Moscow, Russia; A. O. Remizov, SISSA, Trieste, Italy

Linear Algebra and GeometryTranslated by: D. P. Kramer, Lancaster, PA, USA; L. Nekludova, Brookline, MA, USA

This book on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements of matrix theory and continues with vector spaces, linear transfor-mations, inner product spaces, and the theory of affine and projective spaces.

Features 7 Clearly written and easy to read 7 Contains also rather deep and not trivial subjects and theorems and can also be useful for profession-als 7 Good introduction to the subject 7 Nu-merous examples and applications of pure mathematical notions 7 I.R. Shafarevich is an outstanding mathematician and author of well-known books (e.g., "Basic Notions of Algebra")

Contents Preface.- Preliminaries.- 1. Linear Equations.- 2. Matrices and Determinants.- 3. Vector Spaces.- 4. Linear Transformations of a Vector Space to Itself.- 5. Jordan Normal Form.- 6. Quadratic and Bilinear Forms.- 7. Euclidean Spaces.- 8. Affine Spaces.- 9. Projective Spaces.- 10. The Exterior Product and Exterior Algebras.- 11. Quadrics.- 12. Hyperbolic Geometry.- 13. Groups, Rings, and Modules.- 14. Elements of Representation Theory.- Historical Note.- References.- Index

Fields of interestsLinear and Multilinear Algebras, Matrix Theory; Algebra; Geometry

Target groupsLower undergraduate


Due October 2012

2013. XXII, 554 p. 70 illus. Hardcover7 $69.95ISBN 978-3-642-30993-9

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46

G. Zumbach, Consulting in Financial Research, Saconnex d‘Arve, Switzerland

Discrete Time Series, Processes, and Applications in FinanceMost financial and investment decisions are based on considerations of possible future changes and require forecasts on the evolution of the financial world. Time series and processes are the natural tools for describing the dynamic behavior of financial data, leading to the required forecasts.

Features 7 The volume discusses and works on several practical implication and gives a synthesis of the field 7 Important applications of the discrete ARCH framework are presented 7 A balanced presentation of both empirical aspects as well as mathematics and theory

Contents Preface.- List of Figures.-List of Tables.- 1. Intro-duction.- 2.Notation, naming and general defini-tions.- 3.Stylized facts.- 4.Empirical mug shots.- 5.Process Overview.- 6.Logarithmic versus relative random walks.- 7.ARCH processes.- 8.Stochastic volatility processes.- 9.Regime switching process.- 10.Price and volatility using high-frequency data.- 11.Time reversal asymmetry.- 12.Charac-terizing heteroskedasticity.- 13.The innovation distributions.- 14.Leverage effect.- 15.Processes and market risk evaluation.- 16.Option pric-ing.- 17.Properties of large covariance matri-ces.- 18.Multivariate ARCH processes.- 19.The processes compatible with the stylized facts.- 20.Further thoughts.-Bibliography.- Index.

Fields of interestsQuantitative Finance; Probability Theory and Stochastic Processes; Statistics for Business/Eco-nomics/Mathematical Finance/Insurance

Target groupsProfessional/practitioner


Due October 2012

2013. XXIV, 330 p. 103 illus., 101 in color. (Springer Finance) Hardcover7 $99.00ISBN 978-3-642-31741-5

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New SeriesMathematics Textbooks for Science and EngineeringSeries editor: C. K. Chui

Textbooks in the series ‘Mathematics Textbooks for Science and Engineering’ will be aimed at the broad mathematics, science and engineering un-dergraduate and graduate levels, covering all areas of applied and applicable mathematics, interpreted in the broadest sense.

J. d. Villiers, Stellenbosch University, Matieland, South Africa

Mathematics of ApproximationThe approximation of a continuous function by either an algebraic polynomial, a trigonometric polynomial, or a spline, is an important issue in application areas like computer-aided geomet-ric design and signal analysis. This book is an introduction to the mathematical analysis of such approximation, and, with the prerequisites of only calculus and linear algebra, the material is targeted at senior undergraduate level, with a treatment that is both rigorous and self-contained.

Features 7 Prerequisites of only calculus and linear alge-bra 7 Self-contained and rigorous treatment of the mathematics of approximation 7 Includes new results,in particular those on local spline interpolation, and its connection to quadra-ture 7 A new method of proof of the Euler-Maclaurin formula is presented 7 The topic of quadrature formulas and their error analysis is given an extensive treatment 7 The Weierstrass theorem is rigorously proved for both algebraic and trigonometric polynomials 7 Both Fourier series and the Gram-Schmidt procedure are devel-oped from best approximation

Contents Polynomial Interpolation Formulas.- Error Analy-sis For Polynomial Interpolation.- Polynomial Uniform Convergence.- Best Approximation.- Ap-proximation Operators.- Best Uniform Polynomial Approximation.- Orthogonality.- Interpolatory Quadrature.- Approximation of Periodic Func-tions.- Spline Approximation.

Fields of interestsMathematics, general; Computational Mathemat-ics and Numerical Analysis; Approximations and Expansions



Due July 2012

2012. XXI, 406 p. 2 illus. (Mathematics Textbooks for Science and Engineering, Volume 1) Hardcover7 $79.95ISBN 978-94-91216-49-7

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47

K. Williams, Kim Williams Books, Torino, Italy (Ed)

Nexus 14,2This volulme features eight original papers dedicated to the theme “Persian Architecture and Mathematics,” guest edited by Reza Sarhangi. All papers were approved through a rigorous process of blind peer review and edited by an interdisci-plinary scientific editorial committee. Topics range from symmetry in ancient Persian architecture to the elaborate geometric patterns and complex three-dimensional structures of standing monu-ments of historical periods, from the expression of mathematical ideas to architectonic structures, and from decorative ornament to the representa-tion of modern group theory and quasi-crystalline patterns. The articles discuss unique monu-ments Persia, including domed structures and two-dimensional patterns, which have received significant scholarly attention in recent years. This book is a unique contribution to studies of Persian architecture in relation to mathematics.

Features 7 Only book exploring the unique relationship between Persian Architecture and Mathematics in the Western world in recent years 7 New scholarship addressing the theme “Persian Archi-tecture and Mathematics,” including eight articles representing a diversity of perspectives and pre-senting unpublished research 7 Comprehensive overview by guest editor Reza Sarhangi, founder and director of the international series of Bridges conferences, which annually brings together sci-entists, educators, artists and architects to address the mathematical connections in art, architecture, and culture 7 Each research paper includes a bibliography for further reading

Fields of interestsMathematics, general; Architecture, general



Due September 2012

2012. Approx. 250 p. (Nexus Network Journal, Volume 14,2) Softcover7 approx. $109.00ISBN 978-3-0348-0506-3

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Documents

Introduction to Quantitative Basque Center for Applied ... · net; and the building of the Three “M’s” Maple, Mathematica and Matlab. We intend to persuade that Mathematica