Series: Springer Undergraduate Mathematics Series
2010, XXIV, 400 p. 71 illus., Softcover
ISBN: 978-0-85729-059-5
Worlds Out of Nothing is the first book to provide a course on the history of geometry in the 19th century. Based on the latest historical research, the book is aimed primarily at undergraduate and graduate students in mathematics but will also appeal to the reader with a general interest in the history of mathematics. Emphasis is placed on understanding the historical significance of the new mathematics: Why was it done? How - if at all - was it appreciated? What new questions did it generate?
Topics covered in the first part of the book are projective geometry, especially the concept of duality, and non-Euclidean geometry. The book then moves on to the study of the singular points of algebraic curves (Pluckerfs equations) and their role in resolving a paradox in the theory of duality; to Riemannfs work on differential geometry; and to Beltramifs role in successfully establishing non-Euclidean geometry as a rigorous mathematical subject. The final part of the book considers how projective geometry, as exemplified by Kleinfs Erlangen Program, rose to prominence, and looks at Poincarefs ideas about non-Euclidean geometry and their physical and philosophical significance. It then concludes with discussions on geometry and formalism, examining the Italian contribution and Hilbertfs Foundations of Geometry; geometry and physics, with a look at some of Einsteinfs ideas; and geometry and truth.
Three chapters are devoted to writing and assessing work in the history of mathematics, with examples of sample questions in the subject, advice on how to write essays, and comments on what instructors should be looking for.
Mathematics in the French Revolution.- Poncelet (and Pole and Polar).- Theorems in Projective Geometry.- Ponceletfs Traite.- Duality and the Duality Controversy.- Poncelet and Chasles.- Lambert and Legendre.- Gauss.- Janos Bolyai.- Lobachevskii.- To 1855.- Writing.- Mobius.- The Duality Paradox.- The Plucker Formulae.- Higher Plane Curves.- Complex Curves.- Riemann.- Differential Geometry of Surfaces.- Non-Euclidean Geometry Accepted.- Writing.- Fundamental Geometry.- Hilbert.- Italian Foundations.- The Disc Model.- The Geometry of Space.- Summary: Geometry to 1900.- The Formal Side.- The Physical Side.- Is Geometry True?- Writing.- Appendix: Von Staudt and his Influence.- Bibliography.- Index.
Series: Selected Works in Probability and Statistics
1st Edition., 2010, XXXVII, 463 p., Hardcover
ISBN: 978-1-4419-5822-8
Due: September 29, 2010
This volume is dedicated to the memory of the late Professor C.C. (Chris) Heyde (1939-2008), distinguished statistician, mathematician and scientist. Chris worked at a time when many of the foundational building blocks of probability and statistics were being put in place by a phalanx of eminent scientists around the world. He contributed significantly to this effort and took his place deservedly among the top-most rank of researchers. Throughout his career, Chris maintained also a keen interest in applications of probability and statistics, and in the history of the subject. The magnitude of his impact on his chosen area of research, both in Australia and internationally, was well recognised by the abundance of honours he received within and without the profession. The book is comprised of a number of Chrisfs papers covering each one of four major topics to which he contributed. These papers are reproduced herein. The topics, and the papers in them, were selected by four of Chrisfs friends and collaborators: Ishwar Basawa, Peter Hall, Ross Maller (overall Editor of the volume) and Eugene Seneta. Each topic is provided with an overview by the selecting editor. The topics cover a range of areas to which Chris made especially important contributions: Inference in Stochastic Processes, Rates of Convergence in the Central Limit Theorem, the Law of the Iterated Logarithm, and Branching Processes and Population Genetics. The Editor and the other contributors to the volume include well known researchers in probability and statistics. The collection begins with an gauthorfs pickh of a number of his papers which Chris considered most interesting and significant, chosen by him shortly before his death. A biography of Chris by his close friend and collaborator, Joe Gani, is also included. An introduction by the Editor and a comprehensive bibliography of Chrisfs publications complete the volume. The book will be of especial interest to researchers in probability and statistics, and in the history of these subjects.
Series: Springer Undergraduate Mathematics Series
2011, XIII, 334 p. 66 illus., Softcover
ISBN: 978-0-85729-081-6
Due: October 2010
As with the first edition, Mathematics for Finance: An Introduction to Financial Engineering combines financial motivation with mathematical style. Assuming only basic knowledge of probability and calculus, it presents three major areas of mathematical finance, namely Option pricing based on the no-arbitrage principle in discrete and continuous time setting, Markowitz portfolio optimisation and Capital Asset Pricing Model, and basic stochastic interest rate models in discrete setting.
In this second edition, the material has been thoroughly revised and rearranged. New features include:
* A case study to begin each chapter ? a real-life situation motivating the development of theoretical tools;
* A detailed discussion of the case study at the end of each chapter;
* A new chapter on time-continuous models with intuitive outlines of the mathematical arguments and constructions;
* Complete proofs of the two fundamental theorems of mathematical finance in discrete setting.
A Simple Market Model.- Risk-Free Assets.- Portfolio Management.- Forward and Futures Contracts.- Options: General Properties.- Binomial Model.- General Discrete Time Models.- Continuous Time Model.- Interest Rates.
Series: Frontiers in Mathematics
1st Edition., 2011, Approx. 290 p., Softcover
ISBN: 978-3-0348-0014-3
Due: November 30, 2010
The goal of the book is to present, in a complete and comprehensive way, areas of current research interlacing around the Poncelet porism: dynamics of integrable billiards, algebraic geometry of hyperelliptic Jacobians, and classical projective geometry of pencils of quadrics. The most important results and ideas, classical as well as modern, connected to the Poncelet theorem are presented, together with a historical overview analyzing the classical ideas and their natural generalizations. Special attention is paid to the realization of the Griffiths and Harris programme about Poncelet-type problems and addition theorems. This programme, formulated three decades ago, is aimed to understanding the higher-dimensional analogues of Poncelet problems and the realization of the synthetic approach of higher genus addition theorems.
Introduction to Poncelet Porisms.- Billiards ? First Examples.- Hyper-Elliptic Curves and Their Jacobians.- Projective geometry.- Poncelet Theorem and Cayleyfs Condition.- Poncelet?Darboux Curves and Siebeck?Marden Theorem.- Ellipsoidal Billiards and their Periodical Trajectories.- Billiard Law and Hyper-Elliptic Curves.- Poncelet Theorem and Continued Fractions.- Quantum Yang-Baxter equation and (2-2)-correspondences.- Bibliography.- Index.
2011, X, 480 p., Softcover
ISBN: 978-3-0348-0017-4
Due: November 30, 2010
This book started with Lattice Theory, First Concepts, in 1971. Then came General Lattice Theory, First Edition, in 1978, and the Second Edition twenty years later. Since the publication of the first edition in 1978, General Lattice Theory has become the authoritative introduction to lattice theory for graduate students and the standard reference for researchers. The First Edition set out to introduce and survey lattice theory. Some 12,000 papers have been published in the field since then; so Lattice Theory: Foundation focuses on introducing the field, laying the foundation for special topics and applications. Lattice Theory: Foundation, based on the previous three books, covers the fundamental concepts and results. The main topics are distributivity, congruences, constructions, modularity and semimodularity, varieties, and free products. The chapter on constructions is new, all the other chapters are revised and expanded versions from the earlier volumes. Over 40 gdiamond sectionsff, many written by leading specialists in these fields, provide a brief glimpse into special topics beyond the basics.
Preface.- Introduction.- Glossary of Notation.- I First Concepts.- 1 Two Definitions of Lattices.- 2 How to Describe Lattices.- 3 Some Basic Concepts.- 4 Terms, Identities, and Inequalities.- 5 Free Lattices.- 6 Special Elements.- II Distributive Lattices.- 1 Characterization and Representation Theorems.- 2 Terms and Freeness.- 3 Congruence Relations.- 4 Boolean Algebras.- 5 Topological Representation.- 6 Pseudocomplementation.- III Congruences.- 1 Congruence Spreading.- 2 Distributive, Standard, and Neutral Elements.- 3 Distributive, Standard, and Neutral Ideals.- 4 Structure Theorems.- IV Lattice Constructions.- 1 Adding an Element.- 2 Gluing.- 3 Chopped Lattices.- 4 Constructing Lattices with Given Congruence Lattices.- 5 Boolean Triples.- V Modular and Semimodular Lattices.- 1 Modular Lattices.- 2 Semimodular Lattices.- 3 Geometric Lattices.- 4 Partition Lattices.- 5 Complemented Modular Lattices.- VI Varieties of Lattices.- 1 Characterizations of Varieties 397.- 2 The Lattice of Varieties of Lattices.- 3 Finding Equational Bases.- 4 The Amalgamation Property.- VII Free Products.- 1 Free Products of Lattices.- 2 The Structure of Free Lattices.- 3 Reduced Free Products.- 4 Hopfian Lattices.- Afterword.- Bibliography.
Series: Springer Texts in Statistics
2010, XVI, 436 p., Hardcover
ISBN: 978-1-4419-7164-7
Comprehensive coverage of applied probability
Emphasis on concrete calculations and computational methods
Clarity of writing and mathematical explanation
Applied Probability presents a unique blend of theory and applications, with special emphasis on mathematical modeling, computational techniques, and examples from the biological sciences. It can serve as a textbook for graduate students in applied mathematics, biostatistics, computational biology, computer science, physics, and statistics. Readers should have a working knowledge of multivariate calculus, linear algebra, ordinary differential equations, and elementary probability theory. Chapter 1 reviews elementary probability and provides a brief survey of relevant results from measure theory. Chapter 2 is an extended essay on calculating expectations. Chapter 3 deals with probabilistic applications of convexity, inequalities, and optimization theory. Chapters 4 and 5 touch on combinatorics and combinatorial optimization. Chapters 6 through 11 present core material on stochastic processes. If supplemented with appropriate sections from Chapters 1 and 2, there is sufficient material for a traditional semester-long course in stochastic processes covering the basics of Poisson processes, Markov chains, branching processes, martingales, and diffusion processes. The second edition adds two new chapters on asymptotic and numerical methods and an appendix that separates some of the more delicate mathematical theory from the steady flow of examples in the main text. Besides the two new chapters, the second edition includes a more extensive list of exercises, many additions to the exposition of combinatorics, new material on rates of convergence to equilibrium in reversible Markov chains, a discussion of basic reproduction numbers in population modeling, and better coverage of Brownian motion. Because many chapters are nearly self-contained, mathematical scientists from a variety of backgrounds will find Applied Probability useful as a reference. Kenneth Lange is the Rosenfeld Professor of Computational Genetics in the Departments of Biomathematics and Human Genetics at the UCLA School of Medicine and the Chair of the Department of Human Genetics. His research interests include human genetics, population modeling, biomedical imaging, computational statistics, high-dimensional optimization, and applied stochastic processes. Springer previously published his books Mathematical and Statistical Methods for Genetic Analysis, 2nd ed., Numerical Analysis for Statisticians, 2nd ed., and Optimization. He has written over 200 research papers and produced with his UCLA colleague Eric Sobel the computer program Mendel, widely used in statistical genetics.
Related subjects â Mathematical and Computational Biology - Numerical and Computational Mathematics - Probability Theory and Stochastic Processes - Statistical Theory and Methods - Theoretical Computer Science