Self-organized criticality, the spontaneous development of systems to a critical state, is the first general theory of complex systems with a firm mathematical basis. This theory describes how many seemingly desperate aspects of the world, from stock market crashes to mass extinctions, avalanches to solar flares, all share a set of simple, easily described properties.
..".a'must read'...Bak writes with such ease and lucidity, and his ideas are so intriguing...essential reading for those interested in complex systems...it will reward a sufficiently skeptical reader." -NATURE
..".presents the theory (self-organized criticality) in a form easily absorbed by the non-mathematically inclined reader." -BOSTON BOOK REVIEW
"I picture Bak as a kind of scientific musketeer; flamboyant, touchy, full of swagger and ready to join every fray... His book is written with panache. The style is brisk, the content stimulating. I recommend it as a bracing experience." -NEW SCIENTIST

This concise treatment of integral equations has long stood as a standard introduction to the subject. Hochstadt's presentation comprises a reasonable compromise between the precise, but lengthy, classical approach and the faster, but less productive, functional analytic approach, while developing the most desirable features of each. The 7 chapters present an introduction to integral equations, elementary techniques, the theory of compact operators, applications to boundary value problems in more than dimension, a complete treatment of numerous transform techniques, a development of the classical Fredholm technique, and application of Schauder fixed point theorem to nonlinear equations.

Authoritative, well-written basic treatment of extremely useful mathematical tool. Topics include Volterra Equations, Fredholm Equations, Symmetric Kernels and Orthogonal Systems of Functions, Types of Singular or Nonlinear Integral Equations, more. Advanced undergraduate to graduate level. Exercises. Bibliography.

In diesem Lehrbuch wird die klassische Lebesguesche Mass- und Integrationstheorie stringent entwickelt und dargestellt - trotz grossem Tiefgang ist das Buch dadurch gut lesbar. Die einzelnen Abschnitte werden ausserdem durch zahlreiche Beispiele und Aufgaben illustriert und erganzt. Das Buch ist somit sowohl zum Selbststudium als auch als Nachschlagewerk sehr gut geeignet. Grundkenntnisse aus Mengenlehre und Analysis sowie gelegentlich auch Linearer Algebra und Topologie werden vorausgesetzt. Bei Bedarf koennen diese in den beiden Buchern Grundkonzepte der Mathematik und Analysis einer Veranderlichen der Autoren U. Storch und H. Wiebe nachgelesen werden.

Dieses Buch vermittelt ein solides Grundwissen uber Masstheorie, indem es die wichtigsten Teile derselben in detaillierten, gut nachvollziehbaren Schritten darlegt sowie mit zahlreichen Beispielen verbindet. Viele UEbungsaufgaben unterschiedlicher Schwierigkeitsgrade unterstutzen dabei das Verstandnis des Stoffes. Zur Selbstkontrolle werden im Anhang Loesungen zu samtlichen UEbungsaufgaben angegeben. Anwendungen der Masstheorie in der Stochastik werden in Kapiteln uber bedingte Erwartungen und Likelihood-Funktionen aufgezeigt. Die benoetigten Vorkenntnisse sind auf ein Minimum beschrankt, da zu Beginn in ubersichtlicher Form notwendige Grundlagen aus Mengenlehre und Theorie der reellen Zahlen wiederholt und vertieft werden.

Das Buch ist eine kompakte, leicht lesbare Einfuhrung in die Mass- und Integrationstheorie samt Wahrscheinlichkeitstheorie, in der auch auf den fur das Verstandnis wichtigen Bezug zur klassischen Analysis, etwa in Abschnitten uber Funktionen von beschrankter Variation oder dem Hauptsatz der Differential- und Integralrechnung eingegangen wird. Trotz seines verhaltnismassig geringen Umfangs behandelt es alle wesentlichen Themen dieser Fachgebiete, wie Mengensysteme, Mengenfunktionen Massfortsetzung, Unabhangigkeit, Lebesgue-Stieltjes-Masse, Verteilungsfunktionen, messbare Funktionen, Zufallsvariable, Integral, Erwartungswert, Konvergenzsatze, Transformationssatze, Produktraume, Satz von Fubini, Zerlegungssatze, Funktionen von beschrankter Variation, Hauptsatz der Differential- und Integralrechnung, Lp-Raume, Bedingte Erwartungen, Gesetze der grossen Zahlen, Ergodensatze, Martingale, Verteilungskonvergenz, charakteristische Funktionen und die Grenzverteilungssatze von Lindeberg und Feller."

This volume explores A.P. Morse's (1911-1984) development of a formal language for writing mathematics, his application of that language in set theory and mathematical analysis, and his unique perspective on mathematics. The editor brings together a variety of Morse's works in this compilation, including Morse's book A Theory of Sets, Second Edition (1986), in addition to material from another of Morse's publications, Web Derivatives, and notes for a course on analysis from the early 1950's. Because Morse provided very little in the way of explanation in his written works, the editor's commentary serves to outline Morse's goals, give informal explanations of Morse's formal language, and compare Morse's often unique approaches to more traditional approaches. Minor corrections to Morse's previously published works have also been incorporated into the text, including some updated axioms, theorems, and definitions. The editor's introduction thoroughly details the corrections and changes made and provides readers with valuable insight on Morse's methods. A.P. Morse's Set Theory and Analysis will appeal to graduate students and researchers interested in set theory and analysis who also have an interest in logic. Readers with a particular interest in Morse's unique perspective and in the history of mathematics will also find this book to be of interest.

Now in its second edition, this textbook serves as an introduction to probability and statistics for non-mathematics majors who do not need the exhaustive detail and mathematical depth provided in more comprehensive treatments of the subject. The presentation covers the mathematical laws of random phenomena, including discrete and continuous random variables, expectation and variance, and common probability distributions such as the binomial, Poisson, and normal distributions. More classical examples such as Montmort's problem, the ballot problem, and Bertrand's paradox are now included, along with applications such as the Maxwell-Boltzmann and Bose-Einstein distributions in physics. Key features in new edition: * 35 new exercises * Expanded section on the algebra of sets * Expanded chapters on probabilities to include more classical examples * New section on regression * Online instructors' manual containing solutions to all exercises< Advanced undergraduate and graduate students in computer science, engineering, and other natural and social sciences with only a basic background in calculus will benefit from this introductory text balancing theory with applications. Review of the first edition: This textbook is a classical and well-written introduction to probability theory and statistics. ... the book is written 'for an audience such as computer science students, whose mathematical background is not very strong and who do not need the detail and mathematical depth of similar books written for mathematics or statistics majors.' ... Each new concept is clearly explained and is followed by many detailed examples. ... numerous examples of calculations are given and proofs are well-detailed." (Sophie Lemaire, Mathematical Reviews, Issue 2008 m)

This volume comprises selected papers presented at the Volterra Centennial Symposium and is dedicated to Volterra and the contribution of his work to the study of systems - an important concept in modern engineering. Vito Volterra began his study of integral equations at the end of the nineteenth century and this was a significant development in the theory of integral equations and nonlinear functional analysis. Volterra series are of interest and use in pure and applied mathematics and engineering.

Based on proceedings of the International Conference on Integral Methods in Science and Engineering, this collection of papers addresses the solution of mathematical problems by integral methods in conjunction with approximation schemes from various physical domains. Topics and applications include: wavelet expansions, reaction-diffusion systems, variational methods , fracture theory, boundary value problems at resonance, micromechanics, fluid mechanics, combustion problems, nonlinear problems, elasticity theory, and plates and shells.

Equations of Mathematical Diffraction Theory focuses on the comparative analysis and development of efficient analytical methods for solving equations of mathematical diffraction theory. Following an overview of some general properties of integral and differential operators in the context of the linear theory of diffraction processes, the authors provide estimates of the operator norms for various ranges of the wave number variation, and then examine the spectral properties of these operators. They also present a new analytical method for constructing asymptotic solutions of boundary integral equations in mathematical diffraction theory for the high-frequency case.
Clearly demonstrating the close connection between heuristic and rigorous methods in mathematical diffraction theory, this valuable book provides you with the differential and integral equations that can easily be used in practical applications.