RIT Libraries Recent Acquisitions - Math

The Artist and the Mathematician

Thu, 02 Oct 2008 12:00:00 EDT

Description: Nicolas Bourbaki, whose mathematical publications began to appear in the late 1930s and continued to be published through most of the twentieth century, was a direct product as well as a major force behind an important revolution that took place in the early decades of the twentieth century that completely changed Western culture. Pure mathematics, the area of Bourbaki's work, seems on the surface to be an abstract field of human study with no direct connection with the real world. In reality, however, it is closely intertwined with the general culture that surrounds it. Major developments in mathematics have often followed important trends in popular culture; developments in mathematics have acted as harbingers of change in the surrounding human culture. The seeds of change, the beginnings of the revolution that swept the Western world in the early decades of the twentieth century  both in mathematics and in other areas  were sown late in the previous century. This is the story both of Bourbaki and the world that created him in that time. It is the story of an elaborate intellectual joke  because Bourbaki, one of the foremost mathematicians of his day  never existed.

Added: Thursday, Oct 2 2008

A Geometric Approach to Differential Forms / David Bachman

Mon, 29 Sep 2008 12:00:00 EDT

Description: The modern subject of differential forms subsumes classical vector calculus. This text presents differential forms from a geometric perspective accessible at the sophomore undergraduate level. The book begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The author approaches the subject with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually. Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. This facilitates the development of differential forms without assuming a background in linear algebra. Throughout the text, emphasis is placed on applications in 3 dimensions, but all definitions are given so as to be easily generalized to higher dimensions. A centerpiece of the text is the generalized Stokes' theorem. Although this theorem implies all of the classical integral theorems of vector calculus, it is far easier for students to both comprehend and remember. The text is designed to support three distinct course tracks: the first as the primary textbook for third semester (multivariable) calculus, suitable for anyone with a year of calculus; the second is aimed at students enrolled in sophomore-level vector calculus; while the third targets advanced undergraduates and beginning graduate students in physics or mathematics, covering more advanced topics such as Maxwell's equations, foliation theory, and cohomology. Containing excellent motivation, numerous illustrations and solutions to selected problems in an appendix, the material has been tested in the classroom along all three potential course tracks.

Added: Monday, Sep 29 2008

Solved Problems in Geostatistics / Oy Leuangthong, K. Daniel Khan, Clayton V. Deutsch

Thu, 25 Sep 2008 12:00:00 EDT

Description: Solved Problems in Geostatistics brings together exercises and projects that demonstrate key principles and build strong bridges between theory and practice. Each chapter focuses on a comprehensive topic with examples and problems for a technologically evolving audience. Problems in each chapter are classified as analytical, numerical, or practical; exercises are identified as foundational, advanced, or esoteric. Objectives highlight important learning concepts. This hands-on, practical guide offers a supplement to any college-level geostatistics or spatial statistics course, a manual for a geostatistics lab course, or a reference for practicing statisticians.

Added: Thursday, Sep 25 2008

A First Course in Order Statistics / Barry C. Arnold, N. Balakrishnan, H.N. Nagaraja

Thu, 25 Sep 2008 12:00:00 EDT

Description: Written in a simple style that requires no advanced mathematical or statistical background, A First Course in Order Statistics introduces the general theory of order statistics and their applications. The book covers topics such as distribution theory for order statistics from continuous and discrete populations, moment relations, bounds and approximations, order statistics in statistical inference and characterization results, and basic asymptotic theory. There is also a short introduction to record values and related statistics. This classic text will aid readers in understanding much of the current literature on order statistics, a burgeoning field of study that is a requisite for any practicing statistician and an essential part of the training for students in statistics. The authors have updated the text with suggestions for further reading that readers may use for self-study. Audience This book is intended for advanced undergraduate and graduate students in statistics and mathematics, practicing statisticians, engineers, climatologists, economists, and biologists. Contents Preface to the Classics Edition; Further Reading; Preface; Acknowledgments; Notations and Abbreviations; Errata; Chapter 1: Introduction and Preview; Chapter 2: Basic Distribution Theory; Chapter 3: Discrete Order Statistics; Chapter 4: Order Statistics from Some Specific Distributions; Chapter 5: Moment Relations, Bounds, and Approximations; Chapter 6: Characterizations Using Order Statistics; Chapter 7: Order Statistics in Statistical Inference; Chapter 8: Asymptotic Theory; Chapter 9: Record Values; Bibliography; Author Index; Subject Index.

Added: Thursday, Sep 25 2008

Chances Are-- : Adventures in Probability / Michael Kaplan and Ellen Kaplan

Thu, 25 Sep 2008 12:00:00 EDT

Description: A compelling journey through history, mathematics, and philosophy, charting humanity's struggle against randomness Our lives are played out in the arena of chance. However little we recognize it in our day-to-day existence, we are always riding the odds, seeking out certainty but settlingreluctantlyfor likelihood, building our beliefs on the shadowy props of probability. Chances Are is the story of man's millennia-long search for the tools to manage the recurrent but unpredictableto help us prevent, or at least mitigate, the seemingly random blows of disaster, disease, and injustice. In these pages, we meet the brilliant individuals who developed the first abstract formulations of probability, as well as the intrepid visionaries who recognized their practical applicationsfrom gamblers to military strategists to meteorologists to medical researchers, from blackjack to our own mortality.

Added: Thursday, Sep 25 2008

The Numbers Behind NUMB3RS : Solving Crime with Mathematics / Keith Devlin, Gary Lorden

Thu, 25 Sep 2008 12:00:00 EDT

Description: The companion to the hit CBS crime series Numb3rs presents the fascinating way mathematics is used to fight real-life crime Using the popular CBS prime-time TV crime series Numb3rs as a springboard, Keith Devlin (known to millions of NPR listeners as "the Math Guy" on NPR's Weekend Edition with Scott Simon) and Gary Lorden (the principal math advisor to Numb3rs) explain real-life mathematical techniques used by the FBI and other law enforcement agencies to catch and convict criminals. From forensics to counterterrorism, the Riemann hypothesis to image enhancement, solving murders to beating casinos, Devlin and Lorden present compelling cases that illustrate how advanced mathematics can be used in state-of-the-art criminal investigations.

Added: Thursday, Sep 25 2008

Poincare's Prize : the Hundred-year Quest to Solve One of Math's Greatest Puzzles / George G. Szpiro

Wed, 17 Sep 2008 12:00:00 EDT

Description: With a reclusive and eccentric hero, dramatic turns, and a million-dollar payoff, Poincaré's Prize is the stuff of great fiction. Amazingly, the story unveiled in it is true. In the world of math, the Poincaré Conjecture was a holy grail. Decade after decade the theorem that informs how we understand the shape of the universe defied every effort to prove it. Now, after more than a century, an eccentric Russian recluse has found the solution to one of the seven greatest math problems of our time, earning the right to claim the first one-million-dollar Millennium math prize. George Szpiro begins his masterfully told story in 1904 when Frenchman Henri Poincaré formulated a conjecture about a seemingly simple problem. Imagine an ant crawling around on a large surface. How would it know whether the surface is a flat plane, a round sphere, or a bagel- shaped object? The ant would need to lift off into space to observe the object. How could you prove the shape was spherical without actually seeing it? Simply, this is what Poincaré sought to solve. In fact, Poincaré thought he had solved it back at the turn of the twentieth century, but soon realized his mistake. After four more years' work, he gave up. Across the generations from China to Texas, great minds stalked the solution in the wilds of higher dimensions. Among them was Grigory Perelman, a mysterious Russian who seems to have stepped out of a Dostoyevsky novel. Living in near poverty with his mother, he has refused all prizes and academic appointments, and rarely talks to anyone, including fellow mathematicians. It seemed he had lost the race in 2002, when the conjecture was widely but, again, falsely reported as solved. A year later, Perelman dropped three papers onto the Internet that not only proved the Poincaré Conjecture but enlightened the universe of higher dimensions, solving an array of even more mind-bending math with implications that will take an age to unravel. After years of review, his proof has just won him a Fields Medal, the "Nobel of math," awarded only once every four years. With no interest in fame, he refused to attend the ceremony, did not accept the medal, and stayed home to watch television. Perelman is a St. Petersburg hero, devoted to an ascetic life of the mind. The story of the enigma in the shape of space that he cracked is part history, part math, and a fascinating tale of the most abstract kind of creativity.

Added: Wednesday, Sep 17 2008

Statistical DNA Forensics : Theory, Methods and Computation / Wing Kam Fung and Yue-Qing Hu

Wed, 17 Sep 2008 12:00:00 EDT

Description: Statistical methodology plays a key role in ensuring that DNA evidence is collected, interpreted, analyzed and presented correctly. With the recent advances in computer technology, this methodology is more complex than ever before. There are a growing number of books in the area but none are devoted to the computational analysis of evidence. This book presents the methodology of statistical DNA forensics with an emphasis on the use of computational techniques to analyze and interpret forensic evidence.

Added: Wednesday, Sep 17 2008

Inference and Prediction in Large Dimensions / Denis Bosq, Delphine Blanke

Wed, 17 Sep 2008 12:00:00 EDT

Description: This book offers a predominantly theoretical coverage of statistical prediction, with some potential applications discussed, when data and/ or parameters belong to a large or infinite dimensional space. It develops the theory of statistical prediction, non-parametric estimation by adaptive projection — with applications to tests of fit and prediction, and theory of linear processes in function spaces with applications to prediction of continuous time processes. This work is in the Wiley-Dunod Series co-published between Dunod (www.dunod.com) and John Wiley and Sons, Ltd.

Added: Wednesday, Sep 17 2008

Geometric Integration Theory / By Steven G. Krantz, Harold Parks

Wed, 17 Sep 2008 12:00:00 EDT

Description: This textbook introduces geometric measure theory through the notion of currents. Currents, continuous linear functionals on spaces of differential forms, are a natural language in which to formulate types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis. The text provides considerable background for the student and discusses techniques that are applicable to complex geometry, partial differential equations, harmonic analysis, differential geometry, and many other parts of mathematics. Topics include the deformation theorem, the area and coareas formulas, the compactness theorem, the slicing theorem and applications to minimal surfaces. Motivating key ideas with examples and figures, Geometric Integration Theory is a comprehensive introduction ideal for both use in the classroom and for self-study. The exposition demands minimal background, is self-contained and accessible, and thus is ideal for both graduate students and researchers.

Added: Wednesday, Sep 17 2008

Reservoir Simulation : Mathematical Techniques in Oil Recovery / Zhangxin Chen

Thu, 11 Sep 2008 12:00:00 EDT

Description: This book covers and expands upon material presented by the author at a CBMS-NSF Regional Conference during a ten-lecture series on multiphase flows in porous media and their simulation. It begins with an overview of classical reservoir engineering and basic reservoir simulation methods and then progresses through a discussion of types of flows single-phase, two-phase, black oil (three-phase), single phase with multicomponents, compositional, and thermal. The author provides a thorough glossary of petroleum engineering terms and their units, along with basic flow and transport equations and their unusual features, and corresponding rock and fluid properties. The practical aspects of reservoir simulation, such as data gathering and analysis, selection of a simulation model, history matching, and reservoir performance prediction, are summarized. Audience This book can be used as a text for advanced undergraduate and first-year graduate students in geology, petroleum engineering, and applied mathematics; as a reference book for geologists, petroleum engineers, and applied mathematicians; or as a handbook for practitioners in the oil industry. Prerequisites are calculus, basic physics, and some knowledge of partial differential equations and matrix algebra. Contents List of Figures; List of Tables; List of Notation; Preface; Introduction; Chapter 1: A Glossary of Petroleum Terms; Chapter 2: Single-Phase Flow and Numerical Solution; Chapter 3: Well Modeling; Chapter 4: Two-Phase Flow and Numerical Solution; Chapter 5: The Black Oil Model and Numerical Solution; Chapter 6: Transport of Multicomponents in a Fluid and Numerical Solution; Chapter 7: Compositional Flow and Numerical Solution; Chapter 8: Nonisothermal Flow and Numerical Solution; Chapter 9: Practical Topics in Reservoir Simulation; Bibliography; Index.

Added: Thursday, Sep 11 2008

Frames and Bases : an Introductory Course / Ole Christensen

Thu, 11 Sep 2008 12:00:00 EDT

Description: During the last several years, frames have become increasingly popular; they have appeared in a large number of applications, and several concrete constructions of frames of various types have been presented. Most of these constructions were based on quite direct methods rather than the classical sufficient conditions for obtaining a frame. Consequently, there is a need for an updated book on frames, which moves the focus from the classical approach to a more constructive one. Based on a streamlined presentation of the author's previous work, An Introduction to Frames and Riesz Bases, this new textbook fills a gap in the literature, developing frame theory as part of a dialogue between mathematicians and engineers. Newly added sections on applications will help mathematically oriented readers to see where frames are used in practice and engineers to discover the mathematical background for applications in their field. Key features and topics: * Results presented in an accessible way for graduate students, pure and applied mathematicians as well as engineers. * An introductory chapter provides basic results in finite-dimensional vector spaces, enabling readers with a basic knowledge of linear algebra to understand the idea behind frames without the technical complications in infinite-dimensional spaces. * Extensive exercises for use in theoretical graduate courses on bases and frames, or applications-oriented courses focusing on either Gabor analysis or wavelets. * Detailed description of frames with full proofs, an examination of the relationship between frames and Riesz bases, and a discussion of various ways to construct frames. * Content split naturally into two parts: The first part describes the theory on an abstract level, whereas the second part deals with explicit constructions of frames with applications and connections to time-frequency analysis, Gabor analysis, and wavelets. Frames and Bases: An Introductory Course will be an excellent textbook for graduate students as well as a good reference for researchers working in pure and applied mathematics, mathematical physics, and engineering. Practitioners working in digital signal processing who wish to understand the theory behind many modern signal processing tools may also find the book a useful self-study resource.

Added: Thursday, Sep 11 2008

An Invitation to Variational Methods in Differential Equations / David G. Costa

Thu, 04 Sep 2008 12:00:00 EDT

Description: This book is a short introductory text to variational techniques with applications to differential equations. It presents a sampling of topics in critical point theory with applications to existence and multiplicity of solutions in nonlinear problems involving ordinary differential equations (ODEs) and partial differential equations (PDEs). Five simple problems in ODEs which illustrate existence of solutions from a variational point of view are introduced in the first chapter. These problems set the stage for the topics covered, including minimization, deformation results, the mountain-pass theorem, the saddle-point theorem, critical points under constraints, a duality principle, critical points in the presence of symmetry, and problems with lack of compactness. Each topic is presented in a straightforward manner, and followed by one or two illustrative applications. The concise, straightforward, user-friendly approach of this textbook will appeal to graduate students and researchers interested in differential equations, analysis, and functional analysis.