Number theory, the branch of mathematics that studies the properties of the integers, is a repository of interesting and quite varied problems, sometimes impossibly difficult ones. In this book, the authors have gathered together a collection of problems from various topics in number theory that they find beautiful, intriguing, and from a certain point of view instructive.

The unifying approach of functional analysis is to view functions as points in abstract vector space and the differential and integral operators as linear transformations on these spaces. The author's goal is to present the basics of functional analysis in a way that makes them comprehensible to a student who has completed courses in linear algebra and real analysis, and to develop the topics in their historical contexts.

The stories of five mathematical journeys into new realms, pieced together from the writings of the explorers themselves. Some were guided by mere curiosity and the thrill of adventure, others by more practical motives. In each case the outcome was a vast expansion of the known mathematical world and the realisation that still greater vistas remain to be explored. The authors tell these stories by guiding readers through the very words of the mathematicians at the heart of these events, providing an insightinto the art of approaching mathematical problems. The five chapters are completely independent, with varying levels of mathematical sophistication, and will attract students, instructors, and the intellectually curious reader. By working through some of the original sources and supplementary exercises, which discuss and solve -- or attempt to solve -- a great problem, this book helps readers discover the roots of modern problems, ideas, and concepts, even whole subjects. Students will also see the obstacles that earlier thinkers had to clear in order to make their respective contributions to five central themes in the evolution of mathematics.

This book is intended to introduce coding theory and information theory to undergraduate students of mathematics and computer science. It begins with a review of probablity theory as applied to finite sample spaces and a general introduction to the nature and types of codes. The two subsequent chapters discuss information theory: efficiency of codes, the entropy of information sources, and Shannon's Noiseless Coding Theorem. The remaining three chapters deal with coding theory: communication channels, decoding in the presence of errors, the general theory of linear codes, and such specific codes as Hamming codes, the simplex codes, and many others.

Publisher : Springer; 1997th edition (October 17, 1997)
Language : English
Hardcover : 279 pages
ISBN-10 : 0387982272
ISBN-13 : 978-0387982274
Item Weight : 2.8 pounds
Dimensions : 6.14 x 0.69 x 9.21 inches
Intended as a first course in probability at post-calculus level, this book is of special interest to students majoring in computer science as well as in mathematics. Since calculus is used only occasionally in the text, students who have forgotten their calculus can nevertheless easily understand the book, and its slow, gentle style and clear exposition will also appeal. Basic concepts such as counting, independence, conditional probability, random variables, approximation of probabilities, generating functions, random walks and Markov chains are all clearly explained and backed by many worked exercises. The 1,196 numerical answers to the 405 exercises, many with multiple parts, are included at the end of the book, and throughout, there are various historical comments on the study of probability. These include biographical information on such famous contributors as Fermat, Pascal, the Bernoullis, DeMoivre, Bayes, Laplace, Poisson, and Markov. Of interest to a wide range of readers and useful in many undergraduate programs.

Why Math? is designed for a "general education" mathematics course. It helps develop the basic mathematical literacy now generally demanded of liberal arts students. Requiring only a little background knowledge of algebra and geometry - no more than the minimum entrance requirements at most colleges - the book emphasizes quantitative reasoning and critical thinking for real life problems. In a concrete and relevant way, using extensive motivation from everyday problems, Why Math? shows what one can do with elementary mathematics and how to do it.

Many advances have taken place in the field of combinatorial algorithms since Methods of Mathematical Economics first appeared two decades ago. Despite these advances and the development of new computing methods, several basic theories and methods remain important today for understanding mathematical programming and fixed-point theorems. In this easy-to-read classic, readers learn Wolfe's method, which remains useful for quadratic programming, and the Kuhn-Tucker theory, which underlies quadratic programming and most other nonlinear programming methods. In addition, the author presents multiobjective linear programming, which is being applied in environmental engineering and the social sciences. The book presents many useful applications to other branches of mathematics and to economics, and it contains many exercises and examples. The advanced mathematical results are proved clearly and completely.(from google book)

In The Birth of the Mind , award-winning cognitive scientist Gary Marcus irrevocably alters the nature vs. nurture debate by linking the findings of the Human Genome Project to the development of the brain. Scientists have long struggled to understand how a tiny number of genes could contain the instructions for building the human brain, arguably the most complex device in the known universe. Synthesizing up-to-the-minute research with his own original findings on child development, Marcus is the first to resolve this apparent contradiction. Vibrantly written and completely accessible to the lay reader, The Birth of the Mind will forever change the way we think about our origins and ourselves.

A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the reconstruction of scenes from multiple images. The new edition features an extended introduction covering the key ideas in the book (which itself has been updated with additional examples and appendices) and significant new results which have appeared since the first edition. Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly from the book.

This book presents a coherent approach to the fast moving field of machine vision, using a consistent notation based on a detailed understanding of the image formation process. It covers even the most recent research and will provide a useful and current reference for professionals working in the fields of machine vision, image processing, and pattern recognition.An outgrowth of the author's course at MIT, Robot Vision presents a solid framework for understanding existing work and planning future research. Its coverage includes a great deal of material that important to engineers applying machine vision methods in the real world. The chapters on binary image processing, for example, help explain and suggest how to improve the many commercial devices now available. And the material on photometric stereo and the extended Gaussian image points the way to what may be the next thrust in commercialization of the results in this area. The many exercises complement and extend the material in the text, and an extensive bibliography will serve as a useful guide to current research.Contents: Image Formation and Image Sensing. Binary Images: Geometrical Properties; Topological Properties. Regions and Image Segmentation. Image Processing: Continuous Images; Discrete Images. Edges and Edge Finding. Lightness and Color. Reflectance Map: Photometric Stereo Reflectance Map; Shape from Shading. Motion Field and Optical Flow. Photogrammetry and Stereo. Pattern Classification. Polyhedral Objects. Extended Gaussian Images. Passive Navigation and Structure from Motion. Picking Parts out of a Bin.Berthold Klaus Paul Horn is Associate Professor, Department of Electrical Engineering and Computer Science, MIT. Robot Vision is included in the MIT Electrical Engineering and Computer Science Series.

Are we “noble in reason”? Perfect, in God’s image? Far from it, says New York University psychologist Gary Marcus. In this lucid and revealing book, Marcus argues that the mind is not an elegantly designed organ but rather a “kluge,” a clumsy, cobbled-together contraption. He unveils a fundamentally new way of looking at the human mind -- think duct tape, not supercomputer -- that sheds light on some of the most mysterious aspects of human nature.
Taking us on a tour of the fundamental areas of human experience -- memory, belief, decision-making, language, and happiness -- Marcus reveals the myriad ways our minds fall short. He examines why people often vote against their own interests, why money can’t buy happiness, why leaders often stick to bad decisions, and why a sentence like “people people left left” ties us in knots even though it’s only four words long.
Marcus also offers surprisingly effective ways to outwit our inner kluge, for the betterment of ourselves and society. Throughout, he shows how only evolution -- haphazard and undirected -- could have produced the minds we humans have, while making a brilliant case for the power and usefulness of imperfection.

Psychology is now ready for unified theories of cognition--so says Allen Newell, a leading investigator in computer science and cognitive psychology. Not everyone will agree on a single set of mechanisms that will explain the full range of human cognition, but such theories are within reach and we should strive to articulate them. In this book, Newell makes the case for unified theories by setting forth a candidate. After reviewing the foundational concepts of cognitive science--knowledge, representation, computation, symbols, architecture, intelligence, and search--Newell introduces Soar, an architecture for general cognition. A pioneer system in artificial intelligence, Soar is the first problem solver to create its own subgoals and learn continuously from its own experience. Newell shows how Soar's ability to operate within the real-time constraints of intelligent behavior, such as immediate-response and item-recognition tasks, illustrates important characteristics of the human cognitive structure. Throughout, Soar remains an exemplar: we know only enough to work toward a fully developed theory of cognition, but Soar's success so far establishes the viability of the enterprise. Given its integrative approach, Unified Theories of Cognition will be of tremendous interest to researchers in a variety of fields, including cognitive science, artificial intelligence, psychology, and computer science. This exploration of the nature of mind, one of the great problems of philosophy, should also transcend disciplines and attract a large scientific audience.

Recent work in cognitive science, much of it placed in opposition to a computational view of the mind, has argued that the concept of representation and theories based on that concept are not sufficient to explain the details of cognitive processing. These attacks on representation have focused on the importance of context sensitivity in cognitive processing, on the range of individual differences in performance, and on the relationship between minds and the bodies and environments in which they exist. In each case, models based on traditional assumptions about representation have been assumed to be too rigid to account for the effects of these factors on cognitive processing. In place of a representational view of mind, other formalisms and methodologies, such as nonlinear differential equations (or dynamical systems) and situated robotics, have been proposed as better explanatory tools for understanding cognition. This book is based on the notion that, while new tools and approaches for understanding cognition are valuable, representational approaches do not need to be abandoned in the course of constructing new models and explanations. Rather, models that incorporate representation are quite compatible with the kinds of complex situations being modeled with the new methods. This volume illustrates the power of this explicitly representational approach--labeled "cognitive dynamics"--in original essays by prominent researchers in cognitive science. Each chapter explores some aspect of the dynamics of cognitive processing while still retaining representations as the centerpiece of the explanations of the key phenomena. These chapters serve as an existence proof that representation is not incompatible with the dynamics of cognitive processing. The book is divided into sections on foundational issues about the use of representation in cognitive science, the dynamics of low level cognitive processes (such as visual and auditory perception and simple lexical priming), and the dynamics of higher cognitive processes (including categorization, analogy, and decision making).

Unlike some operating systems, Linux doesn't try to hide the important bits from you—it gives you full control of your computer. But to truly master Linux, you need to understand its internals, like how the system boots, how networking works, and what the kernel actually does.
In this completely revised second edition of the perennial best seller How Linux Works, author Brian Ward makes the concepts behind Linux internals accessible to anyone curious about the inner workings of the operating system. Inside, you'll find the kind of knowledge that normally comes from years of experience doing things the hard way. You'll learn:
How Linux boots, from boot loaders to init implementations (systemd, Upstart, and System V)
* How the kernel manages devices, device drivers, and processes
* How networking, interfaces, firewalls, and servers work
* How development tools work and relate to shared libraries
* How to write effective shell scripts
You'll also explore the kernel and examine key system tasks inside user space, including system calls, input and output, and filesystems. With its combination of background, theory, real-world examples, and patient explanations, How Linux Works will teach you what you need to know to solve pesky problems and take control of your operating system.