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Constructive Approximation

The book describes function spaces used in approximation, the needed functional analytic tools. It develops basic properties of polynomials, splines, linear operators that are used for approximation (and interpolation). The book takes the reader up to and into the recent great advances of Approximation Theory and emphasizes good proofs, logical selection of material, avoidance of superfluous details.

Special cases of Haar systems on [a, b] are the Polya systems. Their definition is
based on the following remarks: 1. If V = {vo,...,Vk-\} is a Haar system on \a,b] and
w € C[a, b] is strictly positive, then W := {wv0 wvk-i} is also a Haar system on [a, ...

Problems and Theorems in Analysis II

Theory of Functions. Zeros. Polynomials. Determinants. Number Theory. Geometry

Few mathematical books are worth translating 50 years after original publication. Polyá-Szegö is one! It was published in German in 1924, and its English edition was widely acclaimed when it appeared in 1972. In the past, more of the leading mathematicians proposed and solved problems than today. Their collection of the best in analysis is a heritage of lasting value.

From the reviews: ".

Notes on Introductory Combinatorics

In the winter of 1978, Professor George P61ya and I jointly taught Stanford University's introductory combinatorics course. This was a great opportunity for me, as I had known of Professor P61ya since having read his classic book, How to Solve It, as a teenager. Working with P6lya, who ·was over ninety years old at the time, was every bit as rewarding as I had hoped it would be. His creativity, intelligence, warmth and generosity of spirit, and wonderful gift for teaching continue to be an inspiration to me. Combinatorics is one of the branches of mathematics that play a crucial role in computer sCience, since digital computers manipulate discrete, finite objects. Combinatorics impinges on computing in two ways. First, the properties of graphs and other combinatorial objects lead directly to algorithms for solving graph-theoretic problems, which have widespread application in non-numerical as well as in numerical computing. Second, combinatorial methods provide many analytical tools that can be used for determining the worst-case and expected performance of computer algorithms. A knowledge of combinatorics will serve the computer scientist well. Combinatorics can be classified into three types: enumerative, eXistential, and constructive. Enumerative combinatorics deals with the counting of combinatorial objects. Existential combinatorics studies the existence or nonexistence of combinatorial configurations.

George Pólya Department of Mathematics Stanford University Stanford,
California 94305, USA Robert E. Tarjan Bell Laboratories 600 Mountain Avenue
Murray Hill, New Jersey 07974, USA Donald R. Woods Xerox Corporation 3333
Coyote ...

Problems and Theorems in Analysis I

Series. Integral Calculus. Theory of Functions

From the reviews: "The work is one of the real classics of this century; it has had much influence on teaching, on research in several branches of hard analysis, particularly complex function theory, and it has been an essential indispensable source book for those seriously interested in mathematical problems." Bulletin of the American Mathematical Society

This picture shows G. Pólya (r.) and G. Szegó (1.) delivering their original
manuscript to Springer in Berlin in 1925 (courtesy of G. Alexanderson). George
Pólya Born in Budapest, December 13, 1887, George Pólya initially studied law,
then ...

Functional Equations and How to Solve Them

Many books have been written on the theory of functional equations, but very few help readers solve functional equations in mathematics competitions and mathematical problem solving. This book fills that gap. Each chapter includes a list of problems associated with the covered material. These vary in difficulty, with the easiest being accessible to any high school student who has read the chapter carefully. The most difficult will challenge students studying for the International Mathematical Olympiad or the Putnam Competition. An appendix provides a springboard for further investigation of the concepts of limits, infinite series and continuity.

Many books have been written on the theory of functional equations, but very few help readers solve functional equations in mathematics competitions and mathematical problem solving. This book fills that gap.

How to Solve It: Modern Heuristics

No pleasure lasts long unless there is variety in it. Publilius Syrus, Moral Sayings We've been very fortunate to receive fantastic feedback from our readers during the last four years, since the first edition of How to Solve It: Modern Heuristics was published in 1999. It's heartening to know that so many people appreciated the book and, even more importantly, were using the book to help them solve their problems. One professor, who published a review of the book, said that his students had given the best course reviews he'd seen in 15 years when using our text. There can be hardly any better praise, except to add that one of the book reviews published in a SIAM journal received the best review award as well. We greatly appreciate your kind words and personal comments that you sent, including the few cases where you found some typographical or other errors. Thank you all for this wonderful support.

We have given this very problem to many people, including undergraduate and
graduate students, and even full professors in mathematics, engineering, or
computer science. Fewer than five percent of them solved this problem within an
hour, ...

Smart Education and e-Learning 2016

This book contains the contributions presented at the 3rd international KES conference on Smart Education and Smart e-Learning, which took place in Puerto de la Cruz, Tenerife, Spain, June 15-17, 2016. It contains a total of 56 peer-reviewed book chapters that are grouped into several parts: Part 1 - Smart University: Conceptual Modeling, Part 2 – Smart Education: Research and Case Studies, Part 3 – Smart e-Learning, Part 4 – Smart Education: Software and Hardware Systems, and Part 5 – Smart Technology as a Resource to Improve Education and Professional Training. We believe that the book will serve as a useful source of research data and valuable information for faculty, scholars, Ph.D. students, administrators, and practitioners - those who are interested in innovative areas of smart education and smart e-learning.

This book contains the contributions presented at the 3rd international KES conference on Smart Education and Smart e-Learning, which took place in Puerto de la Cruz, Tenerife, Spain, June 15-17, 2016.

Mathematical Modeling, Simulation, Visualization and e-Learning

Proceedings of an International Workshop held at Rockefeller Foundation' s Bellagio Conference Center, Milan, Italy, 2006

This book features articles written by some of the most prominent leading applied mathematicians as well as young and promising ones. The common objective of these articles is to present an important issue which is currently widely discussed in scientific investigation with major human, economic or ecological implications. Each article is as deep as an expert lecture but is also self-contained, so that even isolated scientists with limited resources can profit greatly from it.

This book is a collection of articles written by some of the most prominent leading applied mathematicians, as well as articles from young and promising scientists from Africa, Asia and Europe.

Content Management for E-Learning

The increasing growth in the use of e-learning environments, in which education is delivered and supported through information and communication technologies, has brought new challenges to academic institutions. From all the current definitions of e-learning, it can be seen that learning contents are one of the key issues for a successful e-learning experience. Therefore, there is a real need for academic staff, managers and librarians to re-think the whole process of delivering courses, information resources and information services. The book focuses on defining content management and its relationship with knowledge management, providing perspectives on how the semantic web could complement content management, how to deal with copyright restrictions, and how to describe information competencies and skills required and acquired by teachers and students in virtual environments. Offered is a design project for managing digital content for classical and distance education institutions, covering all the aspects related to the content lifecycle, integrating it into the learning process. Practical aspects such as standards for content e-learning management, a review of existing experiences of learning repositories, and a survey of available platforms for delivering courses and providing access to information resources is also covered. Lastly, the book addresses the three main factors which make it crucial in the current context: first, the web 2.0 paradigm, which breaks the content producer-consumer barrier; second, the open content movement for educational purposes, which changes the knowledge management transference model; and third, the new European Higher Education Area, where the concept of content needs to be rethought.

The book focuses on defining content management and its relationship with knowledge management, providing perspectives on how the semantic web could complement content management, how to deal with copyright restrictions, and how to describe ...

Endogenous Stem Cell-Based Brain Remodeling in Mammals

This text highlights the endogenous regenerative potential of the central nervous system in neonates and juveniles and discusses possible ways it might be manipulated for medical purposes. The first section provides a descriptive summary of the salient steps of human brain development with a discussion of comparisons with other mammalian brains. It also provides a historical perspective on our understanding of ongoing brain development throughout the lifespan and serve to introduce the concept of brain plasticity following injury. The second part is devoted to the endogenous reparative potential of the brain, including its limitations, and articles focusing on defined pathologies (e.g. anoxia/hypoxia, epilepsy, traumatic brain injury and stress) in animal models and in humans pinpoint eventual ways these pathologies might be manipulated. The third and final focuses on the "dark side" of stem cells for brain repair or of the manipulation of spontaneous adaptive events after injury (e.g. genomic instability, sensitization to cancerous transformation and defective neural networks).

Marie-Pierre Junier and Steven G. Kernie The remarkable progress made over
the last decade in our understanding of and ability to manipulate embryonic and
somatic stem cells has led to the very real potential of cell-based therapies as a ...