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How to Solve It

How to Solve It Author G. Polya
ISBN-10 9781400828678
Release 2014-10-26
Pages 288
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A perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out—from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft—indeed, brilliant—instructions on stripping away irrelevancies and going straight to the heart of the problem.

The Stanford Mathematics Problem Book

The Stanford Mathematics Problem Book Author George Polya
ISBN-10 9780486318325
Release 2013-04-09
Pages 80
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Based on Stanford University's well-known competitive exam, this excellent mathematics workbook offers students at both high school and college levels a complete set of problems, hints, and solutions. 1974 edition.

Solving Mathematical Problems

Solving Mathematical Problems Author Terence Tao
ISBN-10 9780199205615
Release 2006
Pages 103
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Authored by a leading name in mathematics, this engaging and clearly presented text leads the reader through the tactics involved in solving mathematical problems at the Mathematical Olympiad level. With numerous exercises and assuming only basic mathematics, this text is ideal for students of14 years and above in pure mathematics.

Notes on Introductory Combinatorics

Notes on Introductory Combinatorics Author George Polya
ISBN-10 9781475711011
Release 2013-11-27
Pages 193
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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.

Mathematical Methods in Elasticity Imaging

Mathematical Methods in Elasticity Imaging Author Habib Ammari
ISBN-10 9781400866625
Release 2015-04-05
Pages 240
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This book is the first to comprehensively explore elasticity imaging and examines recent, important developments in asymptotic imaging, modeling, and analysis of deterministic and stochastic elastic wave propagation phenomena. It derives the best possible functional images for small inclusions and cracks within the context of stability and resolution, and introduces a topological derivative–based imaging framework for detecting elastic inclusions in the time-harmonic regime. For imaging extended elastic inclusions, accurate optimal control methodologies are designed and the effects of uncertainties of the geometric or physical parameters on stability and resolution properties are evaluated. In particular, the book shows how localized damage to a mechanical structure affects its dynamic characteristics, and how measured eigenparameters are linked to elastic inclusion or crack location, orientation, and size. Demonstrating a novel method for identifying, locating, and estimating inclusions and cracks in elastic structures, the book opens possibilities for a mathematical and numerical framework for elasticity imaging of nanoparticles and cellular structures.

What is Mathematics

What is Mathematics Author Richard Courant
ISBN-10 0195105192
Release 1996
Pages 566
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A discussion of fundamental mathematical principles from algebra to elementary calculus designed to promote constructive mathematical reasoning.

Mathematical Thinking and Problem Solving

Mathematical Thinking and Problem Solving Author Alan H. Schoenfeld
ISBN-10 9781135440930
Release 2016-05-06
Pages 360
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In the early 1980s there was virtually no serious communication among the various groups that contribute to mathematics education -- mathematicians, mathematics educators, classroom teachers, and cognitive scientists. Members of these groups came from different traditions, had different perspectives, and rarely gathered in the same place to discuss issues of common interest. Part of the problem was that there was no common ground for the discussions -- given the disparate traditions and perspectives. As one way of addressing this problem, the Sloan Foundation funded two conferences in the mid-1980s, bringing together members of the different communities in a ground clearing effort, designed to establish a base for communication. In those conferences, interdisciplinary teams reviewed major topic areas and put together distillations of what was known about them.* A more recent conference -- upon which this volume is based -- offered a forum in which various people involved in education reform would present their work, and members of the broad communities gathered would comment on it. The focus was primarily on college mathematics, informed by developments in K-12 mathematics. The main issues of the conference were mathematical thinking and problem solving.

Mathematics and Plausible Reasoning Patterns of plausible inference

Mathematics and Plausible Reasoning  Patterns of plausible inference Author George Pólya
ISBN-10 069102510X
Release 1968
Pages 225
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A guide to the practical art of plausible reasoning, this book has relevance in every field of intellectual activity. Professor Polya, a world-famous mathematician from Stanford University, uses mathematics to show how hunches and guesses play an important part in even the most rigorously deductive science. He explains how solutions to problems can be guessed at; good guessing is often more important than rigorous deduction in finding correct solutions. Vol. II, on Patterns of Plausible Inference, attempts to develop a logic of plausibility. What makes some evidence stronger and some weaker? How does one seek evidence that will make a suspected truth more probable? These questions involve philosophy and psychology as well as mathematics.

Mathematical Methods in Science

Mathematical Methods in Science Author George Pólya
ISBN-10 0883856263
Release 1977
Pages 234
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This book captures some of Pólya's excitement and vision. Its distinctive feature is the stress on the history of certain elementary chapters of science; these can be a source of enjoyment and deeper understanding of mathematics even for beginners who have little, or perhaps no, knowledge of physics.

Over and Over Again

Over and Over Again Author Gengzhe Chang
ISBN-10 0883856417
Release 1997-01-01
Pages 309
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Mathematical theme that relates chaos, graphics and geometry, all with just high school maths background.

Infinity and the Mind

Infinity and the Mind Author Rudy Rucker
ISBN-10 9781400849048
Release 2013-07-14
Pages 368
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In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the "Mindscape," where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Rucker acquaints us with Gödel's rotating universe, in which it is theoretically possible to travel into the past, and explains an interpretation of quantum mechanics in which billions of parallel worlds are produced every microsecond. It is in the realm of infinity, he maintains, that mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise from this merging, we can learn a great deal about the human mind, its powers, and its limitations. Using cartoons, puzzles, and quotations to enliven his text, Rucker guides us through such topics as the paradoxes of set theory, the possibilities of physical infinities, and the results of Gödel's incompleteness theorems. His personal encounters with Gödel the mathematician and philosopher provide a rare glimpse at genius and reveal what very few mathematicians have dared to admit: the transcendent implications of Platonic realism.

Mathematical Discovery on Understanding Learning and Teaching Problem Solving

Mathematical Discovery on Understanding  Learning  and Teaching Problem Solving Author George Pólya
ISBN-10 4871878325
Release 2009
Pages 218
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"Solving problems," writes Polya, "is a practical art, like swimming, or skiing, or playing the piano: You can learn it only by imitation and practice. This book cannot offer you a magic key that opens all the doors and solves all the problems, but it offers you good examples for imitation and many opportunities for practice: If you wish to learn swimming you have to go into the water and if you wish to become a problem solver you have to solve problems." "In enough cases to allay . . . discouragement over not immediately discovering a solution, Professor Polya masterfully leads the reader down several unproductive paths. At the end of each chapter he provides examples for the render to solve. By means of these carefully selected and arranged problems, many of them directly related to others that precede, and guided by just the right suggestions at just the proper time, the reader's own ability is developed and extended. Solutions to the examples and, in many cases, outlines of procedures for discovering solutions. arc given at the back of the book. With striking promise for effectiveness, the entire book as a unit is one great experience in learning processes for problem solving through participation. The author has captured with great success the implication of his basic premise stated in the preface ..." The Mathematics Teacher

How to Solve It Modern Heuristics

How to Solve It  Modern Heuristics Author Zbigniew Michalewicz
ISBN-10 9783662041314
Release 2013-03-14
Pages 467
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This book is the only source that provides a systematic, integrated introduction to problem solving using modern heuristics, presenting the state-of-the-art in both numerical and analytic methods. It covers classic methods of optimization, including dynamic programming, the simplex method, and gradient techniques, as well as recent innovations such as simulated annealing, tabu search, and evolutionary computation. Integrated into the discourse is a series of problems and puzzles to challenge the reader. Written in a lively, engaging style, readers will learn how to use some of the most powerful problem solving tools currently available.

The Princeton Companion to Applied Mathematics

The Princeton Companion to Applied Mathematics Author Nicholas J. Higham
ISBN-10 9781400874477
Release 2015-09-15
Pages 1016
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This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. Features nearly 200 entries organized thematically and written by an international team of distinguished contributors Presents the major ideas and branches of applied mathematics in a clear and accessible way Explains important mathematical concepts, methods, equations, and applications Introduces the language of applied mathematics and the goals of applied mathematical research Gives a wide range of examples of mathematical modeling Covers continuum mechanics, dynamical systems, numerical analysis, discrete and combinatorial mathematics, mathematical physics, and much more Explores the connections between applied mathematics and other disciplines Includes suggestions for further reading, cross-references, and a comprehensive index


Inequalities Author G. H. Hardy
ISBN-10 0521358809
Release 1952
Pages 324
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This classic of the mathematical literature forms a comprehensive study of the inequalities used throughout mathematics. First published in 1934, it presents clearly and lucidly both the statement and proof of all the standard inequalities of analysis. The authors were well-known for their powers of exposition and made this subject accessible to a wide audience of mathematicians.

Data Association for Multi Object Visual Tracking

Data Association for Multi Object Visual Tracking Author Margrit Betke
ISBN-10 9781627059435
Release 2016-10-11
Pages 120
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In the human quest for scientific knowledge, empirical evidence is collected by visual perception. Tracking with computer vision takes on the important role to reveal complex patterns of motion that exist in the world we live in. Multi-object tracking algorithms provide new information on how groups and individual group members move through three-dimensional space. They enable us to study in depth the relationships between individuals in moving groups. These may be interactions of pedestrians on a crowded sidewalk, living cells under a microscope, or bats emerging in large numbers from a cave. Being able to track pedestrians is important for urban planning; analysis of cell interactions supports research on biomaterial design; and the study of bat and bird flight can guide the engineering of aircraft. We were inspired by this multitude of applications to consider the crucial component needed to advance a single-object tracking system to a multi-object tracking system—data association. Data association in the most general sense is the process of matching information about newly observed objects with information that was previously observed about them. This information may be about their identities, positions, or trajectories. Algorithms for data association search for matches that optimize certain match criteria and are subject to physical conditions. They can therefore be formulated as solving a "constrained optimization problem"—the problem of optimizing an objective function of some variables in the presence of constraints on these variables. As such, data association methods have a strong mathematical grounding and are valuable general tools for computer vision researchers. This book serves as a tutorial on data association methods, intended for both students and experts in computer vision. We describe the basic research problems, review the current state of the art, and present some recently developed approaches. The book covers multi-object tracking in two and three dimensions. We consider two imaging scenarios involving either single cameras or multiple cameras with overlapping fields of view, and requiring across-time and across-view data association methods. In addition to methods that match new measurements to already established tracks, we describe methods that match trajectory segments, also called tracklets. The book presents a principled application of data association to solve two interesting tasks: first, analyzing the movements of groups of free-flying animals and second, reconstructing the movements of groups of pedestrians. We conclude by discussing exciting directions for future research.

Data Analysis for Scientists and Engineers

Data Analysis for Scientists and Engineers Author Edward L. Robinson
ISBN-10 9781400883066
Release 2016-09-20
Pages 408
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Data Analysis for Scientists and Engineers is a modern, graduate-level text on data analysis techniques for physical science and engineering students as well as working scientists and engineers. Edward Robinson emphasizes the principles behind various techniques so that practitioners can adapt them to their own problems, or develop new techniques when necessary. Robinson divides the book into three sections. The first section covers basic concepts in probability and includes a chapter on Monte Carlo methods with an extended discussion of Markov chain Monte Carlo sampling. The second section introduces statistics and then develops tools for fitting models to data, comparing and contrasting techniques from both frequentist and Bayesian perspectives. The final section is devoted to methods for analyzing sequences of data, such as correlation functions, periodograms, and image reconstruction. While it goes beyond elementary statistics, the text is self-contained and accessible to readers from a wide variety of backgrounds. Specialized mathematical topics are included in an appendix. Based on a graduate course on data analysis that the author has taught for many years, and couched in the looser, workaday language of scientists and engineers who wrestle directly with data, this book is ideal for courses on data analysis and a valuable resource for students, instructors, and practitioners in the physical sciences and engineering. In-depth discussion of data analysis for scientists and engineers Coverage of both frequentist and Bayesian approaches to data analysis Extensive look at analysis techniques for time-series data and images Detailed exploration of linear and nonlinear modeling of data Emphasis on error analysis Instructor's manual (available only to professors)