How to Solve Mathematical Problems

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Author: Wayne A. Wickelgren

Publisher: Courier Corporation

ISBN: 0486152685

Category: Science

Page: 288

View: 6065

Seven problem-solving techniques include inference, classification of action sequences, subgoals, contradiction, working backward, relations between problems, and mathematical representation. Also, problems from mathematics, science, and engineering with complete solutions.

Solving Tough Problems

An Open Way of Talking, Listening, and Creating New Realities: Easyread Large Bold Edition

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Author: Adam Kahane

Publisher: ReadHowYouWant.com

ISBN: 1442950188

Category: Business & Economics

Page: 220

View: 6693

Facilitating Seven Ways of Learning

A Resource for More Purposeful, Effective, and Enjoyable College Teaching

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Author: James R. Davis,Bridget D. Arend

Publisher: Stylus Publishing, LLC

ISBN: 1579228437

Category: Education

Page: 326

View: 7327

For teachers in higher education who haven’t been able to catch up with developments in teaching and learning, James Davis and Bridget Arend offer an introduction that focuses on seven coherent and proven evidence-based strategies. The underlying rationale is to provide a framework to match teaching goals to distinct ways of learning, based on well-established theories of learning. The authors present approaches that readers can readily and safely experiment with to achieve desired learning outcomes, and build confidence in changing their methods of teaching. Research on learning clearly demonstrates that learning is not one thing, but many. The learning associated with developing a skill is different from the learning associated with understanding and remembering information, which in turn is different from thinking critically and creatively, solving problems, making decisions, or change paradigms in the light of evidence. Differing outcomes involve different ways of learning and teaching strategies. The authors provide the reader with a conceptual approach for selecting appropriate teaching strategies for different types of content, and for achieving specific learning objectives. They demonstrate through examples how a focused and purposeful selection of activities improves student performance, and in the process makes for a more effective and satisfying teaching experience. The core of the book presents a chapter on each of the seven ways of learning. Each chapter offers a full description of the process, illustrates its application with examples from different academic fields and types of institutions, clearly describes the teacher’s facilitation role, and covers assessment and online use. The seven ways of learning are: Behavioral Learning; Cognitive Learning; Learning through Inquiry; Learning with Mental Models; Learning through Groups and Teams; Learning through Virtual Realities; and Experiential Learning. Along the way, the authors provide the reader with a basis for evaluating other approaches to teaching and other learning methodologies so that she or he can confidently go beyond the “seven ways” to adapt or adopt further strategies. This is the ideal companion for teachers who are beginning to explore new ways of teaching, and want to do some serious independent thinking about learning. The book can also be used to prepare graduate students for teaching, and will be welcomed by centers for teaching and learning to help continuing faculty re-examine a particular aspect of their teaching.

How to Solve It

A New Aspect of Mathematical Method

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Author: G. Polya

Publisher: Princeton University Press

ISBN: 1400828678

Category: Mathematics

Page: 288

View: 1637

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.

How to Solve Mathematical Problems

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Author: Wayne A. Wickelgren

Publisher: Courier Corporation

ISBN: 0486152685

Category: Science

Page: 288

View: 5243

Seven problem-solving techniques include inference, classification of action sequences, subgoals, contradiction, working backward, relations between problems, and mathematical representation. Also, problems from mathematics, science, and engineering with complete solutions.

Professional Learning: Gaps and Transitions on the Way from Novice to Expert

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Author: Henny P.A. Boshuizen,Rainer Bromme,Hans Gruber

Publisher: Springer Science & Business Media

ISBN: 1402020945

Category: Education

Page: 308

View: 3519

About the Book Series The idea for the Book Series “Innovation and Change in Professional Education” (ICPE) was born in 1996. While working on another publication in this area, we noticed that professional educators faced similar problems without even knowing from each other. It was this observation that resulted in examining the possibilities for a new publication platform about professional education with input from different professions. We wanted to develop a publication source that would bring together educators and researchers to exchange ideas and knowledge about theory, research and professional practice. But we were not only striving for a book series informing readers about important themes in the professions. A second goal was to focus on processes of change and innovation. We were heavily involved in innovations going on in our institutions, and were convinced that a better understanding was needed in a wide range of issues critically important to the future of professional education. It was our belief that scholarly publications about innovation processes may support fundamental change in professional education. ICPE reflects our view that professional education deserves such a publication platform. It aims to approach critical questions of educational innovations, and to examine dynamics of educational change in various professional domains in the context of innovation processes. The books will include contributions from frontline practitioners, leading researchers, or distinguished scholars in professional education, delivering reports of empirical or theoretical research, reviews, interpretations of evaluation studies, or descriptions of innovative approaches.

Elements of the Theory of Inverse Problems

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Author: A. M. Denisov

Publisher: VSP

ISBN: 9789067643030

Category: Mathematics

Page: 272

View: 2380

This volume focuses on the basic theory of inverse problems. The first chapter offers an introduction to the theory of inverse problems, with examples of both inverse and ill-posed problems, as well as methods of their solution. The following chapters address topics including: inverse problems for ordinary differential equations; inverse problems for linear partial differential equations; inverse coefficient problems for partial differential equations; determining functions for one or two variables by integrals of these functions; and methods of solution of inverse problems. At the end of each chapter exercises are included to assist readers in gaining a better understanding of the subject matter.

Algorithmic Problem Solving

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Author: Roland Backhouse

Publisher: John Wiley & Sons

ISBN: 0470684534

Category: Computers

Page: 432

View: 1124

An entertaining and captivating way to learn the fundamentals of using algorithms to solve problems The algorithmic approach to solving problems in computer technology is an essential tool. With this unique book, algorithm guru Roland Backhouse shares his four decades of experience to teach the fundamental principles of using algorithms to solve problems. Using fun and well-known puzzles to gradually introduce different aspects of algorithms in mathematics and computing. Backhouse presents you with a readable, entertaining, and energetic book that will motivate and challenge you to open your mind to the algorithmic nature of problem solving. Provides a novel approach to the mathematics of problem solving focusing on the algorithmic nature of problem solving Uses popular and entertaining puzzles to teach you different aspects of using algorithms to solve mathematical and computing challenges Features a theory section that supports each of the puzzles presented throughout the book Assumes only an elementary understanding of mathematics Let Roland Backhouse and his four decades of experience show you how you can solve challenging problems with algorithms!

Problem Solving 101

A Simple Book for Smart People

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Author: Ken Watanabe

Publisher: Penguin

ISBN: 9781101029183

Category: Business & Economics

Page: 128

View: 6333

The fun and simple problem-solving guide that took Japan by storm Ken Watanabe originally wrote Problem Solving 101 for Japanese schoolchildren. His goal was to help shift the focus in Japanese education from memorization to critical thinking, by adapting some of the techniques he had learned as an elite McKinsey consultant. He was amazed to discover that adults were hungry for his fun and easy guide to problem solving and decision making. The book became a surprise Japanese bestseller, with more than 370,000 in print after six months. Now American businesspeople can also use it to master some powerful skills. Watanabe uses sample scenarios to illustrate his techniques, which include logic trees and matrixes. A rock band figures out how to drive up concert attendance. An aspiring animator budgets for a new computer purchase. Students decide which high school they will attend. Illustrated with diagrams and quirky drawings, the book is simple enough for a middleschooler to understand but sophisticated enough for business leaders to apply to their most challenging problems.

Representations for Genetic and Evolutionary Algorithms

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Author: Franz Rothlauf

Publisher: Springer Science & Business Media

ISBN: 9783540324447

Category: Mathematics

Page: 325

View: 5067

In the field of genetic and evolutionary algorithms (GEAs), a large amount of theory and empirical study has been focused on operators and test problems, while problem representation has often been taken as given. This book breaks with this tradition and provides a comprehensive overview on the influence of problem representations on GEA performance. The book summarizes existing knowledge regarding problem representations and describes how basic properties of representations, such as redundancy, scaling, or locality, influence the performance of GEAs and other heuristic optimization methods. Using the developed theory, representations can be analyzed and designed in a theory-guided matter. The theoretical concepts are used for solving integer optimization problems and network design problems more efficiently. The book is written in an easy-readable style and is intended for researchers, practitioners, and students who want to learn about representations. This second edition extends the analysis of the basic properties of representations and introduces a new chapter on the analysis of direct representations.

The Elements of Problem Solving

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Author: Jared M. Maruskin

Publisher: Solar Crest Publishing LLC

ISBN: 0985062754

Category: Engineering

Page: 132

View: 1549

This concise volume seeks to address the silent void that university students embarking on mathematical coursework inevitably face: How does one apply ideas, concepts, and theory to story problems that at first seem intractable? We pay equal attention to the abstract aspects of problem solving as well as the practical. We discuss common misperceptions of ability and pay close attention to the attitudes and habits employed by successful problem solvers. We reveal problem solving as both achievable and fun, and illustrate these themes with specific examples and stories throughout the text. We also enumerate simple, executable steps that can be implemented when faced with virtually any new problem: understand the problem; draw a picture; define variables; be consistent; utilize principles. Far from trivial, these steps often lead novice problem solvers to error. In sum, we hope you find this charming work to be an indispensable guide on your journey and an effective means to improving and maturing your problem-solving capabilities.

Computational Intelligence for Decision Support

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Author: Zhengxin Chen

Publisher: CRC Press

ISBN: 9781420049145

Category: Computers

Page: 400

View: 717

Intelligent decision support relies on techniques from a variety of disciplines, including artificial intelligence and database management systems. Most of the existing literature neglects the relationship between these disciplines. By integrating AI and DBMS, Computational Intelligence for Decision Support produces what other texts don't: an explanation of how to use AI and DBMS together to achieve high-level decision making. Threading relevant disciplines from both science and industry, the author approaches computational intelligence as the science developed for decision support. The use of computational intelligence for reasoning and DBMS for retrieval brings about a more active role for computational intelligence in decision support, and merges computational intelligence and DBMS. The introductory chapter on technical aspects makes the material accessible, with or without a decision support background. The examples illustrate the large number of applications and an annotated bibliography allows you to easily delve into subjects of greater interest. The integrated perspective creates a book that is, all at once, technical, comprehensible, and usable. Now, more than ever, it is important for science and business workers to creatively combine their knowledge to generate effective, fruitful decision support. Computational Intelligence for Decision Support makes this task manageable.

Problem-Solving Through Problems

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Author: Loren C. Larson

Publisher: Springer Science & Business Media

ISBN: 1461254981

Category: Mathematics

Page: 352

View: 7486

This is a practical anthology of some of the best elementary problems in different branches of mathematics. Arranged by subject, the problems highlight the most common problem-solving techniques encountered in undergraduate mathematics. This book teaches the important principles and broad strategies for coping with the experience of solving problems. It has been found very helpful for students preparing for the Putnam exam.

Metaphor and Analogy in the Sciences

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Author: F. Hallyn

Publisher: Springer Science & Business Media

ISBN: 9401594422

Category: Philosophy

Page: 244

View: 6403

This collection of papers contains historical case studies, systematic contributions of a general nature, and applications to specific sciences. The bibliographies of the contributions contain references to all central items from the traditions that are relevant today. While providing access to contemporary views on the issue, the papers illustrate the wide variety of functions of metaphors and analogies, as well as the many connections between the study of some of these functions and other subjects and disciplines.

Problem-Solving Methods in Combinatorics

An Approach to Olympiad Problems

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Author: Pablo Soberón

Publisher: Springer Science & Business Media

ISBN: 3034805977

Category: Mathematics

Page: 174

View: 7438

Every year there is at least one combinatorics problem in each of the major international mathematical olympiads. These problems can only be solved with a very high level of wit and creativity. This book explains all the problem-solving techniques necessary to tackle these problems, with clear examples from recent contests. It also includes a large problem section for each topic, including hints and full solutions so that the reader can practice the material covered in the book.​ The material will be useful not only to participants in the olympiads and their coaches but also in university courses on combinatorics.

Encyclopedia of Educational Theory and Philosophy

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Author: D. C. Phillips

Publisher: SAGE Publications

ISBN: 1483364755

Category: Education

Page: 952

View: 3764

Education is a field sometimes beset by theories-of-the-day and with easy panaceas that overpromise the degree to which they can alleviate pressing educational problems. The two-volume Encyclopedia of Educational Theory and Philosophy introduces readers to theories that have stood the test of time and those that have provided the historical foundation for the best of contemporary educational theory and practice. Drawing together a team of international scholars, this invaluable reference examines the global landscape of all the key theories and the theorists behind them and presents them in the context needed to understand their strengths and weaknesses. In addition to interpretations of long-established theories, this work offers essays on cutting-edge research and concise, to-the-point definitions of key concepts, ideas, schools, and figures. Features: Over 300 signed entries by trusted experts in the field are organized into two volumes and overseen by a distinguished General Editor and an international Editorial Board. Entries are followed by cross references and further reading suggestions. A Chronology of Theory within the field of education highlights developments over the centuries; a Reader’s Guide groups entries thematically, and a master Bibliography facilitates further study. The Reader’s Guide, detailed index, and cross references combine for strong search-and-browse capabilities in the electronic version. Available in a choice of print or electronic formats, Encyclopedia of Educational Theory and Philosophy is an ideal reference for anyone interested in the roots of contemporary educational theory.

Integrative Problem-Solving in a Time of Decadence

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Author: George Christakos

Publisher: Springer Science & Business Media

ISBN: 9789048198900

Category: Science

Page: 527

View: 2062

Presents a unique study of Integrative Problem-Solving (IPS). The consideration of 'Decadence' is essential in the scientific study of environmental and other problems and their rigorous solution, because the broad context within which the problems emerge can affect their solution. Stochastic reasoning underlines the conceptual and methodological framework of IPS, and its formulation has a mathematical life of its own that accounts for the multidisciplinarity of real world problems, the multisourced uncertainties characterizing their solution, and the different thinking modes of the people involved. Only by interpolating between the full range of disciplines (including stochastic mathematics, physical science, neuropsychology, philosophy, and sociology) and the associated thinking modes can scientists arrive at a satisfactory account of problem-solving, and be able to distinguish between a technically complete problem-solution, and a solution that has social impact.

Analysis of Aircraft Structures

An Introduction

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Author: Bruce K. Donaldson

Publisher: Cambridge University Press

ISBN: 0521865832

Category: Technology & Engineering

Page: 932

View: 2921

As with the first edition, this textbook provides a clear introduction to the fundamental theory of structural analysis as applied to vehicular structures such as aircraft, spacecraft, automobiles and ships. The emphasis is on the application of fundamental concepts of structural analysis that are employed in everyday engineering practice. All approximations are accompanied by a full explanation of their validity. In this new edition, more topics, figures, examples and exercises have been added. There is also a greater emphasis on the finite element method of analysis. Clarity remains the hallmark of this text and it employs three strategies to achieve clarity of presentation: essential introductory topics are covered, all approximations are fully explained and many important concepts are repeated.