How To Solve Mathematical Problems

Author: Wayne A. Wickelgren
Publisher: Courier Corporation
ISBN: 0486152685
File Size: 30,49 MB
Format: PDF
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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.

The Elements Of Problem Solving

Author: Jared M. Maruskin
Publisher: Solar Crest Publishing LLC
ISBN: 0985062754
File Size: 36,16 MB
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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.

How To Solve It

Author: G. Polya
Publisher: Princeton University Press
ISBN: 1400828678
File Size: 53,17 MB
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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.

Finite Element Solution Of Boundary Value Problems

Author: O. Axelsson
Publisher: Academic Press
ISBN: 1483260569
File Size: 47,81 MB
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Finite Element Solution of Boundary Value Problems: Theory and Computation provides an introduction to both the theoretical and computational aspects of the finite element method for solving boundary value problems for partial differential equations. This book is composed of seven chapters and begins with surveys of the two kinds of preconditioning techniques, one based on the symmetric successive overrelaxation iterative method for solving a system of equations and a form of incomplete factorization. The subsequent chapters deal with the concepts from functional analysis of boundary value problems. These topics are followed by discussions of the Ritz method, which minimizes the quadratic functional associated with a given boundary value problem over some finite-dimensional subspace of the original space of functions. Other chapters are devoted to direct methods, including Gaussian elimination and related methods, for solving a system of linear algebraic equations. The final chapter continues the analysis of preconditioned conjugate gradient methods, concentrating on applications to finite element problems. This chapter also looks into the techniques for reducing rounding errors in the iterative solution of finite element equations. This book will be of value to advanced undergraduates and graduates in the areas of numerical analysis, mathematics, and computer science, as well as for theoretically inclined workers in engineering and the physical sciences.

How To Solve Mathematical Problems

Author: Wayne A. Wickelgren
Publisher: Courier Corporation
ISBN: 0486152685
File Size: 33,23 MB
Format: PDF, Docs
Read: 2361
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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.

Critical Systems Analysis And Design

Author: Nandish Patel
Publisher: Routledge
ISBN: 1134321066
File Size: 44,45 MB
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Taking a unique approach to systems analysis and design, this insightful book provides learners with a critical personal framework for considering and developing knowledge and practice of systems analysis and design. Each chapter begins by highlighting what can be learned on its completion and ends with a critical skills development section containing activities, tasks and discussion questions. Chapters cover: * systems analysis and design in concept and action * structured data modelling * making systems analysis and design inclusive. Although the discussion and examples in this text are drawn primarily from business information systems, the lessons apply to both government and healthcare information systems and to systems development in general. Critical Systems Analysis and Design makes a complex area of study accessible and relevant and as such is an indispensable textbook for both advanced students and professionals concerned with the innovation of information systems.

Facilitating Seven Ways Of Learning

Author: James R. Davis
Publisher: Stylus Publishing, LLC
ISBN: 1579228437
File Size: 24,97 MB
Format: PDF, Mobi
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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.

Professional Learning Gaps And Transitions On The Way From Novice To Expert

Author: Henny P.A. Boshuizen
Publisher: Springer Science & Business Media
ISBN: 1402020945
File Size: 36,66 MB
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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.

Learning To Solve Problems

Author: David H. Jonassen
Publisher: Routledge
ISBN: 1136941886
File Size: 26,64 MB
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This book provides a comprehensive, up-to-date look at problem solving research and practice over the last fifteen years. The first chapter describes differences in types of problems, individual differences among problem-solvers, as well as the domain and context within which a problem is being solved. Part one describes six kinds of problems and the methods required to solve them. Part two goes beyond traditional discussions of case design and introduces six different purposes or functions of cases, the building blocks of problem-solving learning environments. It also describes methods for constructing cases to support problem solving. Part three introduces a number of cognitive skills required for studying cases and solving problems. Finally, Part four describes several methods for assessing problem solving. Key features includes: Teaching Focus – The book is not merely a review of research. It also provides specific research-based advice on how to design problem-solving learning environments. Illustrative Cases – A rich array of cases illustrates how to build problem-solving learning environments. Part two introduces six different functions of cases and also describes the parameters of a case. Chapter Integration – Key theories and concepts are addressed across chapters and links to other chapters are made explicit. The idea is to show how different kinds of problems, cases, skills, and assessments are integrated. Author expertise – A prolific researcher and writer, the author has been researching and publishing books and articles on learning to solve problems for the past fifteen years. This book is appropriate for advanced courses in instructional design and technology, science education, applied cognitive psychology, thinking and reasoning, and educational psychology. Instructional designers, especially those involved in designing problem-based learning, as well as curriculum designers who seek new ways of structuring curriculum will find it an invaluable reference tool.

Elements Of The Theory Of Inverse Problems

Author: A. M. Denisov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110943255
File Size: 71,43 MB
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The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.