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This text on mathematical problem solving provides a comprehensive outline of "problemsolving-ology," concentrating on strategy and tactics. It discusses a number of standard mathematical subjects such as combinatorics and calculus from a problem solver's perspective.
Algorithms are at the heart of every nontrivial computer application, and algorithmics is a modern and active area of computer science. Every computer scientist and every professional programmer should know about the basic algorithmic toolbox: structures that allow efficient organization and retrieval of data, frequently used algorithms, and basic techniques for modeling, understanding and solving algorithmic problems. This book is a concise introduction addressed to students and professionals familiar with programming and basic mathematical language. Individual chapters cover arrays and linked lists, hash tables and associative arrays, sorting and selection, priority queues, sorted sequences, graph representation, graph traversal, shortest paths, minimum spanning trees, and optimization. The algorithms are presented in a modern way, with explicitly formulated invariants, and comment on recent trends such as algorithm engineering, memory hierarchies, algorithm libraries and certifying algorithms. The authors use pictures, words and high-level pseudocode to explain the algorithms, and then they present more detail on efficient implementations using real programming languages like C++ and Java. The authors have extensive experience teaching these subjects to undergraduates and graduates, and they offer a clear presentation, with examples, pictures, informal explanations, exercises, and some linkage to the real world. Most chapters have the same basic structure: a motivation for the problem, comments on the most important applications, and then simple solutions presented as informally as possible and as formally as necessary. For the more advanced issues, this approach leads to a more mathematical treatment, including some theorems and proofs. Finally, each chapter concludes with a section on further findings, providing views on the state of research, generalizations and advanced solutions.
*THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* One of the most significant tasks facing mathematics educators is to understand the role of mathematical reasoning and proving in mathematics teaching, so that its presence in instruction can be enhanced. This challenge has been given even greater importance by the assignment to proof of a more prominent place in the mathematics curriculum at all levels. Along with this renewed emphasis, there has been an upsurge in research on the teaching and learning of proof at all grade levels, leading to a re-examination of the role of proof in the curriculum and of its relation to other forms of explanation, illustration and justification. This book, resulting from the 19th ICMI Study, brings together a variety of viewpoints on issues such as: The potential role of reasoning and proof in deepening mathematical understanding in the classroom as it does in mathematical practice. The developmental nature of mathematical reasoning and proof in teaching and learning from the earliest grades. The development of suitable curriculum materials and teacher education programs to support the teaching of proof and proving. The book considers proof and proving as complex but foundational in mathematics. Through the systematic examination of recent research this volume offers new ideas aimed at enhancing the place of proof and proving in our classrooms.
This book presents the results of a multi-annual project with sustainable Living Labs in the United Kingdom, Sweden, Germany and the Netherlands. Living Labs – as initiated by the authors – have proved to be very promising research, design, co-creation and communication facilities for the development and implementation of sustainable innovations in the home. The book provides an inspiring introduction to both the methodology and business modelling for the Living Lab facilities. Understanding daily living at home is key to designing products and services that support households in their transition to more sustainable lifestyles. This book not only explores new ways of gaining insights into daily practices, but also discusses developing and testing design methods to create sustainable solutions for households. These new methods and tools are needed because those available are either ineffective or cause rebound-effects. Intended for researchers and designers with an interest in the transition to sustainable lifestyles, it also appeals to company leaders interested in new ways of developing sustainable innovations and offers suggestions for effectively applying Living Labs for sustainable urban development.
This revised and updated second edition provides a practical and structured overview of some of the most commonly used and easily available cognitive screening instruments applicable in the outpatient clinic and bedside setting. It now includes additional chapters on AD8 and also methodological aspects of systematic cognitive screening instrument assessment from the Cochrane Dementia and Cognitive Improvement Group. Expert authors from around the world equip the reader with clear instructions on the usage of each screening instrument, its strengths and weaknesses, and the time required for administration. Rules on scoring are also provided, such as how to correct for variations in the patient’s age or education, and suggested cut-off scores. Cognitive Screening Instruments: A Practical Approach, Second Edition is aimed at both clinicians and professionals in disciplines allied to medicine who are called upon to assess patients with possible cognitive disorders, including neurologists, old age psychiatrists, neuropsychologists, primary care physicians, dementia support workers, and members of memory assessment teams.
Psychosis in Childhood and Adolescence offers an in-depth examination of the nature of psychosis, its risk factors and its manifestations in children and adolescents who experience a continuum of emotional disorders. The chapters present a hopeful, research-based framework for treatment. They emphasize combined treatment that is based on psychodynamic and cognitive behavioral psychotherapy principles, pharmacological interventions and supportive family approaches that reflect the vulnerabilities and resources of the individual child. This text highlights the importance of thorough assessment and the need for long-term treatment that facilitates the psychotic child’s healthy maturation. Readers will benefit from the case examples that illustrate the complexity of psychosis and the discussions of diagnostic and treatment issues as presented by experienced clinicians and researchers.
Solutions manual to accompany Logic and Discrete Mathematics: A Concise Introduction This book features a unique combination of comprehensive coverage of logic with a solid exposition of the most important fields of discrete mathematics, presenting material that has been tested and refined by the authors in university courses taught over more than a decade. Written in a clear and reader-friendly style, each section ends with an extensive set of exercises, most of them provided with complete solutions which are available in this accompanying solutions manual.
This book contains AI Escargot, the world famous sudoku puzzle which became the most difficult sudoku puzzle known in 2006. There are also several hints for solving AI Escargot in the shortest and most logical way. In addition, the book has 166 other sudoku puzzles in 11 categories. This makes it very convenient to find out your own level and to learn more! The author, Arto Inkala, is a puzzle creator and a doctor of science in the field of applied mathematics.
Offers easy-to-understand lessons and fun factoids that enable students to enrich their vocabularies.
Corporate Financial Analysis with Microsoft® Excel® visualizes spreadsheets as an effective management tool both for financial analysis and for coordinating its results and actions with marketing, sales, production and service operations, quality control, and other business functions. Taking an integrative view that promotes teamwork across corporate functions and responsibilities, the book contains dozens of charts, diagrams, and actual Excel® screenshots to reinforce the practical applications of every topic it covers. The first two sections—Financial Statements and Cash Budgeting—explain how to use spreadsheets for: Preparing income statements, balance sheets, and cash flow statements Performing vertical and horizontal analyses of financial statements Determining financial ratios and analyzing their trends and significance Combining quantitative and judgmental techniques to improve forecasts of sales revenues and customer demands Calculating and applying the time value of money Managing inventories, safety stocks, and the allocation of resources The third and final section—Capital Budgeting—covers capital structure, the cost of capital, and leverage; the basics of capital budgeting, including taxes and depreciation; applications, such as new facilities, equipment replacement, process improvement, leasing versus buying, and nonresidential real estate; and risk analysis of capital budgets and the potential impacts of unforeseen events. Corporate Financial Analysis with Microsoft® Excel® takes a broad view of financial functions and responsibilities in relation to those of other functional parts of modern corporations, and it demonstrates how to use spreadsheets to integrate and coordinate them. It provides many insightful examples and case studies of real corporations, including Wal- Mart, Sun Microsystems, Nike, H. J. Heinz, Dell, Microsoft, Apple Computer, and IBM. Corporate Financial Analysis with Microsoft® Excel® is the ideal tool for managing your firm’s short-term operations and long-term capital investments.