With numerous exercises and assuming only basic mathematics, this text is ideal for students of 14 years and above in pure mathematics.

Author: Terence Tao

Publisher: Oxford University Press on Demand

ISBN: 0199205604

Category: Mathematics

Page: 103

View: 279

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 of 14 years and above in pure mathematics.

Seven problem-solving techniques include inference, classification of action sequences, subgoals, contradiction, working backward, relations between problems, and mathematical representation.

Author: Wayne A. Wickelgren

Publisher: Courier Corporation

ISBN: 9780486152684

Category: Science

Page: 288

View: 309

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.

Various elementary techniques for solving problems in algebra, geometry, and combinatorics are explored in this second edition of Mathematics as Problem Solving.

Author: Alexander Soifer

Publisher: Springer Science & Business Media

ISBN: 9780387746463

Category: Mathematics

Page: 106

View: 380

Various elementary techniques for solving problems in algebra, geometry, and combinatorics are explored in this second edition of Mathematics as Problem Solving. Each new chapter builds on the previous one, allowing the reader to uncover new methods for using logic to solve problems. Topics are presented in self-contained chapters, with classical solutions as well as Soifer's own discoveries. With roughly 200 different problems, the reader is challenged to approach problems from different angles. Mathematics as Problem Solving is aimed at students from high school through undergraduate levels and beyond, educators, and the general reader interested in the methods of mathematical problem solving.

Equally, this is a must-have for individuals interested in solving difficult and challenging problems.

Author: Arthur Engel

Publisher: Springer Science & Business Media

ISBN: 9780387982199

Category: Mathematics

Page: 403

View: 152

A unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. Written for trainers and participants of contests of all levels up to the highest level, this will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week", thus bringing a creative atmosphere into the classrooms. Equally, this is a must-have for individuals interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. In addition to being a valuable resource of mathematical problems and solution strategies, this is the most complete training book on the market.

Mathematics is a fine art, like painting, sculpture, or music. This book teaches the art of solving challenging mathematics problems. Part I presents a general process for solving problems.

Author: Richard M. Beekman

Publisher: Lulu.com

ISBN: 9781329428904

Category:

Page: 266

View: 270

Mathematics is a fine art, like painting, sculpture, or music. This book teaches the art of solving challenging mathematics problems. Part I presents a general process for solving problems. Part II contains 35 difficult and challenging mathematics problems with complete solutions. The goal is to teach the reader how to proceed from an initial state of "panic and fear" to finding a beautiful and elegant solution to a problem.

This comprehensive book illustrates how MathCAD can be used to solve many mathematical tasks, and provides the mathematical background to the MathCAD package.

Author: Hans Benker

Publisher: Springer Science & Business Media

ISBN: 1852331666

Category: Computers

Page: 505

View: 278

This comprehensive book illustrates how MathCAD can be used to solve many mathematical tasks, and provides the mathematical background to the MathCAD package. Based on the latest Version 8 Professional for Windows, this book Market: contains many solutions to basic mathematical tasks and is designed to be used as both a reference and tutorial for lecturers and students, as well as a practical manual for engineers, mathematicians and computer scientists.

This book contributes to both mathematical problem solving and the communication of mathematics by students, and the role of personal and home technologies in learning beyond school.

Author: Susana Carreira

Publisher: Springer

ISBN: 3319796984

Category: Education

Page: 255

View: 205

This book contributes to both mathematical problem solving and the communication of mathematics by students, and the role of personal and home technologies in learning beyond school. It does this by reporting on major results and implications of the [email protected] project that investigated youngsters’ mathematical problem solving and, in particular, their use of digital technologies in tackling, and communicating the results of their problem solving, in environments beyond school. The book has two focuses: Mathematical problem solving skills and strategies, forms of representing and expressing mathematical thinking, technological-based solutions; and students ́ and teachers ́ perspectives on mathematics learning, especially school compared to beyond-school mathematics.

This book is addressed to people with research interests in the nature of mathematical thinking at any level, to people with an interest in "higher-order thinking skills" in any domain, and to all mathematics teachers.

Author: ALAN H. SCHOENFELD

Publisher: Elsevier

ISBN: 9781483295480

Category: Mathematics

Page: 409

View: 240

This book is addressed to people with research interests in the nature of mathematical thinking at any level, to people with an interest in "higher-order thinking skills" in any domain, and to all mathematics teachers. The focal point of the book is a framework for the analysis of complex problem-solving behavior. That framework is presented in Part One, which consists of Chapters 1 through 5. It describes four qualitatively different aspects of complex intellectual activity: cognitive resources, the body of facts and procedures at one's disposal; heuristics, "rules of thumb" for making progress in difficult situations; control, having to do with the efficiency with which individuals utilize the knowledge at their disposal; and belief systems, one's perspectives regarding the nature of a discipline and how one goes about working in it. Part Two of the book, consisting of Chapters 6 through 10, presents a series of empirical studies that flesh out the analytical framework. These studies document the ways that competent problem solvers make the most of the knowledge at their disposal. They include observations of students, indicating some typical roadblocks to success. Data taken from students before and after a series of intensive problem-solving courses document the kinds of learning that can result from carefully designed instruction. Finally, observations made in typical high school classrooms serve to indicate some of the sources of students' (often counterproductive) mathematical behavior.

This book investigates problem solving approaches to mathematical problems that youngsters use in the wake of the growing availability of digital technologies, and how these approaches can be effective and productive for their unique needs.

Author: Susana Carreira

Publisher:

ISBN: 3319249096

Category: Educational technology

Page:

View: 683

This book investigates problem solving approaches to mathematical problems that youngsters use in the wake of the growing availability of digital technologies, and how these approaches can be effective and productive for their unique needs. The empirical research, conducted in the [email protected] project, delves into the many ways in which students can achieve the solution to a mathematical problem and communicate it with the technological tools they have at their disposal, either in their home environment or in their mathematics classroom. The researchers then address the implications for the future study of a broadened perspective on mathematical problem solving with technology. In addition to exploring how technology has changed mathematical problem solving, the book also provides: A well-developed theoretical framework that integrates the use of technology into mathematical problem-solving Insightful analysis of the young participants' methods of mathematical problem solving, in addition to their teachers and families Examples of student solutions, together with the students' explanations of how they achieved their solution Youngsters Solving Mathematical Problems with Technology is an extremely valuable resource for any researcher or educator interested in mat hematics education, technology in education, or the intersection of both.>.

This book shows how to solve math problems from general math, business math, consumer math, precalculus, calculus, geometry, statistics, and numerical topics using spreadsheets.

Author: Leonard Sperduto

Publisher: CreateSpace

ISBN: 144043753X

Category:

Page: 166

View: 218

This book shows how to solve math problems from general math, business math, consumer math, precalculus, calculus, geometry, statistics, and numerical topics using spreadsheets.

A comprehensive look at four of the most famous problems in mathematics Tales of Impossibility recounts the intriguing story of the renowned problems of antiquity, four of the most famous and studied questions in the history of mathematics.

Author: David S. Richeson

Publisher: Princeton University Press

ISBN: 9780691192963

Category: Mathematics

Page: 456

View: 201

A comprehensive look at four of the most famous problems in mathematics Tales of Impossibility recounts the intriguing story of the renowned problems of antiquity, four of the most famous and studied questions in the history of mathematics. First posed by the ancient Greeks, these compass and straightedge problems—squaring the circle, trisecting an angle, doubling the cube, and inscribing regular polygons in a circle—have served as ever-present muses for mathematicians for more than two millennia. David Richeson follows the trail of these problems to show that ultimately their proofs—which demonstrated the impossibility of solving them using only a compass and straightedge—depended on and resulted in the growth of mathematics. Richeson investigates how celebrated luminaries, including Euclid, Archimedes, Viète, Descartes, Newton, and Gauss, labored to understand these problems and how many major mathematical discoveries were related to their explorations. Although the problems were based in geometry, their resolutions were not, and had to wait until the nineteenth century, when mathematicians had developed the theory of real and complex numbers, analytic geometry, algebra, and calculus. Pierre Wantzel, a little-known mathematician, and Ferdinand von Lindemann, through his work on pi, finally determined the problems were impossible to solve. Along the way, Richeson provides entertaining anecdotes connected to the problems, such as how the Indiana state legislature passed a bill setting an incorrect value for pi and how Leonardo da Vinci made elegant contributions in his own study of these problems. Taking readers from the classical period to the present, Tales of Impossibility chronicles how four unsolvable problems have captivated mathematical thinking for centuries.

Measures student's approach to solving mathematical problems. student writes down entire solution to problems, including those that do not work. each problem is followed by questions about student's approach to the problem.

Author: Alan H. Schoenfeld

Publisher:

ISBN: OCLC:1130980929

Category: Mathematics

Page:

View: 518

Measures student's approach to solving mathematical problems. student writes down entire solution to problems, including those that do not work. each problem is followed by questions about student's approach to the problem.

The authors provide a general overview of the MATLAB language and its graphics abilities before delving into problem solving, making the book useful for readers without prior MATLAB experi

Author:

Publisher: CRC Press

ISBN: 1420082515

Category: Mathematics

Page: 446

View: 152

This textbook presents a variety of applied mathematics topics in science and engineering with an emphasis on problem solving techniques using MATLAB®. The authors provide a general overview of the MATLAB language and its graphics abilities before delving into problem solving, making the book useful for readers without prior MATLAB experience. They explain how to generate code suitable for various applications so that readers can apply the techniques to problems not covered in the book. Examples, figures, and MATLAB scripts enable readers with basic mathematics knowledge to solve various applied math problems in their fields while avoiding unnecessary technical details.

In such cases we provide the proof. The book contains over 300 problems on various topics and detailed solutions of approximately half of them. This book is primarily intended for high school and college students and mathematics teachers.

Solving mathematical problems is both a science and an art. It is a science because we need to learn some basic concepts and skills, and use proper terminology when explaining our solution to other people. It is also an art because very often we need to be creative. There are infinitely many types of math problems, and it is impossible to learn how to solve every problem in the world. However, there are a few basic principles that are good to know. There are a few approaches and methods that are often useful. In this book, we discuss the major ones, including various types of proofs, the pigeon hole principle, the principle of mathematical induction, invariants, coloring, etc. In each chapter, we provide basic definitions and facts to get you started. We do not prove most of the well-known facts given in this book, since our main goal is to learn how to solve problems, i.e. use these facts. They are usually proved in other college courses such as abstract algebra, number theory, and analysis. Sometimes, however, the idea of a proof of a theorem can be used for solving many problems. In such cases we provide the proof. The book contains over 300 problems on various topics and detailed solutions of approximately half of them. This book is primarily intended for high school and college students and mathematics teachers. Most chapters are accessible to middle school students as well. It would especially be helpful for those competing in mathematics contests and wishing to improve their problem solving skills. The first edition contained some minor errors which have been fixed in the second edition. More problems were also added.

This book, written by an accomplished female mathematician, is the second to explore nonstandard mathematical problems – those that are not directly solved by standard mathematical methods but instead rely on insight and the synthesis of ...

Author: Ellina Grigorieva

Publisher: Birkhäuser

ISBN: 9783319198873

Category: Mathematics

Page: 327

View: 326

This book, written by an accomplished female mathematician, is the second to explore nonstandard mathematical problems – those that are not directly solved by standard mathematical methods but instead rely on insight and the synthesis of a variety of mathematical ideas. It promotes mental activity as well as greater mathematical skills, and is an ideal resource for successful preparation for the mathematics Olympiad. Numerous strategies and techniques are presented that can be used to solve intriguing and challenging problems of the type often found in competitions. The author uses a friendly, non-intimidating approach to emphasize connections between different fields of mathematics and often proposes several different ways to attack the same problem. Topics covered include functions and their properties, polynomials, trigonometric and transcendental equations and inequalities, optimization, differential equations, nonlinear systems, and word problems. Over 360 problems are included with hints, answers, and detailed solutions. Methods of Solving Nonstandard Problems will interest high school and college students, whether they are preparing for a math competition or looking to improve their mathematical skills, as well as anyone who enjoys an intellectual challenge and has a special love for mathematics. Teachers and college professors will be able to use it as an extra resource in the classroom to augment a conventional course of instruction in order to stimulate abstract thinking and inspire original thought.

This book is the first in the series of the yearbooks of the Association of Mathematics Educators in Singapore.

Author: Berinderjeet Kaur

Publisher: World Scientific

ISBN: 9789814277228

Category: Education

Page: 287

View: 351

This book is the first in the series of the yearbooks of the Association of Mathematics Educators in Singapore. It is highly unique as it addresses a focused theme of mathematics education. The chapters of the book illustrate the immense diversity within the theme and presents research that translates into classroom pedagogies. The chapters of the book illustrate how mathematical problems may be crafted and infused in classroom teaching. Several novel pedagogies, such as learning mathematics through productive failure, problem posing and generative activities are presented in the book. The chapters are comprehensive and laden with evidence-based examples for both mathematics educators and classroom teachers of mathematics. The book is an invaluable contribution towards the already established field of research of mathematical problem solving. It is also a must read for graduate research students and mathematics educators.

Shuk-Kwan S. Leung Abstract Getting teachers to enact mathematical problem posing (MPP) and having children do mathematics in the making (How to solve it? Princeton University Press, Princeton, NJ, 1945) is not easy.

Author: Patricio Felmer

Publisher: Springer

ISBN: 9783319280233

Category: Education

Page: 402

View: 645

This book collects recent research on posing and solving mathematical problems. Rather than treating these two crucial aspects of school mathematics as separate areas of study, the authors approach them as a unit where both areas are measured on equal grounds in relation to each other. The contributors are from a vast variety of countries and with a wide range of experience; it includes the work from many of the leading researchers in the area and an important number of young researchers. The book is divided in three parts, one directed to new research perspectives and the other two directed to teachers and students, respectively.