Download or read book Principles of Mathematical Problem Solving written by Martin J. Erickson and published by Pearson. This book was released on 1999 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: For introductory undergraduate courses in mathematics and problem-solving, students preparing for such academic contests as the William Lowell Putnam Mathematical Competition, and advanced high school students studying for the American Mathematical Olympiad. This book presents the principles and specific problem-solving methods that can be used to solve a variety of mathematical problems. The book provides clear examples of various problem-solving methods accompanied by numerous exercises and their solutions.
Download or read book Problem Solving Through Problems written by Loren C. Larson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematical Problem Solving written by ALAN H. SCHOENFELD and published by Elsevier. This book was released on 2014-06-28 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is addressed to people with research interests in the nature of mathematical thinking at any level, topeople 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.
Download or read book Principles of Mathematics Book 1 Set written by Katherine Loop and published by Master Books. This book was released on 2016-09-02 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Katherine Loop has done the remarkable! She has written a solid math course with a truly Biblical worldview. This course goes way beyond the same old Christian math course that teaches math with a few Scriptures sprinkled in and maybe some church-based word problems. This course truly transforms the way we see math. Katherine makes the argument that math is not a neutral subject as most have come to believe. She carefully lays the foundation of how math points to our Creator, the God of the Bible. The nature of God, His Creation, and even the Gospel itself is seen through the study of math. Katherine does a marvelous job of revealing His Glory in this one-of-a-kind math course. Katherine Loop's Principles of Mathematics Biblical Worldview Curriculum is a first of its kind. It takes math to a whole new level students and parents are going to love. It is a guaranteed faith grower!
Download or read book Principles of Mathematics Book 1 Teacher Guide written by Katherine Loop and published by New Leaf Publishing Group. This book was released on 2016-08-05 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: Teacher Guide for Book 1 of the Principles of Mathematics - Biblical Worldview Curriculum for junior high! Math is a real-life tool that points us to God and helps us explore His creation, yet it often comes across as dry facts and meaningless rules. Here at last is a curriculum that has a biblical worldview integrated throughout the text and problems, not just added as an afterthought. The resources in the Teacher Guide will help students master and apply the skills learned in the Student Textbook. What does this Teacher Guide include? Worksheets, Quizzes, and Tests: These perforated, three-hole punched pages help provide practice on the principles taught in the main student textbook.Answer Keys: The answers are included for the worksheets, quizzes, and tests found in this Teacher Guide.Schedule: A suggested calendar schedule is provided for completing the material in one year, though this can be adapted to meet individual student needs. There is also an accelerated schedule for completing the material in one semester. Are there any prerequisites for this course? This curriculum is aimed at grades 6-8, fitting into most math approaches the year or two years prior to starting high school algebra. If following traditional grade levels, Book 1 should be completed in grade 6 or 7, and Book 2 in grade 7 or 8. In Book 1 students should have a basic knowledge of arithmetic (basic arithmetic will be reviewed, but at a fast pace and while teaching problem-solving skills and a biblical worldview of math) and sufficient mental development to think through the concepts and examples given. Typically, anyone in sixth grade or higher should be prepared to begin. The focus of the course is actually learning math for life, not simply preparing to pass a test.
Download or read book Problem Solving Strategies written by Arthur Engel and published by Springer Science & Business Media. This book was released on 2008-01-19 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Inventive Principles of Mathematical Problem Solving written by Richard Beekman and published by . This book was released on 2005-08 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents 72 important principles for solving mathematics problems. The principles can be used as a foundation for further study in higher mathematics, or to prepare for mathematical competitions.
Download or read book 5 Principles of the Modern Mathematics Classroom written by Gerald Aungst and published by Corwin Press. This book was released on 2015-10-09 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students pursue problems they’re curious about, not problems they’re told to solve. Creating a math classroom filled with confident problem solvers starts by introducing challenges discovered in the real world, not by presenting a sequence of prescribed problems, says Gerald Aungst. In this groundbreaking book, he offers a thoughtful approach for instilling a culture of learning in your classroom through five powerful, yet straightforward principles: Conjecture, Collaboration, Communication, Chaos, and Celebration. Aungst shows you how to Embrace collaboration and purposeful chaos to help students engage in productive struggle, using non-routine and unsolved problems Put each chapter’s principles into practice through a variety of strategies, activities, and by incorporating technology tools Introduce substantive, lasting cultural changes in your classroom through a manageable, gradual shift in processes and behaviors Five Principles of the Modern Mathematics Classroom offers new ideas for inspiring math students by building a more engaging and collaborative learning environment. "Bravo! This book brings a conceptual framework for K-12 mathematics to life. As a parent and as the executive director of Edutopia, I commend Aungst for sharing his 5 principles. This is a perfect blend of inspiring and practical. Highly recommended!" Cindy Johanson, Executive Director, Edutopia George Lucas Educational Foundation "Aungst ignites the magic of mathematics by reminding us what makes mathematicians so passionate about their subject matter. Grounded in research, his work takes us on a journey into classrooms so that we may take away tips to put into practice today." Erin Klein, Teacher, Speaker, and Author of Redesigning Learning Spaces
Download or read book The Art of Mathematical Problem Solving written by Richard M. Beekman and published by Lulu.com. This book was released on 2016-01-30 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Street Fighting Mathematics written by Sanjoy Mahajan and published by MIT Press. This book was released on 2010-03-05 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.
Download or read book Exploring Mathematics written by Daniel Grieser and published by Springer. This book was released on 2018-05-21 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Have you ever faced a mathematical problem and had no idea how to approach it? Or perhaps you had an idea but got stuck halfway through? This book guides you in developing your creativity, as it takes you on a voyage of discovery into mathematics. Readers will not only learn strategies for solving problems and logical reasoning, but they will also learn about the importance of proofs and various proof techniques. Other topics covered include recursion, mathematical induction, graphs, counting, elementary number theory, and the pigeonhole, extremal and invariance principles. Designed to help students make the transition from secondary school to university level, this book provides readers with a refreshing look at mathematics and deep insights into universal principles that are valuable far beyond the scope of this book. Aimed especially at undergraduate and secondary school students as well as teachers, this book will appeal to anyone interested in mathematics. Only basic secondary school mathematics is required, including an understanding of numbers and elementary geometry, but no calculus. Including numerous exercises, with hints provided, this textbook is suitable for self-study and use alongside lecture courses.
Download or read book Strategies of Problem Solving written by Maria Nogin and published by Createspace Independent Publishing Platform. This book was released on 2014-06-24 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Art and Craft of Problem Solving written by Paul Zeitz and published by John Wiley & Sons. This book was released on 2017 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Puzzles Paradoxes and Problem Solving written by Marilyn A. Reba and published by CRC Press. This book was released on 2014-12-15 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Classroom-Tested, Alternative Approach to Teaching Math for Liberal Arts Puzzles, Paradoxes, and Problem Solving: An Introduction to Mathematical Thinking uses puzzles and paradoxes to introduce basic principles of mathematical thought. The text is designed for students in liberal arts mathematics courses. Decision-making situations that progress from recreational problems to important contemporary applications develop the critical-thinking skills of non-science and non-technical majors. The logical underpinnings of this textbook were developed and refined throughout many years of classroom feedback and in response to commentary from presentations at national conferences. The text’s five units focus on graphs, logic, probability, voting, and cryptography. The authors also cover related areas, such as operations research, game theory, number theory, combinatorics, statistics, and circuit design. The text uses a core set of common representations, strategies, and algorithms to analyze diverse games, puzzles, and applications. This unified treatment logically connects the topics with a recurring set of solution approaches. Requiring no mathematical prerequisites, this book helps students explore creative mathematical thinking and enhance their own critical-thinking skills. Students will acquire quantitative literacy and appreciation of mathematics through the text’s unified approach and wide range of interesting applications.
Download or read book Solving Mathematical Problems written by Terence Tao and published by OUP Oxford. This book was released on 2006-07-28 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Winning Solutions written by Edward Lozansky and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the mathematical tools and problem-solving experience needed to successfully compete in high-level problem solving competitions. Each section presents important background information and then provides a variety of worked examples and exercises to help bridge the gap between what the reader may already know and what is required for high-level competitions. Answers or sketches of the solutions are given for all exercises.
Download or read book The Elements of Problem Solving written by Jared M. Maruskin and published by Solar Crest Publishing LLC. This book was released on 2013 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
