Thinking About Mathematics

Author : Stewart Shapiro
Publisher : OUP Oxford
ISBN 13 : 0192893068
Total Pages : 323 pages
Book Rating : 4.62/5 ( download)

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Download or read book Thinking about Mathematics written by Stewart Shapiro and published by OUP Oxford. This book was released on 2000-07-13 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thinking about Mathematics covers the range of philosophical issues and positions concerning mathematics. The text describes the questions about mathematics that motivated philosophers throughout history and covers historical figures such as Plato, Aristotle, Kant, and Mill. It also presents the major positions and arguments concerning mathematics throughout the twentieth century, bringing the reader up to the present positions and battle lines.

Author : Jordan Ellenberg
Publisher : Penguin
ISBN 13 : 0143127535
Total Pages : 482 pages
Book Rating : 4.36/5 ( download)

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Download or read book How Not to Be Wrong written by Jordan Ellenberg and published by Penguin. This book was released on 2015-05-26 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Witty, compelling, and just plain fun to read . . ." —Evelyn Lamb, Scientific American The Freakonomics of math—a math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it. Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer? How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God. Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.

Author : Peter Liljedahl
Publisher : Corwin Press
ISBN 13 : 1544374844
Total Pages : 454 pages
Book Rating : 4.40/5 ( download)

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Download or read book Building Thinking Classrooms in Mathematics, Grades K-12 written by Peter Liljedahl and published by Corwin Press. This book was released on 2020-09-28 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thinking student is an engaged student Teachers often find it difficult to implement lessons that help students go beyond rote memorization and repetitive calculations. In fact, institutional norms and habits that permeate all classrooms can actually be enabling "non-thinking" student behavior. Sparked by observing teachers struggle to implement rich mathematics tasks to engage students in deep thinking, Peter Liljedahl has translated his 15 years of research into this practical guide on how to move toward a thinking classroom. Building Thinking Classrooms in Mathematics, Grades K–12 helps teachers implement 14 optimal practices for thinking that create an ideal setting for deep mathematics learning to occur. This guide Provides the what, why, and how of each practice and answers teachers’ most frequently asked questions Includes firsthand accounts of how these practices foster thinking through teacher and student interviews and student work samples Offers a plethora of macro moves, micro moves, and rich tasks to get started Organizes the 14 practices into four toolkits that can be implemented in order and built on throughout the year When combined, these unique research-based practices create the optimal conditions for learner-centered, student-owned deep mathematical thinking and learning, and have the power to transform mathematics classrooms like never before.

Author : William Byers
Publisher : Princeton University Press
ISBN 13 : 0691145997
Total Pages : 424 pages
Book Rating : 4.90/5 ( download)

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Download or read book How Mathematicians Think written by William Byers and published by Princeton University Press. This book was released on 2010-05-02 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results. Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure. The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory? Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself.

Author : Ted H. Hull
Publisher : Corwin Press
ISBN 13 : 1452269408
Total Pages : 184 pages
Book Rating : 4.05/5 ( download)

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Download or read book Visible Thinking in the K–8 Mathematics Classroom written by Ted H. Hull and published by Corwin Press. This book was released on 2011-01-21 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Seeing is believing with this interactive approach to math instruction Do you ever wish your students could read each other’s thoughts? Now they can—and so can you! This newest book by veteran mathematics educators provides instructional strategies for maximizing students’ mathematics comprehension by integrating visual thinking into the classroom. Included are numerous grade-specific sample problems for teaching essential concepts such as number sense, fractions, and estimation. Among the many benefits of visible thinking are: Interactive student-to-student learning Increased class participation Development of metacognitive thinking and problem-solving skills

Author : Keith J. Devlin
Publisher :
ISBN 13 : 9780615653631
Total Pages : 0 pages
Book Rating : 4.34/5 ( download)

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Download or read book Introduction to Mathematical Thinking written by Keith J. Devlin and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Mathematical thinking is not the same as 'doing math'--unless you are a professional mathematician. For most people, 'doing math' means the application of procedures and symbolic manipulations. Mathematical thinking, in contrast, is what the name reflects, a way of thinking about things in the world that humans have developed over three thousand years. It does not have to be about mathematics at all, which means that many people can benefit from learning this powerful way of thinking, not just mathematicians and scientists."--Back cover.

Author : Kevin Houston
Publisher : Cambridge University Press
ISBN 13 : 1139477056
Total Pages : 341 pages
Book Rating : 4.55/5 ( download)

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Download or read book How to Think Like a Mathematician written by Kevin Houston and published by Cambridge University Press. This book was released on 2009-02-12 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: Looking for a head start in your undergraduate degree in mathematics? Maybe you've already started your degree and feel bewildered by the subject you previously loved? Don't panic! This friendly companion will ease your transition to real mathematical thinking. Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician.

Author : Edward B. Burger
Publisher : Springer Science & Business Media
ISBN 13 : 9781931914413
Total Pages : 798 pages
Book Rating : 4.19/5 ( download)

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Download or read book The Heart of Mathematics written by Edward B. Burger and published by Springer Science & Business Media. This book was released on 2004-08-18 with total page 798 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hallmark features include: * A focus on the important ideas of mathematics that students will retain long after their formal studies are complete. * An engaging and humorous style, written to be read and enjoyed. * Ten Life Lessons that readers will apply beyond their study of mathematics. * Use of a variety of visualization techniques that direct students to model their thinking and to actively explore the world around them. New to this Edition: * A new chapter, Deciding Wisely: Applications of Rigorous Thought, provides a thought-provoking capstone. * Expanded and improved statistics and probability content in Chapter 7, Taming Uncertainty. * Enhanced Mindscapes at the end of each section which ask the reader to review, apply and think deeply about the ideas presented in the chapter. * Radically superior ancillary package.

Author : Stewart Shapiro
Publisher : Oxford University Press
ISBN 13 : 0190287535
Total Pages : 856 pages
Book Rating : 4.35/5 ( download)

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Download or read book The Oxford Handbook of Philosophy of Mathematics and Logic written by Stewart Shapiro and published by Oxford University Press. This book was released on 2005-02-10 with total page 856 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas. This volume covers these disciplines in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 contributed chapters are by established experts in the field, and their articles contain both exposition and criticism as well as substantial development of their own positions. The essays, which are substantially self-contained, serve both to introduce the reader to the subject and to engage in it at its frontiers. Certain major positions are represented by two chapters--one supportive and one critical. The Oxford Handbook of Philosophy of Math and Logic is a ground-breaking reference like no other in its field. It is a central resource to those wishing to learn about the philosophy of mathematics and the philosophy of logic, or some aspect thereof, and to those who actively engage in the discipline, from advanced undergraduates to professional philosophers, mathematicians, and historians.

Author : Brian P. Katz
Publisher : American Mathematical Society
ISBN 13 : 1470465809
Total Pages : 189 pages
Book Rating : 4.03/5 ( download)

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Download or read book Distilling Ideas written by Brian P. Katz and published by American Mathematical Society. This book was released on 2021-09-01 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is not a spectator sport; successful students of mathematics grapple with ideas for themselves. Distilling Ideas presents a carefully designed sequence of exercises and theorem statements that challenge students to create proofs and concepts. As students meet these challenges, they discover strategies of proofs and strategies of thinking beyond mathematics. In other words, Distilling Ideas helps its users to develop the skills, attitudes, and habits of mind of a mathematician, and to enjoy the process of distilling and exploring ideas. Distilling Ideas is an ideal textbook for a first proof-based course. The text engages the range of students' preferences and aesthetics through a corresponding variety of interesting mathematical content from graphs, groups, and epsilon-delta calculus. Each topic is accessible to users without a background in abstract mathematics because the concepts arise from asking questions about everyday experience. All the common proof structures emerge as natural solutions to authentic needs. Distilling Ideas or any subset of its chapters is an ideal resource either for an organized Inquiry Based Learning course or for individual study.