Ways To Think About Mathematics

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How Not to Be Wrong

Author : Jordan Ellenberg
Publisher : Penguin
ISBN 13 : 0143127535
Total Pages : 482 pages
Book Rating : 4.1/5 (431 download)

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Book Synopsis How Not to Be Wrong by : Jordan Ellenberg

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.

How Mathematicians Think

Author : William Byers
Publisher : Princeton University Press
ISBN 13 : 0691145997
Total Pages : 424 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis How Mathematicians Think by : William Byers

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.

The Art of Logic in an Illogical World

Author : Eugenia Cheng
Publisher : Basic Books
ISBN 13 : 154167250X
Total Pages : 321 pages
Book Rating : 4.5/5 (416 download)

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Book Synopsis The Art of Logic in an Illogical World by : Eugenia Cheng

Download or read book The Art of Logic in an Illogical World written by Eugenia Cheng and published by Basic Books. This book was released on 2018-09-11 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: How both logical and emotional reasoning can help us live better in our post-truth world In a world where fake news stories change election outcomes, has rationality become futile? In The Art of Logic in an Illogical World, Eugenia Cheng throws a lifeline to readers drowning in the illogic of contemporary life. Cheng is a mathematician, so she knows how to make an airtight argument. But even for her, logic sometimes falls prey to emotion, which is why she still fears flying and eats more cookies than she should. If a mathematician can't be logical, what are we to do? In this book, Cheng reveals the inner workings and limitations of logic, and explains why alogic -- for example, emotion -- is vital to how we think and communicate. Cheng shows us how to use logic and alogic together to navigate a world awash in bigotry, mansplaining, and manipulative memes. Insightful, useful, and funny, this essential book is for anyone who wants to think more clearly.

How to Think Like a Mathematician

Author : Kevin Houston
Publisher : Cambridge University Press
ISBN 13 : 1139477056
Total Pages : 341 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis How to Think Like a Mathematician by : Kevin Houston

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.

Ways to Think About Mathematics

Author : Steve Benson
Publisher : Corwin Press
ISBN 13 : 9780761931058
Total Pages : 266 pages
Book Rating : 4.9/5 (31 download)

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Book Synopsis Ways to Think About Mathematics by : Steve Benson

Download or read book Ways to Think About Mathematics written by Steve Benson and published by Corwin Press. This book was released on 2004-10-05 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Funded by the National Science Foundation and successfully field-tested in a variety of settings, the materials presented give teachers the opportunity to grow as learners for the classes they teach.

Introduction to Graph Theory

Author : Richard J. Trudeau
Publisher : Courier Corporation
ISBN 13 : 0486318664
Total Pages : 224 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis Introduction to Graph Theory by : Richard J. Trudeau

Download or read book Introduction to Graph Theory written by Richard J. Trudeau and published by Courier Corporation. This book was released on 2013-04-15 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at "the mathematically traumatized," this text offers nontechnical coverage of graph theory, with exercises. Discusses planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. 1976 edition.

Introduction to Mathematical Thinking

Author : Keith J. Devlin
Publisher :
ISBN 13 : 9780615653631
Total Pages : 0 pages
Book Rating : 4.6/5 (536 download)

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Book Synopsis Introduction to Mathematical Thinking by : Keith J. Devlin

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.

Building Thinking Classrooms in Mathematics, Grades K-12

Author : Peter Liljedahl
Publisher : Corwin Press
ISBN 13 : 1544374844
Total Pages : 454 pages
Book Rating : 4.5/5 (443 download)

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Book Synopsis Building Thinking Classrooms in Mathematics, Grades K-12 by : Peter Liljedahl

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.

Mathematics for Human Flourishing

Author : Francis Su
Publisher : Yale University Press
ISBN 13 : 0300237138
Total Pages : 287 pages
Book Rating : 4.3/5 (2 download)

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Book Synopsis Mathematics for Human Flourishing by : Francis Su

Download or read book Mathematics for Human Flourishing written by Francis Su and published by Yale University Press. This book was released on 2020-01-07 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The ancient Greeks argued that the best life was filled with beauty, truth, justice, play and love. The mathematician Francis Su knows just where to find them."--Kevin Hartnett, Quanta Magazine" This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart."--James Tanton, Global Math Project For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas. In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires--such as for play, beauty, freedom, justice, and love--and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother's, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher's letters to the author appear throughout the book and show how this intellectual pursuit can--and must--be open to all.

How Humans Learn to Think Mathematically

Author : David Tall
Publisher : Cambridge University Press
ISBN 13 : 1107035708
Total Pages : 483 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis How Humans Learn to Think Mathematically by : David Tall

Download or read book How Humans Learn to Think Mathematically written by David Tall and published by Cambridge University Press. This book was released on 2013-09-02 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: How Humans Learn to Think Mathematically describes the development of mathematical thinking from the young child to the sophisticated adult. Professor David Tall reveals the reasons why mathematical concepts that make sense in one context may become problematic in another. For example, a child's experience of whole number arithmetic successively affects subsequent understanding of fractions, negative numbers, algebra, and the introduction of definitions and proof. Tall's explanations for these developments are accessible to a general audience while encouraging specialists to relate their areas of expertise to the full range of mathematical thinking. The book offers a comprehensive framework for understanding mathematical growth, from practical beginnings through theoretical developments, to the continuing evolution of mathematical thinking at the highest level.

Mathematical Mindsets

Author : Jo Boaler
Publisher : John Wiley & Sons
ISBN 13 : 1118418271
Total Pages : 311 pages
Book Rating : 4.1/5 (184 download)

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Book Synopsis Mathematical Mindsets by : Jo Boaler

Download or read book Mathematical Mindsets written by Jo Boaler and published by John Wiley & Sons. This book was released on 2015-10-12 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Banish math anxiety and give students of all ages a clear roadmap to success Mathematical Mindsets provides practical strategies and activities to help teachers and parents show all children, even those who are convinced that they are bad at math, that they can enjoy and succeed in math. Jo Boaler—Stanford researcher, professor of math education, and expert on math learning—has studied why students don't like math and often fail in math classes. She's followed thousands of students through middle and high schools to study how they learn and to find the most effective ways to unleash the math potential in all students. There is a clear gap between what research has shown to work in teaching math and what happens in schools and at home. This book bridges that gap by turning research findings into practical activities and advice. Boaler translates Carol Dweck's concept of 'mindset' into math teaching and parenting strategies, showing how students can go from self-doubt to strong self-confidence, which is so important to math learning. Boaler reveals the steps that must be taken by schools and parents to improve math education for all. Mathematical Mindsets: Explains how the brain processes mathematics learning Reveals how to turn mistakes and struggles into valuable learning experiences Provides examples of rich mathematical activities to replace rote learning Explains ways to give students a positive math mindset Gives examples of how assessment and grading policies need to change to support real understanding Scores of students hate and fear math, so they end up leaving school without an understanding of basic mathematical concepts. Their evasion and departure hinders math-related pathways and STEM career opportunities. Research has shown very clear methods to change this phenomena, but the information has been confined to research journals—until now. Mathematical Mindsets provides a proven, practical roadmap to mathematics success for any student at any age.

What's Math Got to Do with It?

Author : Jo Boaler
Publisher : Penguin
ISBN 13 : 9780670019526
Total Pages : 296 pages
Book Rating : 4.0/5 (195 download)

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Book Synopsis What's Math Got to Do with It? by : Jo Boaler

Download or read book What's Math Got to Do with It? written by Jo Boaler and published by Penguin. This book was released on 2008 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses how to make mathematics for children enjoyable and why it is important for American children to succeed in mathematics and choose math-based career paths in the future.

Math with Bad Drawings

Author : Ben Orlin
Publisher : Black Dog & Leventhal
ISBN 13 : 0316509027
Total Pages : 556 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis Math with Bad Drawings by : Ben Orlin

Download or read book Math with Bad Drawings written by Ben Orlin and published by Black Dog & Leventhal. This book was released on 2018-09-18 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: A hilarious reeducation in mathematics-full of joy, jokes, and stick figures-that sheds light on the countless practical and wonderful ways that math structures and shapes our world. In Math With Bad Drawings, Ben Orlin reveals to us what math actually is; its myriad uses, its strange symbols, and the wild leaps of logic and faith that define the usually impenetrable work of the mathematician. Truth and knowledge come in multiple forms: colorful drawings, encouraging jokes, and the stories and insights of an empathetic teacher who believes that math should belong to everyone. Orlin shows us how to think like a mathematician by teaching us a brand-new game of tic-tac-toe, how to understand an economic crises by rolling a pair of dice, and the mathematical headache that ensues when attempting to build a spherical Death Star. Every discussion in the book is illustrated with Orlin's trademark "bad drawings," which convey his message and insights with perfect pitch and clarity. With 24 chapters covering topics from the electoral college to human genetics to the reasons not to trust statistics, Math with Bad Drawings is a life-changing book for the math-estranged and math-enamored alike.

The Calculus of Friendship

Author : Steven Strogatz
Publisher : Princeton University Press
ISBN 13 : 9781400830886
Total Pages : 184 pages
Book Rating : 4.8/5 (38 download)

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Book Synopsis The Calculus of Friendship by : Steven Strogatz

Download or read book The Calculus of Friendship written by Steven Strogatz and published by Princeton University Press. This book was released on 2011-03-07 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Calculus of Friendship is the story of an extraordinary connection between a teacher and a student, as chronicled through more than thirty years of letters between them. What makes their relationship unique is that it is based almost entirely on a shared love of calculus. For them, calculus is more than a branch of mathematics; it is a game they love playing together, a constant when all else is in flux. The teacher goes from the prime of his career to retirement, competes in whitewater kayaking at the international level, and loses a son. The student matures from high school math whiz to Ivy League professor, suffers the sudden death of a parent, and blunders into a marriage destined to fail. Yet through it all they take refuge in the haven of calculus--until a day comes when calculus is no longer enough. Like calculus itself, The Calculus of Friendship is an exploration of change. It's about the transformation that takes place in a student's heart, as he and his teacher reverse roles, as they age, as they are buffeted by life itself. Written by a renowned teacher and communicator of mathematics, The Calculus of Friendship is warm, intimate, and deeply moving. The most inspiring ideas of calculus, differential equations, and chaos theory are explained through metaphors, images, and anecdotes in a way that all readers will find beautiful, and even poignant. Math enthusiasts, from high school students to professionals, will delight in the offbeat problems and lucid explanations in the letters. For anyone whose life has been changed by a mentor, The Calculus of Friendship will be an unforgettable journey.

A Mind for Numbers

Author : Barbara A. Oakley
Publisher : TarcherPerigee
ISBN 13 : 039916524X
Total Pages : 338 pages
Book Rating : 4.3/5 (991 download)

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Book Synopsis A Mind for Numbers by : Barbara A. Oakley

Download or read book A Mind for Numbers written by Barbara A. Oakley and published by TarcherPerigee. This book was released on 2014-07-31 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. In her book, she offers you the tools needed to get a better grasp of that intimidating but inescapable field.

Understanding the Mathematical Way of Thinking – The Registers of Semiotic Representations

Author : Raymond Duval
Publisher : Springer
ISBN 13 : 3319569104
Total Pages : 117 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Understanding the Mathematical Way of Thinking – The Registers of Semiotic Representations by : Raymond Duval

Download or read book Understanding the Mathematical Way of Thinking – The Registers of Semiotic Representations written by Raymond Duval and published by Springer. This book was released on 2017-07-18 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, Raymond Duval shows how his theory of registers of semiotic representation can be used as a tool to analyze the cognitive processes through which students develop mathematical thinking. To Duval, the analysis of mathematical knowledge is in its essence the analysis of the cognitive synergy between different kinds of semiotic representation registers, because the mathematical way of thinking and working is based on transformations of semiotic representations into others. Based on this assumption, he proposes the use of semiotics to identify and develop the specific cognitive processes required to the acquisition of mathematical knowledge. In this volume he presents a method to do so, addressing the following questions: • How to situate the registers of representation regarding the other semiotic “theories” • Why use a semio-cognitive analysis of the mathematical activity to teach mathematics • How to distinguish the different types of registers • How to organize learning tasks and activities which take into account the registers of representation • How to make an analysis of the students’ production in terms of registers Building upon the contributions he first presented in his classic book Sémiosis et pensée humaine, in this volume Duval focuses less on theoretical issues and more on how his theory can be used both as a tool for analysis and a working method to help mathematics teachers apply semiotics to their everyday work. He also dedicates a complete chapter to show how his theory can be applied as a new strategy to teach geometry. “Understanding the Mathematical Way of Thinking – The Registers of Semiotic Representations is an essential work for mathematics educators and mathematics teachers who look for an introduction to Raymond Duval’s cognitive theory of semiotic registers of representation, making it possible for them to see and teach mathematics with fresh eyes.” Professor Tânia M. M. Campos, PHD.

Mathematical Problem Solving

Author : ALAN H. SCHOENFELD
Publisher : Elsevier
ISBN 13 : 1483295486
Total Pages : 409 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Mathematical Problem Solving by : ALAN H. SCHOENFELD

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 409 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, 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.