Thinking Like A Mathematician

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How to Think Like a Mathematician

Kevin Houston
How to Think Like a Mathematician Book PDF

Author : Kevin Houston
Publisher : Cambridge University Press
Page : 128 pages
File Size : 40,5 Mb
Release : 2009-02-12
Category : Mathematics
ISBN : 1139477056

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How to Think Like a Mathematician by Kevin Houston Pdf

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.

How to Think Like a Mathematician

Kevin Houston
How to Think Like a Mathematician Book PDF

Author : Kevin Houston
Publisher : Cambridge University Press
Page : 279 pages
File Size : 52,9 Mb
Release : 2009-02-12
Category : Juvenile Nonfiction
ISBN : 9780521895460

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How to Think Like a Mathematician by Kevin Houston Pdf

This arsenal of tips and techniques eases new students into undergraduate mathematics, unlocking the world of definitions, theorems, and proofs.

How to Think Like a Mathematician

Kevin Houston
How to Think Like a Mathematician Book PDF

Author : Kevin Houston
Publisher : Unknown
Page : 0 pages
File Size : 43,5 Mb
Release : 2009
Category : Electronic books
ISBN : 0511506457

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How to Think Like a Mathematician by Kevin Houston Pdf

This arsenal of tips and techniques eases new students into undergraduate mathematics, unlocking the world of definitions, theorems, and proofs.

Thinking Like a Mathematician

Mary-Lyons Walk Hanks,Jennifer K. Lampert,Katherine Plum
Thinking Like a Mathematician Book PDF

Author : Mary-Lyons Walk Hanks,Jennifer K. Lampert,Katherine Plum
Publisher : Routledge
Page : 149 pages
File Size : 41,7 Mb
Release : 2021-10-10
Category : Education
ISBN : 9781000489910

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Thinking Like a Mathematician by Mary-Lyons Walk Hanks,Jennifer K. Lampert,Katherine Plum Pdf

Thinking Like a Mathematician focuses on high-interest, career-related topics in the elementary curriculum related to mathematics. Students will explore interdisciplinary content, foster creativity, and develop higher order thinking skills with activities aligned to relevant content area standards. Students will engage in exploration activities, complete mathematical challenges, and then apply what they have learned by making real-world connections. Thinking Like a Mathematician reflects key emphases of curricula from the Center for Gifted Education at William & Mary, including the development of process skills in various content areas and the enhancement of discipline-specific thinking and habits of mind through hands-on activities. Grade 3

The Art of Logic in an Illogical World

Eugenia Cheng
The Art of Logic in an Illogical World Book PDF

Author : Eugenia Cheng
Publisher : Basic Books
Page : 321 pages
File Size : 52,8 Mb
Release : 2018-09-11
Category : Mathematics
ISBN : 9781541672505

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The Art of Logic in an Illogical World by Eugenia Cheng Pdf

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 Mathematicians Think

William Byers
How Mathematicians Think Book PDF

Author : William Byers
Publisher : Princeton University Press
Page : 424 pages
File Size : 53,7 Mb
Release : 2010-05-02
Category : Mathematics
ISBN : 9780691145990

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How Mathematicians Think by William Byers Pdf

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.

How Not to Be Wrong

Jordan Ellenberg
How Not to Be Wrong Book PDF

Author : Jordan Ellenberg
Publisher : Penguin Press
Page : 480 pages
File Size : 42,5 Mb
Release : 2014-05-29
Category : Mathematics
ISBN : 9781594205224

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How Not to Be Wrong by Jordan Ellenberg Pdf

A brilliant tour of mathematical thought and a guide to becoming a better thinker, How Not to Be Wrong shows that math is not just a long list of rules to be learned and carried out by rote. Math touches everything we do; It's what makes the world make sense. Using the mathematician's methods and hard-won insights-minus the jargon-professor and popular columnist Jordan Ellenberg guides general readers through his ideas with rigor and lively irreverence, infusing everything from election results to baseball to the existence of God and the psychology of slime molds with a heightened sense of clarity and wonder. Armed with the tools of mathematics, we can see the hidden structures beneath the messy and chaotic surface of our daily lives. How Not to Be Wrong shows us how--Publisher's description.

Thinking in Problems

Alexander A. Roytvarf
Thinking in Problems Book PDF

Author : Alexander A. Roytvarf
Publisher : Springer Science & Business Media
Page : 405 pages
File Size : 49,8 Mb
Release : 2013-01-04
Category : Mathematics
ISBN : 9780817684068

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Thinking in Problems by Alexander A. Roytvarf Pdf

This concise, self-contained textbook gives an in-depth look at problem-solving from a mathematician’s point-of-view. Each chapter builds off the previous one, while introducing a variety of methods that could be used when approaching any given problem. Creative thinking is the key to solving mathematical problems, and this book outlines the tools necessary to improve the reader’s technique. The text is divided into twelve chapters, each providing corresponding hints, explanations, and finalization of solutions for the problems in the given chapter. For the reader’s convenience, each exercise is marked with the required background level. This book implements a variety of strategies that can be used to solve mathematical problems in fields such as analysis, calculus, linear and multilinear algebra and combinatorics. It includes applications to mathematical physics, geometry, and other branches of mathematics. Also provided within the text are real-life problems in engineering and technology. Thinking in Problems is intended for advanced undergraduate and graduate students in the classroom or as a self-study guide. Prerequisites include linear algebra and analysis.

The Math Gene

Keith Devlin
The Math Gene Book PDF

Author : Keith Devlin
Publisher : Basic Books
Page : 352 pages
File Size : 46,6 Mb
Release : 2001-05-17
Category : Science
ISBN : 9780786725083

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The Math Gene by Keith Devlin Pdf

Why is math so hard? And why, despite this difficulty, are some people so good at it? If there's some inborn capacity for mathematical thinking—which there must be, otherwise no one could do it —why can't we all do it well? Keith Devlin has answers to all these difficult questions, and in giving them shows us how mathematical ability evolved, why it's a part of language ability, and how we can make better use of this innate talent.He also offers a breathtakingly new theory of language development—that language evolved in two stages, and its main purpose was not communication—to show that the ability to think mathematically arose out of the same symbol-manipulating ability that was so crucial to the emergence of true language. Why, then, can't we do math as well as we can speak? The answer, says Devlin, is that we can and do—we just don't recognize when we're using mathematical reasoning.

Introduction to Mathematical Thinking

Keith J. Devlin
Introduction to Mathematical Thinking Book PDF

Author : Keith J. Devlin
Publisher : Unknown
Page : 0 pages
File Size : 55,8 Mb
Release : 2012
Category : Mathematics
ISBN : 0615653634

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Introduction to Mathematical Thinking by Keith J. Devlin Pdf

"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.

Think Like a Mathematician

Anne Rooney
Think Like a Mathematician Book PDF

Author : Anne Rooney
Publisher : 'The Rosen Publishing Group, Inc'
Page : 162 pages
File Size : 50,5 Mb
Release : 2021-07-15
Category : Young Adult Nonfiction
ISBN : 9781499470918

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Think Like a Mathematician by Anne Rooney Pdf

Mathematics is all around us. It is the universal language that allows us to work with numbers, patterns, processes, and the rules that govern the entire universe. Math enables us to understand our surroundings and model and predict phenomena. This insightful and comprehensive volume answers a series of compelling mathematical and life-related questions in an entertaining and informative way, showing inquisitive readers how math is the basis for just about everything they experience in their daily lives.

Secondary Mathematics for Mathematicians and Educators

Michael Weiss
Secondary Mathematics for Mathematicians and Educators Book PDF

Author : Michael Weiss
Publisher : Routledge
Page : 289 pages
File Size : 41,5 Mb
Release : 2020-10-05
Category : Education
ISBN : 9781351587679

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Secondary Mathematics for Mathematicians and Educators by Michael Weiss Pdf

In this engaging text, Michael Weiss offers an advanced view of the secondary mathematics curriculum through the prism of theory, analysis, and history, aiming to take an intellectually and mathematically mature perspective on the content normally taught in high school mathematics courses. Rather than a secondary mathematics textbook, Weiss presents here a textbook about the secondary mathematics curriculum, written for mathematics educators and mathematicians and presenting a long-overdue modern-day integration of the disparate topics and methods of secondary mathematics into a coherent mathematical theory. Areas covered include: Polynomials and polynomial functions; Geometry, graphs, and symmetry; Abstract algebra, linear algebra, and solving equations; Exponential and logarithmic functions; Complex numbers; The historical development of the secondary mathematics curriculum. Written using precise definitions and proofs throughout on a foundation of advanced content knowledge, Weiss offers a compelling and timely investigation into the secondary mathematics curriculum, relevant for preservice secondary teachers as well as graduate students and scholars in both mathematics and mathematics education.

Mathematical Thinking and Writing

Randall Maddox
Mathematical Thinking and Writing Book PDF

Author : Randall Maddox
Publisher : Academic Press
Page : 324 pages
File Size : 42,9 Mb
Release : 2002
Category : Mathematics
ISBN : 9780124649767

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Mathematical Thinking and Writing by Randall Maddox Pdf

The ability to construct proofs is one of the most challenging aspects of the world of mathematics. It is, essentially, the defining moment for those testing the waters in a mathematical career. Instead of being submerged to the point of drowning, readers of Mathematical Thinking and Writing are given guidance and support while learning the language of proof construction and critical analysis. Randall Maddox guides the reader with a warm, conversational style, through the task of gaining a thorough understanding of the proof process, and encourages inexperienced mathematicians to step up and learn how to think like a mathematician. A student's skills in critical analysis will develop and become more polished than previously conceived. Most significantly, Dr. Maddox has the unique approach of using analogy within his book to clarify abstract ideas and clearly demonstrate methods of mathematical precision.

x+y

Eugenia Cheng
x y Book PDF

Author : Eugenia Cheng
Publisher : Profile Books
Page : 128 pages
File Size : 51,9 Mb
Release : 2020-07-16
Category : Mathematics
ISBN : 9781782834434

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x+y by Eugenia Cheng Pdf

From imaginary numbers to the fourth dimension and beyond, mathematics has always been about imagining things that seem impossible at first glance. In x+y, Eugenia Cheng draws on the insights of higher-dimensional mathematics to reveal a transformative new way of talking about the patriarchy, mansplaining and sexism: a way that empowers all of us to make the world a better place. Using precise mathematical reasoning to uncover everything from the sexist assumptions that make society a harder place for women to live to the limitations of science and statistics in helping us understand the link between gender and society, Cheng's analysis replaces confusion with clarity, brings original thinking to well worn arguments - and provides a radical, illuminating and liberating new way of thinking about the world and women's place in it.

Thnking Mathematically

J Mason,L. Burton,K. Stacey
Thnking Mathematically Book PDF

Author : J Mason,L. Burton,K. Stacey
Publisher : Pearson Higher Ed
Page : 266 pages
File Size : 45,6 Mb
Release : 2011-01-10
Category : Mathematics
ISBN : 9780273728924

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Thnking Mathematically by J Mason,L. Burton,K. Stacey Pdf

Thinking Mathematically is perfect for anyone who wants to develop their powers to think mathematically, whether at school, at university or just out of interest. This book is invaluable for anyone who wishes to promote mathematical thinking in others or for anyone who has always wondered what lies at the core of mathematics. Thinking Mathematically reveals the processes at the heart of mathematics and demonstrates how to encourage and develop them. Extremely practical, it involves the reader in questions so that subsequent discussions speak to immediate experience.