What Is Mathematics Pdf Book
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- 1941
- in Mathematics
What is Mathematics?
An Elementary Approach to Ideas and Methods
Author: Richard Courant
Publisher:
ISBN:
Category: Mathematics
Page: 521
View: 482
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- 1996
- in Mathematics
- Herbert Robbins Richard Courant (Ian Stewart)
What is Mathematics?
An Elementary Approach to Ideas and Methods
Author: Herbert Robbins Richard Courant (Ian Stewart)
Publisher: Oxford University Press, USA
ISBN:
Category: Mathematics
Page: 566
View: 651
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A discussion of fundamental mathematical principles from algebra to elementary calculus designed to promote constructive mathematical reasoning.
- 1999
- in Medical
- Reuben Hersh
What is Mathematics, Really?
Author: Reuben Hersh
Publisher: Oxford University Press, USA
ISBN:
Category: Medical
Page: 343
View: 926
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Tries to refine the philosophy of mathematics to reflect what mathematicians really do, and argues that mathematics must be understood in a social context.
- 2021-01-18
- in Education
- Catalin Barboianu
What is Mathematics: School Guide to Conceptual Understanding of Mathematics
Author: Catalin Barboianu
Publisher: PhilScience Press
ISBN:
Category: Education
Page: 316
View: 434
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This is not a mathematics book, but a book about mathematics, which addresses both student and teacher, with a goal as practical as possible, namely to initiate and smooth the way toward the student's full understanding of the mathematics taught in school. The customary procedural-formal approach to teaching mathematics has resulted in students' distorted vision of mathematics as a merely formal, instrumental, and calculatory discipline. Without the conceptual base of mathematics, students develop over time a "mathematical anxiety" and abandon any effort to understand mathematics, which becomes their "traditional enemy" in school. This work materializes the results of the inter- and trans-disciplinary research aimed toward the understanding of mathematics, which concluded that the fields with the potential to contribute to mathematics education in this respect, by unifying the procedural and conceptual approaches, are epistemology and philosophy of mathematics and science, as well as fundamentals and history of mathematics. These results argue that students' fear of mathematics can be annulled through a conceptual approach, and a student with a good conceptual understanding will be a better problem solver. The author has identified those zones and concepts from the above disciplines that can be adapted and processed for familiarizing the student with this type of knowledge, which should accompany the traditional content of school mathematics. The work was organized so as to create for the reader a unificatory image of the complex nature of mathematics, as well as a conceptual perspective ultimately necessary to the holistic understanding of school mathematics. The author talks about mathematics to convince readers that to understand mathematics means first to understand it as a whole, but also as part of a whole. The nature of mathematics, its primary concepts (like numbers and sets), its structures, language, methods, roles, and applicability, are all presented in their essential content, and the explanation of non-mathematical concepts is done in an accessible language and with many relevant examples.
- 1963
- in Mathematics
- Richard Courant
What is Mathematics?
An Elementary Approach to Ideas and Methods
Author: Richard Courant
Publisher:
ISBN:
Category: Mathematics
Page: 521
View: 428
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- 2015-11-02
- in Education
- Jo Boaler
Mathematical Mindsets
Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching
Author: Jo Boaler
Publisher: John Wiley & Sons
ISBN:
Category: Education
Page: 320
View: 918
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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.
- 1978
- in
- R. Courant
What is Mathematics? an Elementary Approach to Edias and Methods
Author: R. Courant
Publisher:
ISBN:
Category:
Page:
View: 385
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- 2017-06-22
- in Psychology
- Elizabeth de Freitas
What is a Mathematical Concept?
Author: Elizabeth de Freitas
Publisher: Cambridge University Press
ISBN:
Category: Psychology
Page:
View: 874
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Responding to widespread interest within cultural studies and social inquiry, this book addresses the question 'what is a mathematical concept?' using a variety of vanguard theories in the humanities and posthumanities. Tapping historical, philosophical, sociological and psychological perspectives, each chapter explores the question of how mathematics comes to matter. Of interest to scholars across the usual disciplinary divides, this book tracks mathematics as a cultural activity, drawing connections with empirical practice. Unlike other books in this area, it is highly interdisciplinary, devoted to exploring the ontology of mathematics as it plays out in different contexts. This book will appeal to scholars who are interested in particular mathematical habits - creative diagramming, structural mappings, material agency, interdisciplinary coverings - that shed light on both mathematics and other disciplines. Chapters are also relevant to social sciences and humanities scholars, as each offers philosophical insight into mathematics and how we might live mathematically.
- 2012-05-01
- in Mathematics
- Patricia Barnes-Svarney
The Handy Math Answer Book
Author: Patricia Barnes-Svarney
Publisher: Visible Ink Press
ISBN:
Category: Mathematics
Page: 528
View: 975
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From modern-day challenges such as balancing a checkbook, following the stock market, buying a home, and figuring out credit card finance charges to appreciating historical developments by Pythagoras, Archimedes, Newton, and other mathematicians, this engaging resource addresses more than 1,000 questions related to mathematics. Organized into chapters that cluster similar topics in an easily accessible format, this reference provides clear and concise explanations about the fundamentals of algebra, calculus, geometry, trigonometry, and other branches of mathematics. It contains the latest mathematical discoveries, including newly uncovered historical documents and updates on how science continues to use math to make cutting-edge innovations in DNA sequencing, superstring theory, robotics, and computers. With fun math facts and illuminating figures, The Handy Math Answer Book explores the uses of math in everyday life and helps the mathematically challenged better understand and enjoy the magic of numbers.
- 2014-12-05
- in Philosophy
- Michele Friend
Introducing Philosophy of Mathematics
Author: Michele Friend
Publisher: Routledge
ISBN:
Category: Philosophy
Page: 240
View: 618
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What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual accessibility and correct representation of the issues. Friend examines the standard theories of mathematics - Platonism, realism, logicism, formalism, constructivism and structuralism - as well as some less standard theories such as psychologism, fictionalism and Meinongian philosophy of mathematics. In each case Friend explains what characterises the position and where the divisions between them lie, including some of the arguments in favour and against each. This book also explores particular questions that occupy present-day philosophers and mathematicians such as the problem of infinity, mathematical intuition and the relationship, if any, between the philosophy of mathematics and the practice of mathematics. Taking in the canonical ideas of Aristotle, Kant, Frege and Whitehead and Russell as well as the challenging and innovative work of recent philosophers like Benacerraf, Hellman, Maddy and Shapiro, Friend provides a balanced and accessible introduction suitable for upper-level undergraduate courses and the non-specialist.
- 1969
- in
What is Mathematics?
An Elementary Approach to Ideas and Methods
Author:
Publisher:
ISBN:
Category:
Page: 521
View: 448
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- 2011
- in Mathematical recreations
- Yan Kow Cheong
More Mathematical Quickies & Trickies
Author: Yan Kow Cheong
Publisher: MathPlus Publishing
ISBN:
Category: Mathematical recreations
Page: 212
View: 174
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This long-awaited sequel of Mathematical Quickies & Trickles comes with many creative worked examples and questions, with cartoons sprinkled throughout the book to keep in line with the same irreverent and fun spirit of the previous book. In addition to 300+ trick and tricky questions, More Mathematical Quickies & Trickles comes with more than 25 five-minute enrichment mathematics items, aimed at enhancing the mathematical problem-solving skills of problem solvers. You won't only be exposed to different problem-solving techniques, commonly used in answering math contests and competitions questions, but also learn to appreciate elegant or intuitive solutions. More Mathematical Quickies & Trickies would appeal primarily to these audiences: * grades 6-8 students and teachers looking for some fertile trick and tricky questions; * mathletes preparing for local and regional contests and competitions; * problem solvers longing to be challenged by questions whose obvious solutions are never the correct ones for what offhand appears to be true is false. Contents 1. Creative GST 2. Are You Calculator-Smart? 3. What Is the Easy Way? 4. The Magic of Three Consecutive Numbers 5. Twitter Math @MathPlus 6. What Is 27 x 37, Really? 7. Humanizing 1, 2, 3 8. A Mathophobia Kit 9. WITs: 13 Ways to Attain Mathematical Excellence 10. Facebook Math: Numeracy vs. Literacy 11. Thou Shalt Not Divide By Zero 12. Math Jokes to Relieve Stress 13. Look-see Proofs 14. Some PhD Math Questions 15. Mathematical Prayers 16. The Largest Product 17. What's Wrong?: A Comedy of Mathematical Errors 18. The Aha! Myth 19. Sam Loyd's Toughies 20. The Tuesday Boy Problem 21. What Is 1 + 1, Really? 22. In Love with Cryptarithms 23. Mathematical Kiasuism 24. The Mathemagic of 142857 25. The Lighter Side of Singapore Math 26. K C Yan's Laws & Lores 27 Flee and Free from the FREE Answers/Hints/Solutions Bibliography & References
- 2011-08-04
- in Juvenile Nonfiction
- Tracey Steffora
What is Maths?
Author: Tracey Steffora
Publisher: Raintree
ISBN:
Category: Juvenile Nonfiction
Page: 24
View: 171
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This series offers readers a first glimpse into a variety of simple mathematical concepts.
- 2017-06-22
- in Education
- Elizabeth de Freitas
What is a Mathematical Concept?
Author: Elizabeth de Freitas
Publisher: Cambridge University Press
ISBN:
Category: Education
Page: 316
View: 288
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Leading thinkers in mathematics, philosophy and education offer new insights into the fundamental question: what is a mathematical concept?
- 2015-10-27
- in Art
- Lynn Gamwell
Mathematics and Art
A Cultural History
Author: Lynn Gamwell
Publisher: Princeton University Press
ISBN:
Category: Art
Page: 576
View: 530
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This is a cultural history of mathematics and art, from antiquity to the present. Mathematicians and artists have long been on a quest to understand the physical world they see before them and the abstract objects they know by thought alone. Taking readers on a tour of the practice of mathematics and the philosophical ideas that drive the discipline, Lynn Gamwell points out the important ways mathematical concepts have been expressed by artists. Sumptuous illustrations of artworks and cogent math diagrams are featured in Gamwell's comprehensive exploration. Gamwell begins by describing mathematics from antiquity to the Enlightenment, including Greek, Islamic, and Asian mathematics. Then focusing on modern culture, Gamwell traces mathematicians' search for the foundations of their science, such as David Hilbert's conception of mathematics as an arrangement of meaning-free signs, as well as artists' search for the essence of their craft, such as Aleksandr Rodchenko's monochrome paintings. She shows that self-reflection is inherent to the practice of both modern mathematics and art, and that this introspection points to a deep resonance between the two fields: Kurt Gödel posed questions about the nature of mathematics in the language of mathematics and Jasper Johns asked "What is art?" in the vocabulary of art. Throughout, Gamwell describes the personalities and cultural environments of a multitude of mathematicians and artists, from Gottlob Frege and Benoît Mandelbrot to Max Bill and Xu Bing. Mathematics and Art demonstrates how mathematical ideas are embodied in the visual arts and will enlighten all who are interested in the complex intellectual pursuits, personalities, and cultural settings that connect these vast disciplines.
- 2020-02-25
- in Philosophy
- Bertrand Russell
Principles of Mathematics
Author: Bertrand Russell
Publisher: Routledge
ISBN:
Category: Philosophy
Page: 576
View: 866
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Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which Principia Mathematica provided the detailed proof, and introduced the work of Frege to a wider audience. In addition to the new introduction by John Slater, this edition contains Russell's introduction to the 1937 edition in which he defends his position against his formalist and intuitionist critics.
- 1994
- in Computers
- Ronald L. Graham
Concrete Mathematics
A Foundation for Computer Science
Author: Ronald L. Graham
Publisher: Addison-Wesley Professional
ISBN:
Category: Computers
Page: 657
View: 900
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This book, updated and improved, introduces the mathematics that support advanced computer programming and the analysis of algorithms. The book's primary aim is to provide a solid and relevant base of mathematical skills. It is an indispensable text and reference for computer scientists and serious programmers in virtually every discipline.
- 2013-05-13
- in Education
- Yuichi Handa
What Does Understanding Mathematics Mean for Teachers?
Relationship as a Metaphor for Knowing
Author: Yuichi Handa
Publisher: Taylor & Francis
ISBN:
Category: Education
Page: 168
View: 458
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This book opens up alternative ways of thinking and talking about ways in which a person can "know" a subject (in this case, mathematics), leading to a reconsideration of what it may mean to be a teacher of that subject. In a number of European languages, a distinction is made in ways of knowing that in the English language is collapsed into the singular word know. In French, for example, to know in the savoir sense is to know things, facts, names, how and why things work, and so on, whereas to know in the connaître sense is to know a person, a place, or even a thing—namely, an other— in such a way that one is familiar with, or in relationship with this other. Primarily through phenomenological reflection with a touch of empirical input, this book fleshes out an image for what a person's connaître knowing of mathematics might mean, turning to mathematics teachers and teacher educators to help clarify this image.
- 2008-01-03
- in Education
- Anne Watson
New Directions for Situated Cognition in Mathematics Education
Author: Anne Watson
Publisher: Springer Science & Business Media
ISBN:
Category: Education
Page: 360
View: 695
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This book draws together a range of papers by experienced writers in mathematics education who have used the concept of situated cognition in their research within recent years. No other books are available which take this view specifically in mathematics education. Thus it provides an up-to-date overview of developments and applications to which other researchers can refer and which will inspire future research.
- 2014-05-29
- in Mathematics
- Jordan Ellenberg
How Not to Be Wrong
The Power of Mathematical Thinking
Author: Jordan Ellenberg
Publisher: Penguin
ISBN:
Category: Mathematics
Page: 480
View: 690
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"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.
What Is Mathematics Pdf Book
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