Advanced Mathematical Thinking PDF Download
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| Author | : David Tall |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 298 |
| Release | : 2006-04-11 |
| Genre | : Education |
| ISBN | : 0306472031 |
Download Advanced Mathematical Thinking Book in PDF, ePub and Kindle
This book is the first major study of advanced mathematical thinking as performed by mathematicians and taught to students in senior high school and university. Topics covered include the psychology of advanced mathematical thinking, the processes involved, mathematical creativity, proof, the role of definitions, symbols, and reflective abstraction. It is highly appropriate for the college professor in mathematics or the general mathematics educator.
| Author | : Pearla Nesher |
| Publisher | : CUP Archive |
| Total Pages | : 234 |
| Release | : 1990-02-23 |
| Genre | : Education |
| ISBN | : 9780521367875 |
Download Mathematics and Cognition Book in PDF, ePub and Kindle
This 1990 book is aimed at teachers, mathematics educators and general readers who are interested in mathematics education from a psychological point of view.
| Author | : Annie Selden |
| Publisher | : Routledge |
| Total Pages | : 76 |
| Release | : 2013-10-15 |
| Genre | : Education |
| ISBN | : 1135478384 |
Download Advanced Mathematical Thinking Book in PDF, ePub and Kindle
This is Volume 7, Issue 1 2005, a Special Issue of 'Mathematical Thinking and Learning' which looks at Advanced Mathematical Thinking. Opening with a brief history of attempts to characterize advanced mathematical thinking, beginning with the deliberations of the Advanced Mathematical Thinking Working Group of the International Group for the Psychology of Mathematics Education. The articles follow the recurring themes: (a) the distinction between identifying kinds of thinking that might be regarded as advanced at any grade level and taking as advanced any thinking about mathematical topics considered advanced; (b) the utility of characterizing such thinking for integrating the entire curriculum; (c) general tests, or criteria, for identifying advanced mathematical thinking; and (d) an emphasis on advancing mathematical practices.
| Author | : David Tall |
| Publisher | : |
| Total Pages | : 316 |
| Release | : 2014-01-15 |
| Genre | : |
| ISBN | : 9789401737487 |
Download Advanced Mathematical Thinking Book in PDF, ePub and Kindle
| Author | : Keith J. Devlin |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 9780615653631 |
Download Introduction to Mathematical Thinking Book in PDF, ePub and Kindle
"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 | : Zalman Usiskin |
| Publisher | : Prentice Hall |
| Total Pages | : 616 |
| Release | : 2003 |
| Genre | : Education |
| ISBN | : |
Download Mathematics for High School Teachers Book in PDF, ePub and Kindle
For algebra or geometry courses for teachers; courses in topics of mathematics; capstone courses for teachers or other students of mathematics; graduate courses for practicing teachers; or students who want a better understanding of mathematics. Filling a wide gap in the market, this text provides current and prospective high school teachers with an advanced treatment of mathematics that will help them understand the connections between the mathematics they will be teaching and the mathematics learned in college. It presents in-depth coverage of the most important concepts in high school mathematics: real numbers, functions, congruence, similarity, and more.
| Author | : William Johnston |
| Publisher | : Oxford University Press |
| Total Pages | : 766 |
| Release | : 2009-07-27 |
| Genre | : Mathematics |
| ISBN | : 0199718660 |
Download A Transition to Advanced Mathematics Book in PDF, ePub and Kindle
A Transition to Advanced Mathematics: A Survey Course promotes the goals of a "bridge'' course in mathematics, helping to lead students from courses in the calculus sequence (and other courses where they solve problems that involve mathematical calculations) to theoretical upper-level mathematics courses (where they will have to prove theorems and grapple with mathematical abstractions). The text simultaneously promotes the goals of a ``survey'' course, describing the intriguing questions and insights fundamental to many diverse areas of mathematics, including Logic, Abstract Algebra, Number Theory, Real Analysis, Statistics, Graph Theory, and Complex Analysis. The main objective is "to bring about a deep change in the mathematical character of students -- how they think and their fundamental perspectives on the world of mathematics." This text promotes three major mathematical traits in a meaningful, transformative way: to develop an ability to communicate with precise language, to use mathematically sound reasoning, and to ask probing questions about mathematics. In short, we hope that working through A Transition to Advanced Mathematics encourages students to become mathematicians in the fullest sense of the word. A Transition to Advanced Mathematics has a number of distinctive features that enable this transformational experience. Embedded Questions and Reading Questions illustrate and explain fundamental concepts, allowing students to test their understanding of ideas independent of the exercise sets. The text has extensive, diverse Exercises Sets; with an average of 70 exercises at the end of section, as well as almost 3,000 distinct exercises. In addition, every chapter includes a section that explores an application of the theoretical ideas being studied. We have also interwoven embedded reflections on the history, culture, and philosophy of mathematics throughout the text.
| Author | : Stanley J. Farlow |
| Publisher | : John Wiley & Sons |
| Total Pages | : 556 |
| Release | : 2019-10-02 |
| Genre | : Mathematics |
| ISBN | : 1119563534 |
Download Advanced Mathematics Book in PDF, ePub and Kindle
Provides a smooth and pleasant transition from first-year calculus to upper-level mathematics courses in real analysis, abstract algebra and number theory Most universities require students majoring in mathematics to take a “transition to higher math” course that introduces mathematical proofs and more rigorous thinking. Such courses help students be prepared for higher-level mathematics course from their onset. Advanced Mathematics: A Transitional Reference provides a “crash course” in beginning pure mathematics, offering instruction on a blendof inductive and deductive reasoning. By avoiding outdated methods and countless pages of theorems and proofs, this innovative textbook prompts students to think about the ideas presented in an enjoyable, constructive setting. Clear and concise chapters cover all the essential topics students need to transition from the "rote-orientated" courses of calculus to the more rigorous "proof-orientated” advanced mathematics courses. Topics include sentential and predicate calculus, mathematical induction, sets and counting, complex numbers, point-set topology, and symmetries, abstract groups, rings, and fields. Each section contains numerous problems for students of various interests and abilities. Ideally suited for a one-semester course, this book: Introduces students to mathematical proofs and rigorous thinking Provides thoroughly class-tested material from the authors own course in transitioning to higher math Strengthens the mathematical thought process of the reader Includes informative sidebars, historical notes, and plentiful graphics Offers a companion website to access a supplemental solutions manual for instructors Advanced Mathematics: A Transitional Reference is a valuable guide for undergraduate students who have taken courses in calculus, differential equations, or linear algebra, but may not be prepared for the more advanced courses of real analysis, abstract algebra, and number theory that await them. This text is also useful for scientists, engineers, and others seeking to refresh their skills in advanced math.
| Author | : David Tall |
| Publisher | : Cambridge University Press |
| Total Pages | : 483 |
| Release | : 2013-09-02 |
| Genre | : Education |
| ISBN | : 1107035708 |
Download How Humans Learn to Think Mathematically Book in PDF, ePub and Kindle
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.
| Author | : John P. D'Angelo |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2018 |
| Genre | : Mathematics |
| ISBN | : 9780134689579 |
Download Mathematical Thinking Book in PDF, ePub and Kindle
For one/two-term courses in Transition to Advanced Mathematics or Introduction to Proofs. Also suitable for courses in Analysis or Discrete Math. This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics-series for a complete list of titles. This text is designed to prepare students thoroughly in the logical thinking skills necessary to understand and communicate fundamental ideas and proofs in mathematics-skills vital for success throughout the upperclass mathematics curriculum. The text offers both discrete and continuous mathematics, allowing instructors to emphasize one or to present the fundamentals of both. It begins by discussing mathematical language and proof techniques (including induction), applies them to easily-understood questions in elementary number theory and counting, and then develops additional techniques of proof via important topics in discrete and continuous mathematics. The stimulating exercises are acclaimed for their exceptional quality.
