Advanced Mathematical Thinking
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Advanced Mathematical Thinking
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Author : David Tall
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-11
Advanced Mathematical Thinking written by David Tall and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-11 with Education categories.
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.
Advanced Mathematical Thinking
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Author : Annie Selden
language : en
Publisher: Routledge
Release Date : 2013-10-15
Advanced Mathematical Thinking written by Annie Selden and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-15 with Education categories.
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.
Advanced Mathematical Thinking
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Author : David Tall
language : en
Publisher:
Release Date : 2014-01-15
Advanced Mathematical Thinking written by David Tall and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Structural Understanding In Advanced Mathematical Thinking
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Author : Naďa Stehlíková
language : en
Publisher: Nada Stehlikova
Release Date : 2004
Structural Understanding In Advanced Mathematical Thinking written by Naďa Stehlíková and has been published by Nada Stehlikova this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
Mathematical Thinking
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Author : John P. D'Angelo
language : en
Publisher:
Release Date : 2018
Mathematical Thinking written by John P. D'Angelo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Mathematics categories.
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.
Forms Of Mathematical Knowledge
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Author : Dina Tirosh
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Forms Of Mathematical Knowledge written by Dina Tirosh and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Education categories.
What mathematics is entailed in knowing to act in a moment? Is tacit, rhetorical knowledge significant in mathematics education? What is the role of intuitive models in understanding, learning and teaching mathematics? Are there differences between elementary and advanced mathematical thinking? Why can't students prove? What are the characteristics of teachers' ways of knowing? This book focuses on various types of knowledge that are significant for learning and teaching mathematics. The first part defines, discusses and contrasts psychological, philosophical and didactical issues related to various types of knowledge involved in the learning of mathematics. The second part describes ideas about forms of mathematical knowledge that are important for teachers to know and ways of implementing such ideas in preservice and in-service education. The chapters provide a wide overview of current thinking about mathematics learning and teaching which is of interest for researchers in mathematics education and mathematics educators. Topics covered include the role of intuition in mathematics learning and teaching, the growth from elementary to advanced mathematical thinking, the significance of genres and rhetoric for the learning of mathematics and the characterization of teachers' ways of knowing.
Discovering Group Theory
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Author : Tony Barnard
language : en
Publisher: CRC Press
Release Date : 2016-12-19
Discovering Group Theory written by Tony Barnard and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-19 with Mathematics categories.
Discovering Group Theory: A Transition to Advanced Mathematics presents the usual material that is found in a first course on groups and then does a bit more. The book is intended for students who find the kind of reasoning in abstract mathematics courses unfamiliar and need extra support in this transition to advanced mathematics. The book gives a number of examples of groups and subgroups, including permutation groups, dihedral groups, and groups of integer residue classes. The book goes on to study cosets and finishes with the first isomorphism theorem. Very little is assumed as background knowledge on the part of the reader. Some facility in algebraic manipulation is required, and a working knowledge of some of the properties of integers, such as knowing how to factorize integers into prime factors. The book aims to help students with the transition from concrete to abstract mathematical thinking.
A Transition To Abstract Mathematics
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Author : Randall Maddox
language : en
Publisher: Academic Press
Release Date : 2008-10-13
A Transition To Abstract Mathematics written by Randall Maddox and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-13 with Mathematics categories.
Constructing concise and correct proofs is one of the most challenging aspects of learning to work with advanced mathematics. Meeting this challenge is a defining moment for those considering a career in mathematics or related fields. A Transition to Abstract Mathematics teaches readers to construct proofs and communicate with the precision necessary for working with abstraction. It is based on two premises: composing clear and accurate mathematical arguments is critical in abstract mathematics, and that this skill requires development and support. Abstraction is the destination, not the starting point. Maddox methodically builds toward a thorough understanding of the proof process, demonstrating and encouraging mathematical thinking along the way. Skillful use of analogy clarifies abstract ideas. Clearly presented methods of mathematical precision provide an understanding of the nature of mathematics and its defining structure. After mastering the art of the proof process, the reader may pursue two independent paths. The latter parts are purposefully designed to rest on the foundation of the first, and climb quickly into analysis or algebra. Maddox addresses fundamental principles in these two areas, so that readers can apply their mathematical thinking and writing skills to these new concepts. From this exposure, readers experience the beauty of the mathematical landscape and further develop their ability to work with abstract ideas. Covers the full range of techniques used in proofs, including contrapositive, induction, and proof by contradiction Explains identification of techniques and how they are applied in the specific problem Illustrates how to read written proofs with many step by step examples Includes 20% more exercises than the first edition that are integrated into the material instead of end of chapter
Mathematical Thinking And Writing
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Author : Randall Maddox
language : en
Publisher: Academic Press
Release Date : 2002
Mathematical Thinking And Writing written by Randall Maddox and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
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.
Mathematics And Cognition
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Author : Pearla Nesher
language : en
Publisher: CUP Archive
Release Date : 1990-02-23
Mathematics And Cognition written by Pearla Nesher and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-02-23 with Education categories.
This 1990 book is aimed at teachers, mathematics educators and general readers who are interested in mathematics education from a psychological point of view.