Introduction to Mathematical Thinking

Introduction to Mathematical Thinking

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  • Author: Keith J. Devlin
  • Publisher:
  • ISBN: 9780615653631
  • Category : Mathematics
  • Languages : en
  • Pages : 0

"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.


Distilling Ideas

Distilling Ideas

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  • Author: Brian P. Katz
  • Publisher: MAA
  • ISBN: 1939512034
  • Category : Education
  • Languages : en
  • Pages : 189

Introduction -- Graphs -- Groups -- Calculus -- Conclusion.


An Introduction to Mathematical Thinking

An Introduction to Mathematical Thinking

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  • Author: William J. Gilbert
  • Publisher: Pearson
  • ISBN: 9780131848689
  • Category : Algebraic logic
  • Languages : en
  • Pages : 0

Besides giving readers the techniques for solving polynomial equations and congruences, An Introduction to Mathematical Thinking provides preparation for understanding more advanced topics in Linear and Modern Algebra, as well as Calculus. This book introduces proofs and mathematical thinking while teaching basic algebraic skills involving number systems, including the integers and complex numbers. Ample questions at the end of each chapter provide opportunities for learning and practice; the Exercises are routine applications of the material in the chapter, while the Problems require more ingenuity, ranging from easy to nearly impossible. Topics covered in this comprehensive introduction range from logic and proofs, integers and diophantine equations, congruences, induction and binomial theorem, rational and real numbers, and functions and bijections to cryptography, complex numbers, and polynomial equations. With its comprehensive appendices, this book is an excellent desk reference for mathematicians and those involved in computer science.


A First Course in Topology

A First Course in Topology

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  • Author: Robert A Conover
  • Publisher: Courier Corporation
  • ISBN: 0486780015
  • Category : Mathematics
  • Languages : en
  • Pages : 276

Students must prove all of the theorems in this undergraduate-level text, which features extensive outlines to assist in study and comprehension. Thorough and well-written, the treatment provides sufficient material for a one-year undergraduate course. The logical presentation anticipates students' questions, and complete definitions and expositions of topics relate new concepts to previously discussed subjects. Most of the material focuses on point-set topology with the exception of the last chapter. Topics include sets and functions, infinite sets and transfinite numbers, topological spaces and basic concepts, product spaces, connectivity, and compactness. Additional subjects include separation axioms, complete spaces, and homotopy and the fundamental group. Numerous hints and figures illuminate the text. Dover (2014) republication of the edition originally published by The Williams & Wilkins Company, Baltimore, 1975. See every Dover book in print at www.doverpublications.com


An Introduction to Mathematical Reasoning

An Introduction to Mathematical Reasoning

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  • Author: Peter J. Eccles
  • Publisher: Cambridge University Press
  • ISBN: 1139632566
  • Category : Mathematics
  • Languages : en
  • Pages : 364

This book eases students into the rigors of university mathematics. The emphasis is on understanding and constructing proofs and writing clear mathematics. The author achieves this by exploring set theory, combinatorics, and number theory, topics that include many fundamental ideas and may not be a part of a young mathematician's toolkit. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the all-time-great classic proofs. The book presents mathematics as a continually developing subject. Material meeting the needs of readers from a wide range of backgrounds is included. The over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas.


Puzzles, Paradoxes, and Problem Solving

Puzzles, Paradoxes, and Problem Solving

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  • Author: Marilyn A. Reba
  • Publisher: CRC Press
  • ISBN: 1482297930
  • Category : Mathematics
  • Languages : en
  • Pages : 605

A Classroom-Tested, Alternative Approach to Teaching Math for Liberal Arts Puzzles, Paradoxes, and Problem Solving: An Introduction to Mathematical Thinking uses puzzles and paradoxes to introduce basic principles of mathematical thought. The text is designed for students in liberal arts mathematics courses. Decision-making situations that progress


Introduction to Mathematical Thinking

Introduction to Mathematical Thinking

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  • Author: Friedrich Waismann
  • Publisher: Courier Corporation
  • ISBN: 0486167429
  • Category : Mathematics
  • Languages : en
  • Pages : 292

Examinations of arithmetic, geometry, and theory of integers; rational and natural numbers; complete induction; limit and point of accumulation; remarkable curves; complex and hypercomplex numbers; more. Includes 27 figures. 1959 edition.


How Not to Be Wrong

How Not to Be Wrong

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  • Author: Jordan Ellenberg
  • Publisher: Penguin Press
  • ISBN: 1594205221
  • Category : Mathematics
  • Languages : en
  • Pages : 480

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.


Mathematical Reasoning

Mathematical Reasoning

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  • Author: Theodore A. Sundstrom
  • Publisher: Prentice Hall
  • ISBN: 9780131877184
  • Category : Logic, Symbolic and mathematical
  • Languages : en
  • Pages : 0

Focusing on the formal development of mathematics, this book shows readers how to read, understand, write, and construct mathematical proofs.Uses elementary number theory and congruence arithmetic throughout. Focuses on writing in mathematics. Reviews prior mathematical work with “Preview Activities” at the start of each section. Includes “Activities” throughout that relate to the material contained in each section. Focuses on Congruence Notation and Elementary Number Theorythroughout.For professionals in the sciences or engineering who need to brush up on their advanced mathematics skills. Mathematical Reasoning: Writing and Proof, 2/E Theodore Sundstrom


Understanding Emotions in Mathematical Thinking and Learning

Understanding Emotions in Mathematical Thinking and Learning

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  • Author: Ulises Xolocotzin
  • Publisher: Academic Press
  • ISBN: 0128024895
  • Category : Psychology
  • Languages : en
  • Pages : 476

Emotions play a critical role in mathematical cognition and learning. Understanding Emotions in Mathematical Thinking and Learning offers a multidisciplinary approach to the role of emotions in numerical cognition, mathematics education, learning sciences, and affective sciences. It addresses ways in which emotions relate to cognitive processes involved in learning and doing mathematics, including processing of numerical and physical magnitudes (e.g. time and space), performance in arithmetic and algebra, problem solving and reasoning attitudes, learning technologies, and mathematics achievement. Additionally, it covers social and affective issues such as identity and attitudes toward mathematics. - Covers methodologies in studying emotion in mathematical knowledge - Reflects the diverse and innovative nature of the methodological approaches and theoretical frameworks proposed by current investigations of emotions and mathematical cognition - Includes perspectives from cognitive experimental psychology, neuroscience, and from sociocultural, semiotic, and discursive approaches - Explores the role of anxiety in mathematical learning - Synthesizes unifies the work of multiple sub-disciplines in one place