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Contemporary Mathematical Thinking
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Book Synopsis Contemporary Mathematical Thinking by : Frédéric Patras
Download or read book Contemporary Mathematical Thinking written by Frédéric Patras and published by Springer Nature. This book was released on 2023-04-13 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the evolution of mathematical thought during the 20th century. Representing a unique point of view combining mathematics, philosophy and history on this issue, it presents an original analysis of key authors, for example Bourbaki, Grothendieck and Husserl. As a product of 19th and early 20th century science, a canon of knowledge or a scientific ideology, mathematical structuralism had to give way. The succession is difficult, still in progress, and uncertain. To understand contemporary mathematics, its progressive liberation from the slogans of "modern mathematics" and the paths that remain open today, it is first necessary to deconstruct the history of this long dominant current. Another conception of mathematical thought emerged in the work of mathematicians such as Hilbert or Weyl, which went beyond the narrow epistemological paths of science in the making. In this tradition, mathematical thought was accompanied by a philosophical requirement. Modernity teaches us to revive it. The book is intended for a varied public: mathematicians concerned with understanding their discipline, philosophers of science, and the erudite public curious about the progress of mathematics.
Book Synopsis Introduction to Mathematical Thinking by : Friedrich Waismann
Download or read book Introduction to Mathematical Thinking written by Friedrich Waismann and published by Courier Corporation. This book was released on 2012-08-07 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Essence of Numbers by : Frédéric Patras
Download or read book The Essence of Numbers written by Frédéric Patras and published by Springer Nature. This book was released on 2020-10-06 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book considers the manifold possible approaches, past and present, to our understanding of the natural numbers. They are treated as epistemic objects: mathematical objects that have been subject to epistemological inquiry and attention throughout their history and whose conception has evolved accordingly. Although they are the simplest and most common mathematical objects, as this book reveals, they have a very complex nature whose study illuminates subtle features of the functioning of our thought. Using jointly history, mathematics and philosophy to grasp the essence of numbers, the reader is led through their various interpretations, presenting the ways they have been involved in major theoretical projects from Thales onward. Some pertain primarily to philosophy (as in the works of Plato, Aristotle, Kant, Wittgenstein...), others to general mathematics (Euclid's Elements, Cartesian algebraic geometry, Cantorian infinities, set theory...). Also serving as an introduction to the works and thought of major mathematicians and philosophers, from Plato and Aristotle to Cantor, Dedekind, Frege, Husserl and Weyl, this book will be of interest to a wide variety of readers, from scholars with a general interest in the philosophy or mathematics to philosophers and mathematicians themselves.
Book Synopsis Contemporary Perspectives on Mathematics in Early Childhood Education by : Olivia Saracho
Download or read book Contemporary Perspectives on Mathematics in Early Childhood Education written by Olivia Saracho and published by IAP. This book was released on 2008-02-01 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a comprehensive critical analysis of the research in mathematics education for young children. The researchers who conducted the critical analysis focused on the relationship between (1) mathematics learning in the early years and domain specific approaches to cognitive development, (2) the children’s social learning and their developing understanding of math, and (3) the children’s learning in a natural context and their understanding of mathematics concepts. The work of these scholars can help guide those researchers who are interested in pursuing studies in early childhood mathematics in a specific area of study. This volume will facilitate the research conducted by both novice and expert researchers. The volume has accomplished its major goals, which consists of critically analyzing important research in a specific area that would be most useful in advancing the field and provide recommendations for both researchers and educators.
Book Synopsis How Humans Learn to Think Mathematically by : David Tall
Download or read book How Humans Learn to Think Mathematically written by David Tall and published by Cambridge University Press. This book was released on 2013-09-02 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Essentials of Mathematical Thinking by : Steven G. Krantz
Download or read book Essentials of Mathematical Thinking written by Steven G. Krantz and published by CRC Press. This book was released on 2017-10-06 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Essentials of Mathematical Thinking addresses the growing need to better comprehend mathematics today. Increasingly, our world is driven by mathematics in all aspects of life. The book is an excellent introduction to the world of mathematics for students not majoring in mathematical studies. The author has written this book in an enticing, rich manner that will engage students and introduce new paradigms of thought. Careful readers will develop critical thinking skills which will help them compete in today’s world. The book explains: What goes behind a Google search algorithm How to calculate the odds in a lottery The value of Big Data How the nefarious Ponzi scheme operates Instructors will treasure the book for its ability to make the field of mathematics more accessible and alluring with relevant topics and helpful graphics. The author also encourages readers to see the beauty of mathematics and how it relates to their lives in meaningful ways.
Book Synopsis Interdisciplinary Perspectives on Math Cognition by : Marcel Danesi
Download or read book Interdisciplinary Perspectives on Math Cognition written by Marcel Danesi and published by Springer Nature. This book was released on 2019-09-14 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an anthology of contemporary studies from various disciplinary perspectives written by some of the world's most renowned experts in each of the areas of mathematics, neuroscience, psychology, linguistics, semiotics, education, and more. Its purpose is not to add merely to the accumulation of studies, but to show that math cognition is best approached from various disciplinary angles, with the goal of broadening the general understanding of mathematical cognition through the different theoretical threads that can be woven into an overall understanding. This volume will be of interest to mathematicians, cognitive scientists, educators of mathematics, philosophers of mathematics, semioticians, psychologists, linguists, anthropologists, and all other kinds of scholars who are interested in the nature, origin, and development of mathematical cognition.
Book Synopsis Invitation to Mathematics by : Konrad Jacobs
Download or read book Invitation to Mathematics written by Konrad Jacobs and published by Princeton University Press. This book was released on 1992-08-02 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a well-received course designed for philosophy students, this book is an informal introduction to mathematical thinking. The work will be rewarding not only for philosophers concerned with mathematical questions but also for serious amateur mathematicians with an interest in the "frontiers" as well as the foundations of mathematics. In what might be termed a sampler of the discipline, Konrad Jacobs discusses an unusually wide range of topics, including such items of contemporary interest as knot theory, optimization theory, and dynamical systems. Using Euclidean geometry and algebra to introduce the mathematical mode of thought, the author then turns to recent developments. In the process he offers what he calls a "Smithsonian of mathematical showpieces": the five Platonic Solids, the Mbius Strip, the Cantor Discontinuum, the Peano Curve, Reidemeister's Knot Table, the plane ornaments, Alexander's Horned Sphere, and Antoine's Necklace. The treatments of geometry and algebra are followed by a chapter on induction and one on optimization, game theory, and mathematical economics. The chapter on topology includes a discussion of topological spaces and continuous mappings, curves and knots, Euler's polyhedral formula for surfaces, and the fundamental group. The last chapter deals with dynamics and contains material on the Game of Life, circle rotation, Smale's "horseshoe," and stability and instability, among other topics.
Book Synopsis Topics in Contemporary Mathematical Analysis and Applications by : Hemen Dutta
Download or read book Topics in Contemporary Mathematical Analysis and Applications written by Hemen Dutta and published by CRC Press. This book was released on 2020-12-22 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics in Contemporary Mathematical Analysis and Applications encompasses several contemporary topics in the field of mathematical analysis, their applications, and relevancies in other areas of research and study. The readers will find developments concerning the topics presented to a reasonable extent with various new problems for further study. Each chapter carefully presents the related problems and issues, methods of solutions, and their possible applications or relevancies in other scientific areas. Aims at enriching the understanding of methods, problems, and applications Offers an understanding of research problems by presenting the necessary developments in reasonable details Discusses applications and uses of operator theory, fixed-point theory, inequalities, bi-univalent functions, functional equations, and scalar-objective programming, and presents various associated problems and ways to solve such problems This book is written for individual researchers, educators, students, and department libraries.
Book Synopsis Topics in Contemporary Mathematics by : Ignacio Bello
Download or read book Topics in Contemporary Mathematics written by Ignacio Bello and published by Brooks/Cole. This book was released on 2005 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics in Contemporary Mathematics is uniquely designed to help students see math at work in the contemporary world by presenting problem solving in purposeful and meaningful contexts. This Expanded Eighth Edition contains two additional chapters on Voting and Apportionment and Graph Theory. Strong technology focus encourages students to learn and apply their knowledge using the most up-to-date web links maintained by the author on a companion web site. Instructors may also use this site to access PowerPoint slides for convenient class presentations. In addition to these web resources, lecture and practice test videos have been developed to provide extra support and foster confidence outside of the classroom. For those students in Florida, a CLAST Test software package and video are available as well. A variety of pedagogical features reinforce ideas and motivate students to learn. Getting Started offers a motivating introduction for the techniques and ideas in each section. Through web references and Web It exercises, students utilize the Internet as an educational and creative tool to study mathematical concepts. Collaborative Learning encourages student interaction as they work together to solve problems. The Graph It feature found in the book margins provides step-by-step directions for solving specific examples using the TI-83 graphing calculator. Problem-solving approach throughout the text helps students learn techniques and methods that will benefit them throughout their lives and careers. These special examples use George Polya\'s problem-solving strategy (RSTUV—Read, Select, Think of a plan, Use the techniques, Verify) and a unique two-column format for describing the general problem-solving method and demonstrating specific uses. Abundant applications and examples include more than 500 examples and 4100 carefully developed exercises that cover a wide range of topics and provide the instructor and student with flexibility in choosing computational, drill, or conceptual problems. Real-world applications motivate students and pique their interest. Other problems such as Using Your Knowledge, Discovery, Calculator Corner, and Research questions help reinforce concepts and further develop the students critical-thinking and problem-solving skills. Skill Checker helps students test their knowledge with a variety of problems to ensure they have a thorough grasp of the material before continuing on to new concepts. The Chapter Summary provides definitions and section references for key topics within a given chapter. A Practice Test after each chapter is followed by Answers to the Practice Test, with references to the appropriate section, page, and example for review, as needed.
Book Synopsis Mathematical Thinking and Problem Solving by : Alan H. Schoenfeld
Download or read book Mathematical Thinking and Problem Solving written by Alan H. Schoenfeld and published by Routledge. This book was released on 2016-05-06 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the early 1980s there was virtually no serious communication among the various groups that contribute to mathematics education -- mathematicians, mathematics educators, classroom teachers, and cognitive scientists. Members of these groups came from different traditions, had different perspectives, and rarely gathered in the same place to discuss issues of common interest. Part of the problem was that there was no common ground for the discussions -- given the disparate traditions and perspectives. As one way of addressing this problem, the Sloan Foundation funded two conferences in the mid-1980s, bringing together members of the different communities in a ground clearing effort, designed to establish a base for communication. In those conferences, interdisciplinary teams reviewed major topic areas and put together distillations of what was known about them.* A more recent conference -- upon which this volume is based -- offered a forum in which various people involved in education reform would present their work, and members of the broad communities gathered would comment on it. The focus was primarily on college mathematics, informed by developments in K-12 mathematics. The main issues of the conference were mathematical thinking and problem solving.
Book Synopsis Contemporary Research and Perspectives on Early Childhood Mathematics Education by : Iliada Elia
Download or read book Contemporary Research and Perspectives on Early Childhood Mathematics Education written by Iliada Elia and published by Springer. This book was released on 2018-02-21 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together a collection of research-based papers on current issues in early childhood mathematics education that were presented in the Topic Study Group 1 (TSG 1) at the 13th International Congress on Mathematical Education (ICME-13), held at the University of Hamburg in 2016. It will help readers understand a range of key issues that early childhood mathematics educators encounter today. Research on early childhood mathematics education has grown in recent years, due in part to the well-documented, positive relation between children’s early mathematical knowledge and their later mathematics learning, and to the considerable emphasis many countries are now placing on preschool education. The book addresses a number of central questions, including: What is mathematical structural development and how can we promote it in early childhood? How can multimodality and embodiment contribute to early mathematics learning and to acquiring a better understanding of young children’s mathematical development? How can children’s informal mathematics-related experiences affect instruction and children’s learning in different mathematics content areas? What is the role of tools, including technology and picture books, in supporting early mathematics learning? What are the challenges in early childhood mathematics education for teachers’ education and professional development?
Download or read book Distilling Ideas written by Brian P. Katz and published by MAA. This book was released on 2013 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction -- Graphs -- Groups -- Calculus -- Conclusion.
Book Synopsis Advanced Mathematical Thinking by : Annie Selden
Download or read book Advanced Mathematical Thinking written by Annie Selden and published by Routledge. This book was released on 2013-10-15 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Contemporary Mathematics in Context by : Arthur F. Coxford
Download or read book Contemporary Mathematics in Context written by Arthur F. Coxford and published by . This book was released on 1998 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contemporary Mathematics in Context is a four-year, integrated mathematics program developed by the Core-Plus Mathematics Project (CPMP) at the Everyday Learning Corporation. The program features student and teacher materials for a three-year core curriculum for all students as well as a fourth-year course continuing the preparation of students for college mathematics. The materials were designed to implement the vision of high school mathematics as portrayed in the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics and Professional Standards for Teaching Mathematics. This booklet provides an overview of the curriculum, presents information about the implementation the curriculum, and offers suggestions for managing the classroom activities and assessment. (ASK)
Book Synopsis Mathematical Thinking by : John P. D'Angelo
Download or read book Mathematical Thinking written by John P. D'Angelo and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Summing it Up written by Avner Ash and published by . This book was released on 2016 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: The power and properties of numbers, from basic addition and sums of squares to cutting-edge theory We use addition on a daily basis--yet how many of us stop to truly consider the enormous and remarkable ramifications of this mathematical activity? Summing It Up uses addition as a springboard to present a fascinating and accessible look at numbers and number theory, and how we apply beautiful numerical properties to answer math problems. Mathematicians Avner Ash and Robert Gross explore addition's most basic characteristics as well as the addition of squares and other powers before moving onward to infinite series, modular forms, and issues at the forefront of current mathematical research. Ash and Gross tailor their succinct and engaging investigations for math enthusiasts of all backgrounds. Employing college algebra, the first part of the book examines such questions as, can all positive numbers be written as a sum of four perfect squares? The second section of the book incorporates calculus and examines infinite series--long sums that can only be defined by the concept of limit, as in the example of 1+1/2+1/4+. . .=? With the help of some group theory and geometry, the third section ties together the first two parts of the book through a discussion of modular forms--the analytic functions on the upper half-plane of the complex numbers that have growth and transformation properties. Ash and Gross show how modular forms are indispensable in modern number theory, for example in the proof of Fermat's Last Theorem. Appropriate for numbers novices as well as college math majors, Summing It Up delves into mathematics that will enlighten anyone fascinated by numbers.
