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Author : Milena Damrau
Publisher : Springer Nature
ISBN 13 : 3658437634
Total Pages : 222 pages
Book Rating : 4.6/5 (584 download)
Download or read book Understanding the Generality of Mathematical Statements written by Milena Damrau and published by Springer Nature. This book was released on with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Victor Lowe
Publisher : JHU Press
ISBN 13 : 1421435942
Total Pages : 402 pages
Book Rating : 4.4/5 (214 download)
Download or read book Understanding Whitehead written by Victor Lowe and published by JHU Press. This book was released on 2020-02-03 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1962. The central aim of this book is to discuss the development of Alfred North Whitehead's thought and to underscore how it is unique. Understanding Whitehead collects nine essays written by Victor Lowe originally published between 1941 and 1961. The essays have been revised for inclusion in this volume.
Author : Karine Chemla
Publisher : Oxford University Press
ISBN 13 : 0198777264
Total Pages : 529 pages
Book Rating : 4.1/5 (987 download)
Download or read book The Oxford Handbook of Generality in Mathematics and the Sciences written by Karine Chemla and published by Oxford University Press. This book was released on 2016 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of original essays aims to inquire into the diversity of Generality. Through case studies taken from the history of mathematics, physics and the life sciences, the book provides evidence of different ways of understanding the general in various contexts.
Author : Jerry P. King
Publisher : Prometheus Books
ISBN 13 : 1615921591
Total Pages : 394 pages
Book Rating : 4.6/5 (159 download)
Download or read book Mathematics in 10 Lessons written by Jerry P. King and published by Prometheus Books. This book was released on 2010-12-29 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditional Chinese edition of Mathematics in 10 Lessons: The Grand Tour. This is one of the best books to help lay a solid foundation of math skills for children and for adults who are a little rusty. It goes into details to explain concepts and wordings from the very beginning and build up step-by-step. In Chinese. Distributed by Tsai Fong Books, Inc.
Author : Gregory Hine
Publisher : Cambridge University Press
ISBN 13 : 1108983405
Total Pages : 377 pages
Book Rating : 4.1/5 (89 download)
Download or read book Teaching Secondary Mathematics written by Gregory Hine and published by Cambridge University Press. This book was released on 2021-09-24 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: Secondary mathematics teachers working in the Australian education sector are required to plan lessons that engage with students of different genders, cultures and levels of literacy and numeracy. Teaching Secondary Mathematics engages directly with the Australian Curriculum: Mathematics and the Australian Professional Standards for Teachers to help preservice teachers develop lesson plans that resonate with students. This edition has been thoroughly revised and features a new chapter on supporting Aboriginal and Torres Strait Islander students by incorporating Aboriginal and Torres Strait Islander cultures and ways of knowing into lessons. Chapter content is supported by new features including short-answer questions, opportunities for reflection and in-class activities. Further resources, additional activities, and audio and visual recordings of mathematical problems are also available for students on the book's companion website. Teaching Secondary Mathematics is the essential guide for preservice mathematics teachers who want to understand the complex and ever-changing Australian education landscape.
Author : Agustín Rayo
Publisher : Oxford University Press
ISBN 13 : 0199276420
Total Pages : 407 pages
Book Rating : 4.1/5 (992 download)
Download or read book Absolute Generality written by Agustín Rayo and published by Oxford University Press. This book was released on 2006-11-23 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: Is it possible to quantify over absolutely all there is? Or must all of our quantifiers range over a less-than-all-inclusive domain? It has commonly been thought that the question of absolute generality is intimately connected with the set-theoretic antinomies. But the topic of absolute generality has enjoyed a surge of interest in recent years. It has become increasingly apparent that its ramifications extend well beyond the foundations of set theory. Connections include semanticindeterminacy, logical consequence, higher-order languages, and metaphysics.Rayo and Uzquiano present for the first time a collection of essays on absolute generality. These newly commissioned articles -- written by an impressive array of international scholars -- draw the reader into the forefront of contemporary research on the subject. The volume represents a variety of approaches to the problem, with some of the contributions arguing for the possibility of all-inclusive quantification and some of them arguing against it. An introduction by the editors draws ahelpful map of the philosophical terrain.
Author : Elizabeth Fennema
Publisher : Routledge
ISBN 13 : 113567650X
Total Pages : 217 pages
Book Rating : 4.1/5 (356 download)
Download or read book Mathematics Classrooms That Promote Understanding written by Elizabeth Fennema and published by Routledge. This book was released on 1999-04-01 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics Classrooms That Promote Understanding synthesizes the implications of research done by the National Center for Research in Mathematical Sciences on integrating two somewhat diverse bodies of scholarly inquiry: the study of teaching and the study of learning mathematics. This research was organized around content domains and/or continuing issues of education, such as equity and assessment of learning, and was guided by two common goals--defining the mathematics content of the K-12 curriculum in light of the changing mathematical needs of citizens for the 21st century, and identifying common components of classrooms that enable students to learn the redefined mathematics with understanding. To accomplish these goals, classrooms in which instruction facilitated the growth of understanding were established and/or studied. This volume reports and discusses the findings which grew out of this research, and subsequent papers and discussions among the scholars engaged in the endeavor. Section I, "Setting the Stage," focuses on three major threads: What mathematics should be taught; how we should define and increase students' understanding of that mathematics; and how learning with understanding can be facilitated for all students. Section II, "Classrooms That Promote Understanding," includes vignettes from diverse classrooms that illustrate classroom discourse, student work, and student engagement in the mathematics described in Chapter 1 as well as the mental activities described in Chapter 2. These chapters also illustrate how teachers deal with the equity concerns described in Chapter 3. Section III addresses "Developing Classrooms That Promote Understanding." The knowledge of the teaching/learning process gained from the research reported in this volume is a necessary prerequisite for implementing the revisions called for in the current reform movement. The classrooms described show that innovative reform in teaching and learning mathematics is possible. Unlike many volumes reporting research, this book is written at a level appropriate for master's degree students. Very few references are included in the chapters themselves; instead, each chapter includes a short annotated list of articles for expanded reading which provides the scholarly basis and research substantiation for this volume.
Author : Alan H. Schoenfeld
Publisher : Routledge
ISBN 13 : 1135440867
Total Pages : 360 pages
Book Rating : 4.1/5 (354 download)
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 360 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.
Author :
Publisher : Elsevier
ISBN 13 : 008046663X
Total Pages : 1219 pages
Book Rating : 4.0/5 (84 download)
Download or read book Philosophy of Logic written by and published by Elsevier. This book was released on 2006-11-29 with total page 1219 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert's program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights.- Written by leading logicians and philosophers- Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic- Clear, in-depth expositions of technical detail- Progressive organization from general considerations to informal to symbolic logic to nonclassical logics- Presents current work in symbolic logic within a unified framework- Accessible to students, engaging for experts and professionals- Insightful philosophical discussions of all aspects of logic- Useful bibliographies in every chapter
Author :
Publisher : BRILL
ISBN 13 : 9087903510
Total Pages : 321 pages
Book Rating : 4.0/5 (879 download)
Download or read book New Mathematics Education Research and Practice written by and published by BRILL. This book was released on 2006-01-01 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics education research has blossomed into many different areas which we can see in the programmes of the ICME conferences as well as in the various survey articles in the Handbooks. However, all of these lines of research are trying to grapple with a common problem, the complexity of the process of learning mathematics.
Author : Charles Parsons
Publisher : Cambridge University Press
ISBN 13 : 1139467271
Total Pages : 400 pages
Book Rating : 4.1/5 (394 download)
Download or read book Mathematical Thought and its Objects written by Charles Parsons and published by Cambridge University Press. This book was released on 2007-12-24 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Charles Parsons examines the notion of object, with the aim to navigate between nominalism, denying that distinctively mathematical objects exist, and forms of Platonism that postulate a transcendent realm of such objects. He introduces the central mathematical notion of structure and defends a version of the structuralist view of mathematical objects, according to which their existence is relative to a structure and they have no more of a 'nature' than that confers on them. Parsons also analyzes the concept of intuition and presents a conception of it distantly inspired by that of Kant, which describes a basic kind of access to abstract objects and an element of a first conception of the infinite.
Author : Alan Richardson
Publisher : Cambridge University Press
ISBN 13 : 1009103016
Total Pages : 325 pages
Book Rating : 4.0/5 (91 download)
Download or read book Interpreting Carnap written by Alan Richardson and published by Cambridge University Press. This book was released on 2024-01-31 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rudolf Carnap (1891–1970), one of the most important philosophers of the twentieth century, helped found logical positivism, was one of the originators of the field of philosophy of science, and was a leading contributor to semantics and inductive logic. This volume of new essays, written by leading international experts, places Carnap in his philosophical context and studies his topics, his interests, and the major stages of his thought. The essays reassess Carnap's place in the history of analytic philosophy through his approach to metaphysics, values, politics, epistemology and philosophy of science. They delve into important topics of Carnap's mature thought, namely explication, naturalism, and his defence of analyticity; and they recover the logical and the linguistic components of philosophy and how they unfolded in the syntax-semantics relation, induction, and language-planning. The resulting interpretation of Carnap will be illuminating for both current and future research.
Author : Dawn Leslie
Publisher : Routledge
ISBN 13 : 1134483724
Total Pages : 280 pages
Book Rating : 4.1/5 (344 download)
Download or read book Debates in Mathematics Education written by Dawn Leslie and published by Routledge. This book was released on 2013-10-01 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Debates in Mathematics Education explores the major issues that mathematics teachers encounter in their daily lives. It engages with established and contemporary debates, promotes and supports critical reflection and aims to stimulate both novice and experienced teachers to reach informed judgements and argue their point of view with deeper theoretical knowledge and understanding. Written by experts in the field of mathematics education, it investigates and offers fresh insight into topics of central importance, including: Gender, social inequality and mathematics Mathematics, politics and climate change The history and culture of mathematics Using popular culture in the mathematics classroom The concept of ‘ability’ and its impact on learning What we mean by ‘teaching for understanding’ Choosing and using examples in teaching The fitness of formal examinations. Designed to stimulate discussion and support you in your own research, writing and practice, Debates in Mathematics Education will be a valuable resource for any student or practising teacher engaged in initial teacher training, continuing professional development or Masters level study. It also has much to offer to those leading initial teacher education programmes, and to beginning doctoral students looking for a survey of the field of mathematics education research.
Author : N. Bednarz
Publisher : Springer Science & Business Media
ISBN 13 : 9400917325
Total Pages : 342 pages
Book Rating : 4.4/5 (9 download)
Download or read book Approaches to Algebra written by N. Bednarz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot be actually numerically calculated, except if those magnitudes are exactly measured by a certain unit. The theory of proportions does not have access to such operations. It cannot be seen as an "arithmetic" of ratios. Even if Euclidean geometry is done in a highly theoretical context, its axioms are essentially semantic. This is contrary to Mahoney's second characteristic. This cannot be said of the theory of proportions, which is less semantic. Only synthetic proofs are considered rigorous in Greek geometry. Arithmetic reasoning is also synthetic, going from the known to the unknown. Finally, analysis is an approach to geometrical problems that has some algebraic characteristics and involves a method for solving problems that is different from the arithmetical approach. 3. GEOMETRIC PROOFS OF ALGEBRAIC RULES Until the second half of the 19th century, Euclid's Elements was considered a model of a mathematical theory. This may be one reason why geometry was used by algebraists as a tool to demonstrate the accuracy of rules otherwise given as numerical algorithms. It may also be that geometry was one way to represent general reasoning without involving specific magnitudes. To go a bit deeper into this, here are three geometric proofs of algebraic rules, the frrst by Al-Khwarizmi, the other two by Cardano.
Author : Christine Hopkins
Publisher : Routledge
ISBN 13 : 1135398453
Total Pages : 257 pages
Book Rating : 4.1/5 (353 download)
Download or read book Understanding Primary Mathematics written by Christine Hopkins and published by Routledge. This book was released on 2013-01-11 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this textbook, the foundations of mathematics are made explicit and the reader is guided through the background knowledge and understanding that are required for the subject, offering a well-structured overview of the important issues to be considered when learning about mathematics on a Primary QTS course, and a coherent approach to the content to be found in the standards for QTS, the National Curriculum at Key Stages 1 and 2 and the numeracy strategy. The authors aim to help teachers review and restructure the understanding of mathematics gained during their education, progressing from partial memories of a few process to an understanding of why the skills they were taught make sense and how they fit into a coherent mathematics curriculum, arguing that to teach mathematics effectively it is not enough to be able to do the mathematics, you need to understand why you do what you do. Aimed at all teachers of primary mathematics, this book is also likely to be valuable to secondary teachers, parents, administrators and others interested in the foundations of school mathematics. Written for trainee and practicing teachers, this book de-mystifies the primary mathematics UK curriculum and offers a valuable reference for effective mathematicss teaching.
Author : Jason Matthiopoulos
Publisher : John Wiley & Sons
ISBN 13 : 1119991722
Total Pages : 501 pages
Book Rating : 4.1/5 (199 download)
Download or read book How to be a Quantitative Ecologist written by Jason Matthiopoulos and published by John Wiley & Sons. This book was released on 2011-04-12 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ecological research is becoming increasingly quantitative, yet students often opt out of courses in mathematics and statistics, unwittingly limiting their ability to carry out research in the future. This textbook provides a practical introduction to quantitative ecology for students and practitioners who have realised that they need this opportunity. The text is addressed to readers who haven't used mathematics since school, who were perhaps more confused than enlightened by their undergraduate lectures in statistics and who have never used a computer for much more than word processing and data entry. From this starting point, it slowly but surely instils an understanding of mathematics, statistics and programming, sufficient for initiating research in ecology. The book’s practical value is enhanced by extensive use of biological examples and the computer language R for graphics, programming and data analysis. Key Features: Provides a complete introduction to mathematics statistics and computing for ecologists. Presents a wealth of ecological examples demonstrating the applied relevance of abstract mathematical concepts, showing how a little technique can go a long way in answering interesting ecological questions. Covers elementary topics, including the rules of algebra, logarithms, geometry, calculus, descriptive statistics, probability, hypothesis testing and linear regression. Explores more advanced topics including fractals, non-linear dynamical systems, likelihood and Bayesian estimation, generalised linear, mixed and additive models, and multivariate statistics. R boxes provide step-by-step recipes for implementing the graphical and numerical techniques outlined in each section. How to be a Quantitative Ecologist provides a comprehensive introduction to mathematics, statistics and computing and is the ideal textbook for late undergraduate and postgraduate courses in environmental biology. "With a book like this, there is no excuse for people to be afraid of maths, and to be ignorant of what it can do." —Professor Tim Benton, Faculty of Biological Sciences, University of Leeds, UK
Author : Paul Loya
Publisher : Springer
ISBN 13 : 1493967959
Total Pages : 730 pages
Book Rating : 4.4/5 (939 download)
Download or read book Amazing and Aesthetic Aspects of Analysis written by Paul Loya and published by Springer. This book was released on 2018-05-11 with total page 730 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lively prose and imaginative exercises draw the reader into this unique introductory real analysis textbook. Motivating the fundamental ideas and theorems that underpin real analysis with historical remarks and well-chosen quotes, the author shares his enthusiasm for the subject throughout. A student reading this book is invited not only to acquire proficiency in the fundamentals of analysis, but to develop an appreciation for abstraction and the language of its expression. In studying this book, students will encounter: the interconnections between set theory and mathematical statements and proofs; the fundamental axioms of the natural, integer, and real numbers; rigorous ε-N and ε-δ definitions; convergence and properties of an infinite series, product, or continued fraction; series, product, and continued fraction formulæ for the various elementary functions and constants. Instructors will appreciate this engaging perspective, showcasing the beauty of these fundamental results.
