What is Mathematics?

An Elementary Approach to Ideas and Methods

Author: Richard Courant,Herbert Robbins,Ian Stewart

Publisher: Oxford University Press, USA

ISBN: 9780195105193

Category: Mathematics

Page: 566

View: 1800

A discussion of fundamental mathematical principles from algebra to elementary calculus designed to promote constructive mathematical reasoning.

What is Mathematics, Really?

Author: Reuben Hersh

Publisher: Oxford University Press, USA

ISBN: 9780195130874

Category: Medical

Page: 343

View: 6208

Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos. What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.


Author: Timothy Gowers

Publisher: Sterling Publishing Company, Inc.

ISBN: 9781402768972

Category: Mathematics

Page: 180

View: 9822

Mathematics is a subject we are all exposed to in our daily lives, but one that many of us fear. Timothy Gowers’s entertaining overview of the topic explains the differences between what we learn at school and advanced mathematics, and helps the math phobic emerge with a clearer understanding of such paradoxical-sounding concepts as “infinity,” “curved space,” and “imaginary numbers.” From basic ideas to philosophical queries to common sociological questions about the mathematical community, this book unravels the mysteries of space and numbers.

Philosophy of Mathematics

Selected Readings

Author: Paul Benacerraf,Hilary Putnam

Publisher: Cambridge University Press

ISBN: 9780521296489

Category: Mathematics

Page: 600

View: 6214

The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.

Understanding Mathematics

Author: K.B. Sinha

Publisher: Universities Press

ISBN: 9788173713552

Category: Mathematics

Page: 236

View: 679

The book explains the 'hows' and 'ways' and also whets the appetite of a good student for more of good mathematics.

Chinese Mathematics in the Thirteenth Century

Author: Ulrich Libbrecht

Publisher: Courier Corporation

ISBN: 0486446190

Category: Mathematics

Page: 555

View: 7380

An exploration of the life and work of the thirteenth-century mathematician Ch'in, this fascinating book examines a range of mathematical issues that reflect Chinese life of a millennium ago. Its first part consists of four closely related studies of Ch'in and his work. The first study brings together what is known of the mathematician's life and of the history of his only extant work, the Shu-shu chiu-chang. Subsequent studies examine the entire range of mathematical techniques and problems found within Ch'in's book. The core of this book consists of an in-depth study of what modern mathematicians still refer to as the Chinese remainder theorem for the solution of indeterminate equations of the first degree. This was Ch'in's most original contribution to mathematics--so original that no one could correctly explain Ch'in's procedure until the early nineteenth century. This volume's concluding study unites information on artisanal, economic, administrative, and military affairs dispersed throughout Ch'in's writings, providing rare insights into thirteenth-century China.

Multiple Perspectives on Mathematics Teaching and Learning

Author: Jo Boaler

Publisher: Greenwood Publishing Group

ISBN: 9781567505344

Category: Education

Page: 278

View: 448

Authors analyze mathematics education from a range of perspectives. They address such practical problems as: maximizing the impact of teacher education programmes; increasing learning opportunities for students working in groups; and the impact of male domination in mixed classrooms.


The Core Course for A-level

Author: Linda Bostock,Suzanne Chandler

Publisher: Nelson Thornes

ISBN: 9780859503068

Category: Juvenile Nonfiction

Page: 752

View: 7213

Written for the Edexcel Syllabus B and similar schemes offered by the major Awarding Bodies. The authors have incorported many modern approaches to mathematical understanding whilst retaining the most effective traditional methods. Plenty of worked examples and stimulating exercises also support this highly popular text.

Science and Civilisation in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth

Author: Joseph Needham

Publisher: Cambridge University Press

ISBN: 9780521058018

Category: Body, Mind & Spirit

Page: 926

View: 8686

After two volumes mainly introductory, Dr Needham now embarks upon his systematic study of the development of the natural sciences in China. The Sciences of the Earth follow: geography and cartography, geology, seismology and mineralogy. Dr Needham distinguishes parallel traditions of scientific cartography and religious cosmography in East and West, discussing orbocentric wheel-maps, the origins of the rectangular grid system, sailing charts and relief maps, Chinese survey methods, and the impact of Renaissance cartography on the East. Finally-and here Dr Needham's work has no Western predecessors-there are full accounts of the Chinese contribution to geology and mineralogy.

New Common Entrance Mathematics

Author: Walter Phillips

Publisher: Nelson Thornes

ISBN: 9780748717613

Category: Juvenile Nonfiction

Page: 224

View: 1176

Covering all the topics included in the Primary Mathematics syllabus for the Caribbean countries, this textbook, and the corresponding workbook, are designed to prepare pupils for the Common Entrance Examination. They are also suitable for less able pupils who are in the early stages of the secondary-school course.

Women in Mathematics

Author: Lynn M. Osen

Publisher: MIT Press

ISBN: 9780262650090

Category: Biography & Autobiography

Page: 185

View: 6911

Examines the lives and scholarly endeavors of women who have profoundly affected mathematical thought since antiquity

Power in Numbers

The Rebel Women of Mathematics

Author: Talithia Williams

Publisher: Race Point Publishing

ISBN: 0760360286

Category: Mathematics

Page: 288

View: 7775

Prepare to be inspired. Power in Numbers: The Rebel Women of Mathematics is a full-color volume that takes aim at the forgotten influence of women on the development of mathematics over the last two millennia. You'll see each eminent mathematician come to life on each page, women like the astronomer-philosopher Hypatia, theoretical physicist Emmy Noether, and rocket scientist Annie Easley. Power in Numbers: The Rebel Women of Mathematics is an affirmation of female genius and a celebration of the boundless applications of mathematics. See their stories!

Learning Mathematics

Issues, Theory and Classroom Practice

Author: Anthony Orton

Publisher: A&C Black

ISBN: 1441140018

Category: Education

Page: 242

View: 7276

• Why do some students achieve more than others? • Do we have to wait until pupils are "ready"? • Can children discover math for themselves? • Does language interfere with the learning of math? This classic text, written from the viewpoint of the math teacher, provides answers to these and many more questions. Each chapter explores a particular issue that illustrates the interaction between theory and practice. New chapters have been included on cognition, pattern, and ICT.


Philosophy of Mathematics

Author: Michael A. E. Dummett

Publisher: Harvard University Press

ISBN: 9780674319356

Category: Philosophy

Page: 331

View: 2596

No one has figured more prominently in the study of the German philosopher Gottlob Frege than Michael Dummett. His magisterial Frege: Philosophy of Language is a sustained, systematic analysis of Frege's thought, omitting only the issues in philosophy of mathematics. In this work Dummett discusses, section by section, Frege's masterpiece The Foundations of Arithmetic and Frege's treatment of real numbers in the second volume of Basic Laws of Arithmetic, establishing what parts of the philosopher's views can be salvaged and employed in new theorizing, and what must be abandoned, either as incorrectly argued or as untenable in the light of technical developments. Gottlob Frege (1848-1925) was a logician, mathematician, and philosopher whose work had enormous impact on Bertrand Russell and later on the young Ludwig Wittgenstein, making Frege one of the central influences on twentieth-century Anglo-American philosophy; he is considered the founder of analytic philosophy. His philosophy of mathematics contains deep insights and remains a useful and necessary point of departure for anyone seriously studying or working in the field.

The Words of Mathematics

An Etymological Dictionary of Mathematical Terms Used in English

Author: Steven Schwartzman

Publisher: MAA

ISBN: 9780883855119

Category: Mathematics

Page: 261

View: 4503

This book explains the origins of over 1500 mathematical terms used in English.

Children's Errors in Mathematics

Author: Alice Hansen

Publisher: SAGE

ISBN: 9781844457687

Category: Education

Page: 208

View: 5441

This practical guide to children's common errors and misconceptions in mathematics is ideal for primary trainees, helping them gain a deeper understanding of the difficulties encountered in mathematical development. This Second Edition has been fully revised and all links to the EYFS and the Revised Primary Framework have been updated. New research and literature are included, additional errors are considered, and using and applying mathematics is fully embedded throughout. Individual misconceptions are dealt with and in each case a description and explanation of the error is provided. The teacher's role in understanding and addressing common misconceptions is also covered.

A History of Mathematics

Author: Florian Cajori

Publisher: American Mathematical Soc.

ISBN: 9780821821022

Category: Mathematics

Page: 524

View: 9413

Originally published in 1893, this book was significantly revised and extended by the author (second edition, 1919) to cover the history of mathematics from antiquity to the end of World War I. Since then, three more editions were published, and the current volume is a reproduction of the fifth edition (1991). The book covers the history of ancient mathematics (Babylonian, Egyptian, Roman, Chinese, Japanese, Mayan, Hindu, and Arabic, with a major emphasis on ancient Greek mathematics). The chapters that follow explore European mathematics in the Middle Ages and the mathematics of the sixteenth, seventeenth, and eighteenth centuries (Vieta, Decartes, Newton, Euler, and Lagrange). The last and longest chapter discusses major mathematics events of the nineteenth and early twentieth centuries. Topics discussed in this chapter include synthetic and analytic geometry, algebra, analysis, the theory of functions, the theory of numbers, and others. In one concise volume, the author presents an interesting and reliable account of mathematics history. Cajori has mastered the art of incorporating an enormous amount of material into a smoothly flowing narrative. The review of the volume's third edition in Mathematical Reviews ends with the following words: "Chaque mathematicien devrait lire ce livre!"