The World of Mathematics

A reprint of volume 3 of the four-volume edition originally published by Simon and Schuster in 1956. Annotation c. Book News, Inc., Portland, OR (

Author: James Roy Newman

Publisher: Courier Corporation

ISBN: 0486411532

Category: Mathematics

Page: 768

View: 338


Presents 33 essays on such topics as statistics and the design of experiments, group theory, the mathematics of infinity, the mathematical way of thinking, the unreasonableness of mathematics, and mathematics as an art. A reprint of volume 3 of the four-volume edition originally published by Simon and Schuster in 1956. Annotation c. Book News, Inc., Portland, OR (

Ramanujan s Place in the World of Mathematics

Finally, the book describes various current efforts to ensure that the legacy of Ramanujan will be preserved and continue to thrive in the future. Thus the book is an enlightening study of Ramanujan as a mathematician and a human being.

Author: Krishnaswami Alladi

Publisher: Springer Science & Business Media

ISBN: 9788132207672

Category: Mathematics

Page: 178

View: 926


This book is a collection of articles, all by the author, on the Indian mathematical genius Srinivasa Ramanujan as well as on some of the greatest mathematicians throughout the history whose life and works have things in common with Ramanujan. It presents a unique comparative study of Ramanujan’s spectacular discoveries and remarkable life and of the monumental contributions of various mathematical luminaries, some of whom, like Ramanujan, overcame great difficulties in life. In the book, some aspects of Ramanujan’s contributions, such as his remarkable formulae for the number pi, his pathbreaking work in the theory of partitions, and his fundamental observations on quadratic forms, are discussed. Finally, the book describes various current efforts to ensure that the legacy of Ramanujan will be preserved and continue to thrive in the future. Thus the book is an enlightening study of Ramanujan as a mathematician and a human being.

Philosophy of Mathematics

An Introduction to a World of Proofs and Pictures James Robert Brown.
heuristically useful in drawing consequences from ... Perhaps mathematics
describes the world. The Pythagoreans, for example, thought that the world is

Author: James Robert Brown

Publisher: Routledge

ISBN: 9781134806430

Category: Philosophy

Page: 232

View: 247


Philosophy of Mathematics is an excellent introductory text. This student friendly book discusses the great philosophers and the importance of mathematics to their thought. It includes the following topics: * the mathematical image * platonism * picture-proofs * applied mathematics * Hilbert and Godel * knots and nations * definitions * picture-proofs and Wittgenstein * computation, proof and conjecture. The book is ideal for courses on philosophy of mathematics and logic.

Reading and Writing the World with Mathematics

The Relationship of Teaching for Social Justice and Mathematics in Context Well,
I thought of mathematics as another subject in school that I hated. And I didn't
bother to think too much about world issues or everyday issues. Now I know it all

Author: Eric Gutstein

Publisher: Routledge

ISBN: 9781136284656

Category: Education

Page: 272

View: 623


Mathematics education in the United States can reproduce social inequalities whether schools use either "basic-skills" curricula to prepare mainly low-income students of color for low-skilled service jobs or "standards-based" curricula to ready students for knowledge-intensive positions. And working for fundamental social change and rectifying injustice are rarely included in any mathematics curriculum. Reading and Writing the World with Mathematics argues that mathematics education should prepare students to investigate and critique injustice, and to challenge, in words and actions, oppressive structures and acts. Based on teacher-research, the book provides a theoretical framework and practical examples for how mathematics educators can connect schooling to a larger sociopolitical context and concretely teach mathematics for social justice.

Mathematics and Science Education Around the World

How are biology and physics taught in the French curriculum? What are textbooks like elsewhere, and how much latitude do teachers have in the way they follow the texts?

Author: National Research Council

Publisher: National Academies Press

ISBN: 9780309056311

Category: Education

Page: 32

View: 240


Amid current efforts to improve mathematics and science education in the United States, people often ask how these subjects are organized and taught in other countries. They hear repeatedly that other countries produce higher student achievement. Teachers and parents wonder about the answers to questions like these: Why do the children in Asian cultures seem to be so good at science and mathematics? How are biology and physics taught in the French curriculum? What are textbooks like elsewhere, and how much latitude do teachers have in the way they follow the texts? Do all students receive the same education, or are they grouped by ability or perceived educational promise? If students are grouped, how early is this done? What are tests like, and what are the consequences for students? Are other countries engaged in Standards-like reforms? Does anything like "standards" play a role in other countries? Questions such as these reflect more than a casual interest in other countries' educational practices. They grow out of an interest in identifying ways to improve mathematics and science education in the United States. The focus of this short report is on what the Third International Mathematics and Science Study (TIMSS), a major international investigation of curriculum, instruction, and learning in mathematics and science, will be able to contribute to understandings of mathematics and science education around the world as well as to current efforts to improve student learning, particularly in the United States.

The World of Maria Gaetana Agnesi Mathematician of God

The name Maria Gaetana Agnesi and the dates of her birth and death (1718–99)
will probably be familiar only to the friendly but restricted community of historians
of mathematics. Agnesi was indeed the first woman to publish a mathematics ...

Author: Massimo Mazzotti

Publisher: JHU Press

ISBN: 0801887097

Category: Mathematics

Page: 240

View: 441


She is best known for her curve, the witch of Agnesi, which appears in almost all high school and undergraduate math books. She was a child prodigy who frequented the salon circuit, discussing mathematics, philosophy, history, and music in multiple languages. She wrote one of the first vernacular textbooks on calculus and was appointed chair of mathematics at the university in Bologna. In later years, however, she became a prominent figure within the Catholic Enlightenment, gave up the academic world, and devoted herself to the poor, the sick, the hungry, and the homeless. Indeed, the life of Maria Agnesi reveals a complex and enigmatic figure—one of the most fascinating characters in the history of mathematics. Using newly discovered archival documents, Massimo Mazzotti reconstructs the wide spectrum of Agnesi's social experience and examines her relationships to various traditions—religious, political, social, and mathematical. This meticulous study shows how she and her fellow Enlightenment Catholics modified tradition in an effort to reconcile aspects of modern philosophy and science with traditional morality and theology. Mazzotti's original and provocative investigation is also the first targeted study of the Catholic Enlightenment and its influence on modern science. He argues that Agnesi's life is the perfect lens through which we can gain a greater understanding of mid-eighteenth-century cultural trends in continental Europe. -- Paula Findlen

The Transformation of Mathematics in the Early Mediterranean World

... to focus on Khayyam is to a certain extent arbitrary: the problem had a
significant history in the Arabic world before and ... this divide, in terms of
changes in the practice of mathematics from the world of Archimedes to the world
of Khayyam.

Author: Reviel Netz

Publisher: Cambridge University Press

ISBN: 0521041740

Category: Mathematics

Page: 212

View: 903


The transformation of mathematics from ancient Greece to the medieval Arab-speaking world is here approached by focusing on a single problem proposed by Archimedes and the many solutions offered. In this trajectory Reviel Netz follows the change in the task from solving a geometrical problem to its expression as an equation, still formulated geometrically, and then on to an algebraic problem, now handled by procedures that are more like rules of manipulation. From a practice of mathematics based on the localized solution (and grounded in the polemical practices of early Greek science) we see a transition to a practice of mathematics based on the systematic approach (and grounded in the deuteronomic practices of Late Antiquity and the Middle Ages). With three chapters ranging chronologically from Hellenistic mathematics, through late Antiquity, to the medieval world, Reviel Netz offers an alternate interpretation of the historical journey of pre-modern mathematics.

Mathematics in the Real World

This introductory text will be an excellent resource for such courses, and will show students where mathematics arises in their everyday lives.

Author: W.D. Wallis

Publisher: Birkhäuser

ISBN: 1493948334

Category: Mathematics

Page: 270

View: 755


Mathematics in the Real World is a self-contained, accessible introduction to the world of mathematics for non-technical majors. With a focus on everyday applications and context, the topics in this textbook build in difficulty and are presented sequentially, starting with a brief review of sets and numbers followed by an introduction to elementary statistics, models, and graph theory. Data and identification numbers are then covered, providing the pathway to voting and finance. Each subject is covered in a concise and clear fashion through the use of real-world applications and the introduction of relevant terminology. Many sample problems – both writing exercises and multiple-choice questions – are included to help develop students’ level of understanding and to offer a variety of options to instructors. Covering six major units and outlining a one-semester course, Mathematics in the Real World is aimed at undergraduate liberal art students fulfilling the mathematics requirement in their degree program. This introductory text will be an excellent resource for such courses, and will show students where mathematics arises in their everyday lives.

Engaging Young Students in Mathematics Through Competitions World Perspectives and Practices Volume I Competition Ready Mathematics Entertaining and Informative Problems from the Wfnmc8 Congress in Semriach Austria 2018

The two volumes of Engaging Young Students in Mathematics through Competitions present a wide scope of aspects relating to mathematics competitions and their meaning in the world of mathematical research, teaching and entertainment.Volume I ...

Author: Robert Geretschlager

Publisher: World Scientific Publishing Company

ISBN: 9811205825

Category: Mathematics

Page: 200

View: 640


The two volumes of Engaging Young Students in Mathematics through Competitions present a wide scope of aspects relating to mathematics competitions and their meaning in the world of mathematical research, teaching and entertainment.Volume I contains a wide variety of fascinating mathematical problems of the type often presented at mathematics competitions as well as papers by an international group of authors involved in problem development, in which we can get a sense of how such problems are created in various specialized areas of competition mathematics as well as recreational mathematics.It will be of special interest to anyone interested in solving original mathematics problems themselves for enjoyment to improve their skills. It will also be of special interest to anyone involved in the area of problem development for competitions, or just for recreational purposes.The various chapters were written by the participants of the 8th Congress of the World Federation of National Mathematics Competitions in Austria in 2018.

An Historical Introduction to the Philosophy of Mathematics A Reader

Plato's work in the philosophy of mathematics contains a variety of influential
assertions and arguments. Among them are the following seven claims: PC1
Knowledge is of eternal objects. (Phaedo, Republic) PC2 The sensible world is ...

Author: Russell Marcus

Publisher: Bloomsbury Publishing

ISBN: 9781472532916

Category: Philosophy

Page: 896

View: 152


A comprehensive collection of historical readings in the philosophy of mathematics and a selection of influential contemporary work, this much-needed introduction reveals the rich history of the subject. An Historical Introduction to the Philosophy of Mathematics: A Reader brings together an impressive collection of primary sources from ancient and modern philosophy. Arranged chronologically and featuring introductory overviews explaining technical terms, this accessible reader is easy-to-follow and unrivaled in its historical scope. With selections from key thinkers such as Plato, Aristotle, Descartes, Hume and Kant, it connects the major ideas of the ancients with contemporary thinkers. A selection of recent texts from philosophers including Quine, Putnam, Field and Maddy offering insights into the current state of the discipline clearly illustrates the development of the subject. Presenting historical background essential to understanding contemporary trends and a survey of recent work, An Historical Introduction to the Philosophy of Mathematics: A Reader is required reading for undergraduates and graduate students studying the philosophy of mathematics and an invaluable source book for working researchers.

Exploring the World of Mathematics

It's amazing how ten simple digits can be used in an endless number of ways to benefit man. The development of these ten digits and their many uses is the fascinating story you hold in your hands: Exploring the World of Mathematics.

Author: John Hudson Tiner


ISBN: 0890514127

Category: Mathematics

Page: 157

View: 704


Numbers surround us. Just try to make it through a day without using any. It's impossible: telephone numbers, calendars, volume settings, shoe sizes, speed limits, weights, street numbers, microwave timers, TV channels, and the list goes on and on. The many advancements and branches of mathematics were developed through the centuries as people encountered problems and relied upon math to solve them. It's amazing how ten simple digits can be used in an endless number of ways to benefit man. The development of these ten digits and their many uses is the fascinating story you hold in your hands: Exploring the World of Mathematics. Book jacket.

How the World Works Mathematics

Numbers have entranced p3eople ever since. This book tells the story of mankind through mathematics from cave dwelling to modern life.

Author: Arcturus Publishing

Publisher: How the World Works

ISBN: 1838575545

Category: Mathematics

Page: 208

View: 342


In order to understand the universe you must know the language in which it is written. And that language is mathematics. - Galileo (1564-1642) For hundreds of thousands of years, we have sought order in the apparent chaos of the universe. Mathematics has been our most valuable tool in that search, uncovering the patterns and rules that govern our world and beyond. How the World Works: Mathematics serves as a brilliant introduction to the history and enigmas of this vast discipline, plotting a journey from innumerate cave-dwellers, through the towering mathematical intellects of the last 4,000 years, to the breakthroughs of today. This book includes: * Accessible explanations of mathematical principles, such as chaos theory and set theory * Profiles of famed and lesser-known mathematicians, including Pythagoras, Descartes and Madhava of Sangamagrama * Quirky facts and anecdotes * A useful glossary of mathematical terms ABOUT THE SERIES: How the World Works is an illustrated series by Arcturus Publishing. Each book provides an engaging introduction to a branch of human knowledge, outlining key principles and charting its development across history up to the present day.

The Art of Mathematics

There exist, for each mathematician, two clearly defined worlds. The first is the
world of mathematics and the other is the world of reality. The real world is just
what you think it is. It is the world of sense experience—the world you see and
feel; ...

Author: Jerry P. King

Publisher: Springer

ISBN: 9781489963390

Category: Mathematics

Page: 313

View: 415


The beauty of mathematics eludes all but a small, select handful of people. This monumental classic will illuminate the aesthetic delights of mathematics for all to behold. Why should only a tiny aristocracy hold the key to appreciating the elegance of mathematics? Why should intelligent, cultured people, who can easily articulate the brilliance of Shakespeare's imagery, quake at the prospect of deciphering a simple algebraic formula? Jerry King, a mathematics professor and a poet, razes the barriers between a world of two cultures and hands us the tools for appreciating the art and treasures of this elegant discipline. In his fluid, poetic voice, he initiates us into the splendid wonders of the Mathworld. He provides us with an original framework for contemplating mathematics as art. He deepens our ultimate comprehension of art by comparing the beauty of a Rembrandt as well as a Jackson Pollock with the riches to be mined in an elegant proof. Like the great philosophers of the past, Dr. King searches for pure Truth--a quest possible today only in the realm of mathematics. With his infectious enthusiasm, he explains with utmost clarity the intellectually stimulating underpinnings of both pure and applied mathematics. He goes on to decry how our educational system has failed by perfunctorily teaching us mathematics, depriving us of the pillars of beauty upon which mathematics rests. Never before has a book spoken so eloquently to our soul in instilling an appreciation for the grandeur of mathematics. Through Dr. King, the muses of mathematics will no longer sing for others and not for us. The elegant world of mathematics awaits us all to savor.

Digital And The Real World The Computational Foundations Of Mathematics Science Technology And Philosophy

Obviously, there are deep relations between complex dynamical systems in
mathematics, computational complexity in computer science, and modeling
formal languages in logic. These complexity classes are not restricted to the
digital world, ...

Author: Mainzer Klaus

Publisher: World Scientific

ISBN: 9789813225503

Category: Mathematics

Page: 472

View: 887


In the 21st century, digitalization is a global challenge of mankind. Even for the public, it is obvious that our world is increasingly dominated by powerful algorithms and big data. But, how computable is our world? Some people believe that successful problem solving in science, technology, and economies only depends on fast algorithms and data mining. Chances and risks are often not understood, because the foundations of algorithms and information systems are not studied rigorously. Actually, they are deeply rooted in logics, mathematics, computer science and philosophy. Therefore, this book studies the foundations of mathematics, computer science, and philosophy, in order to guarantee security and reliability of the knowledge by constructive proofs, proof mining and program extraction. We start with the basics of computability theory, proof theory, and information theory. In a second step, we introduce new concepts of information and computing systems, in order to overcome the gap between the digital world of logical programming and the analog world of real computing in mathematics and science. The book also considers consequences for digital and analog physics, computational neuroscience, financial mathematics, and the Internet of Things (IoT). Contents: Introduction Basics of Computability Hierarchies of Computability Constructive Proof Theory Computational Mathematics and Digital Information Systems Intuitionistic Mathematics and Human Creativity Proof Mining bridging Logic, Mathematics, and Computer Science Reverse Mathematics Bridging Logic, Mathematics, and Computer Science From Intuitionistic to Homotopy Type Theory — Bridging Logic, Mathematics, and Computer Science Real Computability and Real Analysis Complexity Theory of Real Computing Real Computing and Neural Networks Complexity of Algorithmic Information Complexity of Information Dynamics Digital and Real Physics Digital and Real Computing in the Social World Philosophical Outlook Readership: Undergraduate and graduate students, scientists and readers who are interested in foundational, interdisciplinary, and philosophical questions of mathematics, computer science, and science in general. Keywords: Computability;Complexity;Constructive Mathematics;Proof Mining;Real Computing;Analog Networks;Information System;Digital PhysicsReview: Key Features: Compact introduction into the foundations of modern mathematics and computer science Bridging the gap between digital, real and analog computing by new concepts of information systems Consequences in natural and social sciences with respect to scientific computing

The World as a Mathematical Game

This explains why the theory of games was developed above all in the context of
mathematical economics research and with more of a supporting than a
foundational role, while it failed to make progress in the world of mathematics

Author: Giorgio Israel

Publisher: Springer Science & Business Media

ISBN: 9783764398965

Category: Science

Page: 208

View: 109


Galileo and Newton’s work towards the mathematisation of the physical world; Leibniz’s universal logical calculus; the Enlightenment’s mathématique sociale. John von Neumann inherited all these aims and philosophical intuitions, together with an idea that grew up around the Vienna Circle of an ethics in the form of an exact science capable of guiding individuals to make correct decisions. With the help of his boundless mathematical capacity, von Neumann developed a conception of the world as a mathematical game, a world globally governed by a universal logic in which individual consciousness moved following different strategies: his vision guided him from set theory to quantum mechanics, to economics and to his theory of automata (anticipating artificial intelligence and cognitive science). This book provides the first comprehensive scientific and intellectual biography of John von Neumann, a man who perhaps more than any other is representative of twentieth century science.

50 Greatest Mathematicians of the World

Remarkable Mathematician: Ioan James World's Great Mathematician: G.R.
Chatwal, S.C. Anand, Rajkumar, S.K. Arora, K. Narang 3. Mathematics and Its
History: John Stillwell 4. A Contextual History of Mathematics: Ronald Calinger 5.

Author: Rajesh Thakur

Publisher: Prabhat Prakashan

ISBN: 9788184302158

Category: Biography & Autobiography

Page: 200

View: 732


Mathematics is considered the most dreaded subject. However it is extremely interesting and one should read about it. Had this subject not been interesting then some of the great physicist, doctors, lawyers, poets, story writers, etc., in their later life would not have turned to study it and made great discoveries in the field of mathematics. While mathematics itself may be a form idable subject for many, the lives and accomplishments of history’s greatest mathematicians are fascinating. This book is intended for people interested to know the heroic journey of those great mathematicians who have made important contribution to mathematics, through their ideas, teaching or in other ways. The main emphasis is on their work and achievement in the field of mathematics. I hope this book will serve adual purpose: firstly help students realize mathematics is not to be dreaded but helpful in achieving in other subjects; secondly help those who hate the subject respect it.