Are Numbers Real?

The Uncanny Relationships Between Maths and the Physical World

Author: Brian Clegg

Publisher: Hachette UK

ISBN: 1472139771

Category: Science

Page: 304

View: 7666

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Have you ever wondered what humans did before numbers existed? How they organized their lives, traded goods, or kept track of their treasures? What would your life be like without them? Numbers began as simple representations of everyday things, but mathematics rapidly took on a life of its own, occupying a parallel virtual world. In Are Numbers Real? Brian Clegg explores the way that maths has become more and more detached from reality, yet despite this is driving the development of modern physics. From devising a new counting system based on goats, through the weird and wonderful mathematics of imaginary numbers and infinity to the debate over whether mathematics has too much influence on the direction of science, this fascinating and accessible book opens the reader's eyes to the hidden reality of the strange yet familiar world of numbers.

Precalculus with Calculus Previews

Author: Dennis G. Zill,Jacqueline M. Dewar

Publisher: Jones & Bartlett Publishers

ISBN: 1449645151

Category: Mathematics

Page: 549

View: 8125

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Building off the success of Zill and Dewar's popular Essentials of Precalculus with Calculus Previews, the new Fifth Edition continues to include all of the outstanding features and learning tools found in the original text while incorporating additional topics of coverage that some courses may require. With a continued effort to keep the text complete, yet concise, the authors have included four additional chapters making the text a clear choice for many mainstream courses. Additional chapters include a new chapter on Polar Coordinates, as well as Triangle Trigonometry, Systems of Equations and Inequalities, and Sequences and Series. This student-friendly, full-color text offers numerous exercise sets and examples to aid in students' learning and understanding, and graphs and figures throughout serve to better illuminate key concepts. The exercise sets include engaging problems that focus on algebra, graphing, and function theory, the subtext of so many calculus problems. The authors are careful to use the terminology of calculus in an informal and comprehensible way to facilitate the student's successful transition into future calculus courses. New to the Fifth Edition: Includes a new Chapter 8, Polar Coordinates. A new appendix on Complex Numbers has been added. Available with a new graphing calculator manual, Exploring Mathematics: Solving Problems with the TI-84 Plus Graphing Calculator. Available with WebAssign Key Features: Vibrant full-color design illuminates key concepts and improves students' comprehension of graphs and figures. Translating Words into Functions section illustrates how to translate a verbal description into a symbolic representation of a function and demonstrates these translations with actual calculus problems. Chapter Review Exercises include problems that focus on algebra, graphing and function theory, the sub-text of so many calculus problems. Review questions include conceptual fill-in-the-blank and true-false questions, as well as numerous thought-provoking exercises. The Calculus Preview found at the end of each chapter offers students a glimpse of a single calculus concept along with the algebraic, logarithmic, and trigonometric manipulations that are necessary for the successful completion of typical problems related to that concept.

Essentials of Precalculus with Calculus Previews

Author: Dennis G. Zill,Jacqueline M. Dewar

Publisher: Jones & Bartlett Publishers

ISBN: 1449614973

Category: Mathematics

Page: 440

View: 3639

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Perfect for the one-term course, Essentials of Precalculus with Calculus Previews, Fifth Edition provides a complete, yet concise, introduction to precalculus concepts, focusing on important topics that will be of direct and immediate use in most calculus courses. Consistent with Professor Zill's eloquent writing style , this full-color text offers numerous exercise sets and examples to aid in student comprehension, while graphs and figures throughout serve to illuminate key concepts. The exercise sets include engaging problems that focus on algebra, graphing, and function theory, the sub-text of many calculus problems. The authors are careful to use calculus terminology in an informal and accessible way to facilitate the students successful transition into future calculus courses. With an outstanding collection of student and instructor resources, Essentials of Precalculus with Calculus Previews offers a complete teaching and learning package. Key Features: • Available with WebAssign Online Homework and Grading System • Vibrant four-color design illuminates key concepts and improves students' comprehension of graphs and figures. • Translating Words into Functions section illustrates how to translate a verbal description into a symbolic representation of a function and demonstrates these translations with actual calculus problems. • Chapter Review Exercises include problems that focus on the algebra, graphing, and function theory, the sub-text of so many calculus problems. Review questions include conceptual fill--in-the-blank and true/false, as well as numerous thought-provoking exercises. • The Calculus Preview found at the end of each chapter offers students a glimpse of a single calculus concept along with the algebraic, logarithmic, and trigonometric manipulations that are necessary for the successful completion on typical problems related to that concept. • Provides a complete teaching and learning program with numerous student and instructor resources, including the Student Resource Manual, WebAssign Access, Complete eLearning Center, and • Complete Instructor Solutions Manual. • Includes a new section on simple harmonic motion in Chapter 4. • A new section of parametric equations, as well as a new calculus preview of 3-space, has been added to Chapter 6. • Rotation of polar graphs is now discussed in Section 6.6 • The discussion of the hyperbolic functions in Section 5.4 has been expanded. • Numerous new problems have been added throughout the text. • The final exam at the end of the text has been expanded.

Number and Numbers

Author: Alain Badiou

Publisher: Polity

ISBN: 0745638791

Category: Mathematics

Page: 240

View: 3571

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Badiou goes through the most important innovations in the 19th-century theory of numbers, covering Frege, Dedekind, Peano and Cantor, and presents his own theory of numbers, one that has broader implications for social and political philosophy.

Precalculus with Calculus Previews

Expanded Volume

Author: Dennis G. Zill,Jacqueline M. Dewar

Publisher: Jones & Bartlett Learning

ISBN: 0763766313

Category: Mathematics

Page: 528

View: 7665

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Instructors are always faced with the dilemma of too much material and too little time. Perfect for the one-term course, Precalculus with Calculus Previews, Fourth Edition provides a complete, yet manageable, introduction to precalculus concepts while focusing on important topics that will be of direct and immediate use in most calculus courses. Consistent with Professor Zill's eloquent writing style, this four-color text offers numerous exercise sets and examples to aid in students' learning and understanding, while graphs and figures throughout serve to illuminate key concepts. The exercise sets include engaging problems that focus on algebra, graphing, and function theory, the sub-text of so many calculus problems. The authors are careful to use the terminology of calculus in an informal and comprehensible way to facilitate the student's successful transition into future calculus courses. With an extensive Student Study Guide and a full Solutions Manual for instructors, Precalculus with Calculus Previews offers a complete teaching and learning package!

The Real Numbers

An Introduction to Set Theory and Analysis

Author: John Stillwell

Publisher: Springer Science & Business Media

ISBN: 331901577X

Category: Mathematics

Page: 244

View: 5567

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While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory—uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself. By focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines a down-to-earth introduction to set theory with an exposition of the essence of analysis—the study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate students and professional mathematicians who, until now, have been content to "assume" the real numbers. Its prerequisites are calculus and basic mathematics. Mathematical history is woven into the text, explaining how the concepts of real number and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich presentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will help motivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncountable sets, countable ordinals, the continuum problem, the Cantor–Schröder–Bernstein theorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions.

High Performance MySQL

Optimization, Backups, and Replication

Author: Baron Schwartz,Peter Zaitsev,Vadim Tkachenko

Publisher: "O'Reilly Media, Inc."

ISBN: 1449332498

Category: Computers

Page: 826

View: 7684

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How can you bring out MySQL’s full power? With High Performance MySQL, you’ll learn advanced techniques for everything from designing schemas, indexes, and queries to tuning your MySQL server, operating system, and hardware to their fullest potential. This guide also teaches you safe and practical ways to scale applications through replication, load balancing, high availability, and failover. Updated to reflect recent advances in MySQL and InnoDB performance, features, and tools, this third edition not only offers specific examples of how MySQL works, it also teaches you why this system works as it does, with illustrative stories and case studies that demonstrate MySQL’s principles in action. With this book, you’ll learn how to think in MySQL. Learn the effects of new features in MySQL 5.5, including stored procedures, partitioned databases, triggers, and views Implement improvements in replication, high availability, and clustering Achieve high performance when running MySQL in the cloud Optimize advanced querying features, such as full-text searches Take advantage of modern multi-core CPUs and solid-state disks Explore backup and recovery strategies—including new tools for hot online backups

Prime Obsession

Bernhard Riemann and the Greatest Unsolved Problem in Mathematics

Author: John Derbyshire

Publisher: Joseph Henry Press

ISBN: 0309141257

Category: Science

Page: 446

View: 3059

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In August 1859 Bernhard Riemann, a little-known 32-year old mathematician, presented a paper to the Berlin Academy titled: "On the Number of Prime Numbers Less Than a Given Quantity." In the middle of that paper, Riemann made an incidental remark â€" a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. Today, after 150 years of careful research and exhaustive study, the question remains. Is the hypothesis true or false? Riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic â€" defining a precise formula to track and identify the occurrence of prime numbers. But it is that incidental remark â€" the Riemann Hypothesis â€" that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant shrouded in the shadows â€" subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age. It has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp, holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. Hunting down the solution to the Riemann Hypothesis has become an obsession for many â€" the veritable "great white whale" of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution. Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. Posited a century and a half ago, the Riemann Hypothesis is an intellectual feast for the cognoscenti and the curious alike. Not just a story of numbers and calculations, Prime Obsession is the engrossing tale of a relentless hunt for an elusive proof â€" and those who have been consumed by it.

Algebra in Ancient and Modern Times

Author: V. S. Varadarajan

Publisher: American Mathematical Soc.

ISBN: 9780821809891

Category: Mathematics

Page: 142

View: 5928

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From the reviews: This is a fine book on two counts. First ... there is the singularly excellent treatment of the solution of biquadratic equations. Second, it paints a strong picture of mathematics as a very long sequence of accomplishments, each building on the ones before, in a way that beginning mathematicians can understand and appreciate it. It paints the picture in a concise and economical style, the style that mathematicians find elegant. I would particularly recommend Algebra in Ancient and Modern Times to strong high school students, to high school algebra teachers, to people who want a history of mathematics with a lot of mathematics in the history, and to anyone who needs to know how to find an analytic solution to a nasty fourth degree polynomial. -- MAA Online Varadarajan spins a captivating tale, and the mathematics is first-rate. The book belongs on the shelf of any teacher of algebra ... The great treasure of this book is the discussion of the work of the great Hindu mathematicians Aryabhata (c.476-550), Brahmagupta (c.598-665), and Bhaskara (c.1114-1185). Teachers of mathematics history will be especially interested in Varadarajan's exposition of the remarkable cakravala, an algorithm for solving $X^2 - NY^2= \pm 1$. The book contains many exercises that enhance and supplement the text and that also include historical information. Many of the exercises ask readers to apply the historical techniques. Some of the exercises are quite difficult and will challenge any student. --Mathematics Teacher This text offers a special account of Indian work in diophantine equations during the 6th through 12th centuries and Italian work on solutions of cubic and biquadratic equations from the 11th through 16th centuries. The volume traces the historical development of algebra and the theory of equations from ancient times to the beginning of modern algebra, outlining some modern themes such as the fundamental theorem of algebra, Clifford algebras, and quaternions. It is geared toward undergraduates who have no background in calculus. V. S. Varadarajan is a professor of mathematics at the University of California, Los Angeles.

The Encyclopedia Britannica

A Dictionary of Arts, Sciences, and General Literature

Author: Thomas Spencer Baynes

Publisher: N.A

ISBN: N.A

Category: Encyclopedias and dictionaries

Page: N.A

View: 4138

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Russell's Unknown Logicism

A Study in the History and Philosophy of Mathematics

Author: S. Gandon

Publisher: Springer

ISBN: 1137024658

Category: Mathematics

Page: 263

View: 7555

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In this excellent book Sebastien Gandon focuses mainly on Russell's two major texts, Principa Mathematica and Principle of Mathematics , meticulously unpicking the details of these texts and bringing a new interpretation of both the mathematical and the philosophical content. Winner of The Bertrand Russell Society Book Award 2013.

The Irrationals

A Story of the Numbers You Can’t Count On

Author: Julian Havil

Publisher: Princeton University Press

ISBN: 1400841704

Category: Mathematics

Page: 312

View: 403

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The ancient Greeks discovered them, but it wasn't until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed. In The Irrationals, the first popular and comprehensive book on the subject, Julian Havil tells the story of irrational numbers and the mathematicians who have tackled their challenges, from antiquity to the twenty-first century. Along the way, he explains why irrational numbers are surprisingly difficult to define—and why so many questions still surround them. Fascinating and illuminating, this is a book for everyone who loves math and the history behind it.

Geometry: Euclid and Beyond

Author: Robin Hartshorne

Publisher: Springer Science & Business Media

ISBN: 9780387986500

Category: Mathematics

Page: 528

View: 3389

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This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra.

Aristotelian Logic

Author: William T. Parry,Edward A. Hacker

Publisher: SUNY Press

ISBN: 9780791406908

Category: Philosophy

Page: 545

View: 9753

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Proceedings of an international research and development conference, Tuscon, Arizona, October 1985. One hundred and twenty-eight papers are presented in this hefty volume. They are grouped into chapters covering climate, underutilized plants, irrigation and water management, biosphere reserves, water policy, animal resources, desert ecology, crop physiology and agronomy, urban environments, desertification, land intensification, and other topics related to the economy and management of arid lands. Provides detailed treatment of topics in traditional logic: theory of terms, theory of definition, informal fallacies, and division and classification.

Complex Numbers and Geometry

Author: Liang-shin Hahn

Publisher: Cambridge University Press

ISBN: 9780883855102

Category: Mathematics

Page: 192

View: 2444

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The purpose of this book is to demonstrate that complex numbers and geometry can be blended together beautifully. This results in easy proofs and natural generalizations of many theorems in plane geometry, such as the Napoleon theorem, the Ptolemy-Euler theorem, the Simson theorem, and the Morley theorem. The book is self-contained - no background in complex numbers is assumed - and can be covered at a leisurely pace in a one-semester course. Many of the chapters can be read independently. Over 100 exercises are included. The book would be suitable as a text for a geometry course, or for a problem solving seminar, or as enrichment for the student who wants to know more.

Introductory Mathematics: Algebra and Analysis

Author: Geoffrey C. Smith

Publisher: Springer Science & Business Media

ISBN: 9783540761785

Category: Mathematics

Page: 215

View: 8354

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This text provides a lively introduction to pure mathematics. It begins with sets, functions and relations, proof by induction and contradiction, complex numbers, vectors and matrices, and provides a brief introduction to group theory. It moves onto analysis, providing a gentle introduction to epsilon-delta technology and finishes with continuity and functions. The book features numerous exercises of varying difficulty throughout the text.

Myths and Realities

Conflicting Currents of Culture and Science

Author: John Whedbee

Publisher: iUniverse

ISBN: 0595362397

Category: History

Page: 464

View: 5941

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Myths and Realities creates a comprehensive picture of human life and culture, while at the same time placing it within the larger cosmic context. In recent decades, all areas of human knowledge have expanded to an unprecedented degree, so the overall context of human existence is at last beginning to emerge. In order to present such a wide-ranging portrait, Myths and Realities looks at history and human nature from several different viewpoints, giving special attention to four major topics: culture, science, religion and war. Science is a major contributor because it is the most reliable means of acquiring knowledge. Religion is part of the wider subject of beliefs in general, and these have been given particular consideration because any kind of ideology or belief tends to distort the worldview. War has been mankind's constant companion, but without its underlying mythology, it would lose all glory and romance. It would just be senseless savagery. Although man has many distinctive qualities, one of his most remarkable characteristics is his capacity to believe in all kinds of nonsensical notions. In fact, "the human animal will believe practically anything-so long as it makes absolutely no sense at all."