Download or read book A Dictionary of Real Numbers written by Jonathan Borwein and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: How do we recognize that the number . 93371663 . . . is actually 2 IoglQ(e + 7r)/2 ? Gauss observed that the number 1. 85407467 . . . is (essentially) a rational value of an elliptic integral-an observation that was critical in the development of nineteenth century analysis. How do we decide that such a number is actually a special value of a familiar function without the tools Gauss had at his disposal, which were, presumably, phenomenal insight and a prodigious memory? Part of the answer, we hope, lies in this volume. This book is structured like a reverse telephone book, or more accurately, like a reverse handbook of special function values. It is a list of just over 100,000 eight-digit real numbers in the interval [0,1) that arise as the first eight digits of special values of familiar functions. It is designed for people, like ourselves, who encounter various numbers computationally and want to know if these numbers have some simple form. This is not a particularly well-defined endeavor-every eight-digit number is rational and this is not interesting. However, the chances of an eight digit number agreeing with a small rational, say with numerator and denominator less than twenty-five, is small. Thus the list is comprised primarily of special function evaluations at various algebraic and simple transcendental values. The exact numbers included are described below. Each entry consists of the first eight digits after the decimal point of the number in question.

Download or read book Exploring the Real Numbers written by Frederick W. Stevenson and published by . This book was released on 2000 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring the Real Numbers helps readers understand the real number system. Stevenson brings readers up to date with the study of the nature of real numbers, and provides a sense of the historical journey that has led to our current knowledge of the subject. Presents many interesting topics that arise during study of the real numbers. Offers 21 exploratory projects, encouraging readers to pursue concepts beyond the book. Includes over 100 carefully worked examples. Features abundant exercises throughout. For anyone interested in learning more about some of the very different and often beautiful aspects of mathematics.

Download or read book The Real Numbers written by John Stillwell and published by Springer Science & Business Media. This book was released on 2013-10-16 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The Story Of Numbers written by Asok Kumar Mallik and published by #N/A. This book was released on 2017-07-27 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: '… this could make an ideal end-of-year prize for a high-school student who is fascinated by all aspects of number. The subsections provide ideas and opportunities for mathematical exploration. This book might also be deemed a suitable resource for first-year undergraduates in that, via independent study, it would allow such students to broaden their knowledge of various number-theoretic ideas. I would recommend it for the purposes given above.'The Mathematical GazetteThis book is more than a mathematics textbook. It discusses various kinds of numbers and curious interconnections between them. Without getting into hardcore and difficult mathematical technicalities, the book lucidly introduces all kinds of numbers that mathematicians have created. Interesting anecdotes involving great mathematicians and their marvelous creations are included. The reader will get a glimpse of the thought process behind the invention of new mathematics. Starting from natural numbers, the book discusses integers, real numbers, imaginary and complex numbers and some special numbers like quaternions, dual numbers and p-adic numbers.Real numbers include rational, irrational and transcendental numbers. Iterations on real numbers are shown to throw up some unexpected behavior, which has given rise to the new science of 'Chaos'. Special numbers like e, pi, golden ratio, Euler's constant, Gauss's constant, amongst others, are discussed in great detail.The origin of imaginary numbers and the use of complex numbers constitute the next topic. It is shown why modern mathematics cannot even be imagined without imaginary numbers. Iterations on complex numbers are shown to generate a new mathematical object called 'Fractal', which is ubiquitous in nature. Finally, some very special numbers, not mentioned in the usual textbooks, and their applications, are introduced at an elementary level.The level of mathematics discussed in this book is easily accessible to young adults interested in mathematics, high school students, and adults having some interest in basic mathematics. The book concentrates more on the story than on rigorous mathematics.

Download or read book Math Dictionary With Solutions written by Chris Kornegay and published by SAGE Publications. This book was released on 1999-03-06 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: "I have never seen anything even close to this level of breadth. It′s a very thorough and comprehensive source book for mathematical ideas, terminology, definitions, and examples. Math Dictionary with Solutions, 2nd would be an excellent reference book for instructors of basic mathematics and statistics courses as well as for non-math majors taking required math and statistics courses." --Paul R. Swank, University of Houston "In addition to providing definitions as every dictionary must, it also provides clear and easy-to-follow examples that show how to carry out the most important mathematical operations to be used across these levels. This book is also a valuable resource for graduate students and academicians in the social sciences who are coping with the rapidly increasing emphasis on quantitative methods that, to be understood, require more familiarity with mathematical underpinnings than are typically a part of the academic background of many individuals in these fields." --Dennis W. Roncek, University of Nebraska, Omaha "This is a highly readable, accessible, reference source, the product of a huge amount of labor, obviously." --Hoben Thomas, The Pennsylvania State University Have you ever suddenly become stuck and not remembered how to divide a fraction or turn a fraction into a percentage? Or, have you taken a graduate statistics course and discovered that you can′t remember any of the terminology or techniques from a calculus course you took years ago? If either of these scenarios sounds familiar, then this book will provide you with the quick and easy review that you need. This reference book has math topics ranging from arithmetic through calculus arranged alphabetically by topic. Each topic is provided with a definition, explanation, and an example or two of how to solve a particular problem using the topic′s technique. Depending on the degree of difficulty of the topic, this material is covered in one or two paragraphs to several pages. To further facilitate learning, the topics are cross-referenced so that the reader can backtrack to easier topics if the current one is too difficult. This book is a "mathematics tutor-in-a-book" and provides a reliable reference for any researcher or manager who works with numbers or needs a review of mathematical concepts.

Download or read book An Introduction to Proof through Real Analysis written by Daniel J. Madden and published by John Wiley & Sons. This book was released on 2017-08-10 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: An engaging and accessible introduction to mathematical proof incorporating ideas from real analysis A mathematical proof is an inferential argument for a mathematical statement. Since the time of the ancient Greek mathematicians, the proof has been a cornerstone of the science of mathematics. The goal of this book is to help students learn to follow and understand the function and structure of mathematical proof and to produce proofs of their own. An Introduction to Proof through Real Analysis is based on course material developed and refined over thirty years by Professor Daniel J. Madden and was designed to function as a complete text for both first proofs and first analysis courses. Written in an engaging and accessible narrative style, this book systematically covers the basic techniques of proof writing, beginning with real numbers and progressing to logic, set theory, topology, and continuity. The book proceeds from natural numbers to rational numbers in a familiar way, and justifies the need for a rigorous definition of real numbers. The mathematical climax of the story it tells is the Intermediate Value Theorem, which justifies the notion that the real numbers are sufficient for solving all geometric problems. • Concentrates solely on designing proofs by placing instruction on proof writing on top of discussions of specific mathematical subjects • Departs from traditional guides to proofs by incorporating elements of both real analysis and algebraic representation • Written in an engaging narrative style to tell the story of proof and its meaning, function, and construction • Uses a particular mathematical idea as the focus of each type of proof presented • Developed from material that has been class-tested and fine-tuned over thirty years in university introductory courses An Introduction to Proof through Real Analysis is the ideal introductory text to proofs for second and third-year undergraduate mathematics students, especially those who have completed a calculus sequence, students learning real analysis for the first time, and those learning proofs for the first time. Daniel J. Madden, PhD, is an Associate Professor of Mathematics at The University of Arizona, Tucson, Arizona, USA. He has taught a junior level course introducing students to the idea of a rigorous proof based on real analysis almost every semester since 1990. Dr. Madden is the winner of the 2015 Southwest Section of the Mathematical Association of America Distinguished Teacher Award. Jason A. Aubrey, PhD, is Assistant Professor of Mathematics and Director, Mathematics Center of the University of Arizona.

Download or read book Mathematics Dictionary written by R.C. James and published by Springer Science & Business Media. This book was released on 1992-07-31 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: For more than 50 years, this classic reference has provided fundamental data in an accessible, concise form. This edition of the Mathematics Dictionary incorporates updated terms and concepts in its span of more than 8,000 topics from a broad spectrum of mathematical specialties. It features review-length descriptions of theories, practices and principles as well as a multilingual index.

Download or read book Webster s New World Dictionary of Mathematics written by William Karush and published by John Wiley & Sons. This book was released on 1989 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics, like many other specialized fields, has evolved a complex vocabulary of its own, a language not always intelligible to the newcomer. Webster's New World Dictionary of Mathematics defines, in a clear, easy-to-understand style, the terms all math students and laypersons need to know. Over 1400 important mathematical terms are listed in A-Z format, with dozens of charts and line drawings. As an added feature, the handy appendix directs readers to source material for further, in-depth study. Whether you're solving trigonometry problems - or studying geometry theorems - accessible, thorough definitions of unfamiliar terms make Webster's New World Dictionary of Mathematics a necessary resource. -- from back cover.

Download or read book The Encyclop dia Britannica written by Hugh Chisholm and published by . This book was released on 1911 with total page 1062 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Dictionary of Philosophy written by Antony Flew and published by Macmillan. This book was released on 1984-02-15 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a new, updated and revised edition of a reference work that has proved invaluable as a tool for the student of philosophy, as well as a handbook for the general reader. From the classical thinkers through Aquinas, Descartes, Spinoza, Kant, up to the modern age of Russell and Wittgenstein, this comprehensive dictionary spans the personalities, terminology, and vocabulary of hundreds of philosophers over thousands of years. This second edition of an important and invaluable work has been completely revised, and fifteen new major articles have been added. Now, more than ever before, A Dictionary of Philosophy is a necessary and timely work for the modern student of thought.

Download or read book The Encyclopedia Britannica written by and published by . This book was released on 1911 with total page 1054 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Concise Dictionary of Mathematics written by EDITORIAL BOARD and published by V&S Publishers. This book was released on 2015-06-01 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Remarkable progress continues to be made in mathematical sciences. This advancement has made inter-relationships amongst various branches within mathematics and with other branches of science highly evolving; leading to newer 'terms' being invented and getting added. These additions make mathematics a little more complex. Emerging complexity translates into more difficulties for students in grasping the problem. And what makes the comprehension problematic? It is the introduction of 'terms', their definition and how to apply them in physical, chemical, biological, biotechnology, and social sciences works. And if these terms are not adequately explained, students and other interested readers face a herculean task in understanding what the question is all about, and unless readers clearly understand the terminology, finding a solution is next to impossible. This book contains mathematical terms related to arithmetic, algebra, trigonometry, geometry, analytic geometry, differential & integral calculus and differential equations, probability, statistics, logic etc. Appendices in the form of important formulas from algebra, geometry, trigonometry, calculus, logarithms and antilogarithms have been added. A few entries contain cross references indicating where to find further applications of the topic under discussion. It is an ideal manual for mathematics complete with illustrative diagrams and formulas. Inclusion of Greek Alphabets, metric systems and other useful mathematical symbols in the book helps make the dictionary a complete mathematical reference tool.

Download or read book The Penguin Dictionary of Curious and Interesting Numbers written by David Wells and published by Penguin. This book was released on 1997-09-04 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides information on numbers and what makes particular ones noteworthy

Download or read book Handbook of the History and Philosophy of Mathematical Practice written by Bharath Sriraman and published by Springer Nature. This book was released on with total page 3221 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Book of Numbers written by John H. Conway and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: "...the great feature of the book is that anyone can read it without excessive head scratching...You'll find plenty here to keep you occupied, amused, and informed. Buy, dip in, wallow." -IAN STEWART, NEW SCIENTIST "...a delightful look at numbers and their roles in everything from language to flowers to the imagination." -SCIENCE NEWS "...a fun and fascinating tour of numerical topics and concepts. It will have readers contemplating ideas they might never have thought were understandable or even possible." -WISCONSIN BOOKWATCH "This popularization of number theory looks like another classic." -LIBRARY JOURNAL

Download or read book Encyclopedic Dictionary of Mathematics written by Nihon Sūgakkai and published by MIT Press. This book was released on 1993 with total page 1180 pages. Available in PDF, EPUB and Kindle. Book excerpt: V.1. A.N. v.2. O.Z. Apendices and indexes.

Download or read book Mathematics Illustrated Dictionary written by Jeanne Bendick and published by . This book was released on 1965 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over 150 entries define mathematical principles, terms, symbols, and abbreviations, and present short profiles of work of famous mathematicians. An appendix includes tables of mathematical symbols, formulas, weights and measures, and square roots, and logarithms.