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Author : Jean E. Cunningham
Publisher : Jcc Press
ISBN 13 : 9780999380109
Total Pages : 200 pages
Book Rating : 4.3/5 (81 download)
Download or read book Real Numbers written by Jean E. Cunningham and published by Jcc Press. This book was released on 2017-09-30 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: How management accounting evolved with Lean principles.
Author : Ethan D. Bloch
Publisher : Springer Science & Business Media
ISBN 13 : 0387721762
Total Pages : 577 pages
Book Rating : 4.3/5 (877 download)
Download or read book The Real Numbers and Real Analysis written by Ethan D. Bloch and published by Springer Science & Business Media. This book was released on 2011-05-27 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs. It is organized in a distinctive, flexible way that would make it equally appropriate to undergraduate mathematics majors who want to continue in mathematics, and to future mathematics teachers who want to understand the theory behind calculus. The Real Numbers and Real Analysis will serve as an excellent one-semester text for undergraduates majoring in mathematics, and for students in mathematics education who want a thorough understanding of the theory behind the real number system and calculus.
Author : John Stillwell
Publisher : Springer Science & Business Media
ISBN 13 : 331901577X
Total Pages : 253 pages
Book Rating : 4.3/5 (19 download)
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.
Author : Jonathan Borwein
Publisher : Springer Science & Business Media
ISBN 13 : 1461585104
Total Pages : 433 pages
Book Rating : 4.4/5 (615 download)
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.
Author : John M. H. Olmsted
Publisher : Courier Dover Publications
ISBN 13 : 048682764X
Total Pages : 241 pages
Book Rating : 4.4/5 (868 download)
Download or read book The Real Number System written by John M. H. Olmsted and published by Courier Dover Publications. This book was released on 2018-09-12 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise but thorough and systematic, this categorical discussion presents a series of step-by-step axioms. The highly accessible text includes numerous examples and more than 300 exercises, all with answers. 1962 edition.
Author : J. B. Roberts
Publisher : Courier Dover Publications
ISBN 13 : 0486829863
Total Pages : 160 pages
Book Rating : 4.4/5 (868 download)
Download or read book The Real Number System in an Algebraic Setting written by J. B. Roberts and published by Courier Dover Publications. This book was released on 2018-03-21 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceeding from a review of the natural numbers to the positive rational numbers, this text advances to the nonnegative real numbers and the set of all real numbers. 1962 edition.
Author : P. Ehrlich
Publisher : Springer Science & Business Media
ISBN 13 : 9401582483
Total Pages : 313 pages
Book Rating : 4.4/5 (15 download)
Download or read book Real Numbers, Generalizations of the Reals, and Theories of Continua written by P. Ehrlich and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their appearance in the late 19th century, the Cantor--Dedekind theory of real numbers and philosophy of the continuum have emerged as pillars of standard mathematical philosophy. On the other hand, this period also witnessed the emergence of a variety of alternative theories of real numbers and corresponding theories of continua, as well as non-Archimedean geometry, non-standard analysis, and a number of important generalizations of the system of real numbers, some of which have been described as arithmetic continua of one type or another. With the exception of E.W. Hobson's essay, which is concerned with the ideas of Cantor and Dedekind and their reception at the turn of the century, the papers in the present collection are either concerned with or are contributions to, the latter groups of studies. All the contributors are outstanding authorities in their respective fields, and the essays, which are directed to historians and philosophers of mathematics as well as to mathematicians who are concerned with the foundations of their subject, are preceded by a lengthy historical introduction.
Author : Joseph T. Sinclair
Publisher : Real Estate Investment Press
ISBN 13 : 9781886907003
Total Pages : 478 pages
Book Rating : 4.9/5 (7 download)
Download or read book Real Numbers written by Joseph T. Sinclair and published by Real Estate Investment Press. This book was released on 2008-10 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Maria H. Andersen
Publisher : Cengage Learning
ISBN 13 : 9780538493604
Total Pages : 0 pages
Book Rating : 4.4/5 (936 download)
Download or read book Elementary Algebra written by Maria H. Andersen and published by Cengage Learning. This book was released on 2010-01-05 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Claude W. Burrill
Publisher :
ISBN 13 :
Total Pages : 182 pages
Book Rating : 4.F/5 ( download)
Download or read book Foundations of Real Numbers written by Claude W. Burrill and published by . This book was released on 1967 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jay Abramson
Publisher :
ISBN 13 : 9789888407439
Total Pages : 892 pages
Book Rating : 4.4/5 (74 download)
Download or read book College Algebra written by Jay Abramson and published by . This book was released on 2018-01-07 with total page 892 pages. Available in PDF, EPUB and Kindle. Book excerpt: College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they've learned. Coverage and Scope In determining the concepts, skills, and topics to cover, we engaged dozens of highly experienced instructors with a range of student audiences. The resulting scope and sequence proceeds logically while allowing for a significant amount of flexibility in instruction. Chapters 1 and 2 provide both a review and foundation for study of Functions that begins in Chapter 3. The authors recognize that while some institutions may find this material a prerequisite, other institutions have told us that they have a cohort that need the prerequisite skills built into the course. Chapter 1: Prerequisites Chapter 2: Equations and Inequalities Chapters 3-6: The Algebraic Functions Chapter 3: Functions Chapter 4: Linear Functions Chapter 5: Polynomial and Rational Functions Chapter 6: Exponential and Logarithm Functions Chapters 7-9: Further Study in College Algebra Chapter 7: Systems of Equations and Inequalities Chapter 8: Analytic Geometry Chapter 9: Sequences, Probability and Counting Theory
Author : John Harrison
Publisher : Springer Science & Business Media
ISBN 13 : 1447115910
Total Pages : 193 pages
Book Rating : 4.4/5 (471 download)
Download or read book Theorem Proving with the Real Numbers written by John Harrison and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the use of the real numbers in theorem proving. Typ ically, theorem provers only support a few 'discrete' datatypes such as the natural numbers. However the availability of the real numbers opens up many interesting and important application areas, such as the verification of float ing point hardware and hybrid systems. It also allows the formalization of many more branches of classical mathematics, which is particularly relevant for attempts to inject more rigour into computer algebra systems. Our work is conducted in a version of the HOL theorem prover. We de scribe the rigorous definitional construction of the real numbers, using a new version of Cantor's method, and the formalization of a significant portion of real analysis. We also describe an advanced derived decision procedure for the 'Tarski subset' of real algebra as well as some more modest but practically useful tools for automating explicit calculations and routine linear arithmetic reasoning. Finally, we consider in more detail two interesting application areas. We discuss the desirability of combining the rigour of theorem provers with the power and convenience of computer algebra systems, and explain a method we have used in practice to achieve this. We then move on to the verification of floating point hardware. After a careful discussion of possible correctness specifications, we report on two case studies, one involving a transcendental function.
Author : Michael Henle
Publisher : American Mathematical Soc.
ISBN 13 : 0883857774
Total Pages : 231 pages
Book Rating : 4.8/5 (838 download)
Download or read book Which Numbers Are Real? written by Michael Henle and published by American Mathematical Soc.. This book was released on 2012-12-31 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: Everyone knows the real numbers, those fundamental quantities that make possible all of mathematics from high school algebra and Euclidean geometry through the Calculus and beyond; and also serve as the basis for measurement in science, industry, and ordinary life. This book surveys alternative real number systems: systems that generalize and extend the real numbers yet stay close to these properties that make the reals central to mathematics. Alternative real numbers include many different kinds of numbers, for example multidimensional numbers (the complex numbers, the quaternions and others), infinitely small and infinitely large numbers (the hyperreal numbers and the surreal numbers), and numbers that represent positions in games (the surreal numbers). Each system has a well-developed theory, including applications to other areas of mathematics and science, such as physics, the theory of games, multi-dimensional geometry, and formal logic. They are all active areas of current mathematical research and each has unique features, in particular, characteristic methods of proof and implications for the philosophy of mathematics, both highlighted in this book. Alternative real number systems illuminate the central, unifying role of the real numbers and include some exciting and eccentric parts of mathematics. Which Numbers Are Real? Will be of interest to anyone with an interest in numbers, but specifically to upper-level undergraduates, graduate students, and professional mathematicians, particularly college mathematics teachers.
Author : Matthew Hill
Publisher : AuthorHouse
ISBN 13 : 1467026670
Total Pages : 39 pages
Book Rating : 4.4/5 (67 download)
Download or read book Real World Numbers written by Matthew Hill and published by AuthorHouse. This book was released on 2011-12 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides support in keeping with the major goals of National Council of Teachers of Mathematics curriculum. It provides an important mathematical topic, the number system, which will be learned through K-8th grade, and used through high school and college. The instructional emphasis is designed to communicate knowledge and skills in mathematics across different grade levels, while offering the opportunity for children to learn about the number system in a fun and easy way. The book focuses on key areas of important emphasis, necessary for building math fluency in pre-algebra and algebra.
Author : George Pedrick
Publisher : Springer Science & Business Media
ISBN 13 : 1441985549
Total Pages : 293 pages
Book Rating : 4.4/5 (419 download)
Download or read book A First Course in Analysis written by George Pedrick and published by Springer Science & Business Media. This book was released on 2012-09-10 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text on advanced calculus discusses such topics as number systems, the extreme value problem, continuous functions, differentiation, integration and infinite series. The reader will find the focus of attention shifted from the learning and applying of computational techniques to careful reasoning from hypothesis to conclusion. The book is intended both for a terminal course and as preparation for more advanced studies in mathematics, science, engineering and computation.
Author : Elliott Mendelson
Publisher : Dover Books on Mathematics
ISBN 13 : 9780486457925
Total Pages : 0 pages
Book Rating : 4.4/5 (579 download)
Download or read book Number Systems and the Foundations of Analysis written by Elliott Mendelson and published by Dover Books on Mathematics. This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geared toward undergraduate and beginning graduate students, this study explores natural numbers, integers, rational numbers, real numbers, and complex numbers. Numerous exercises and appendixes supplement the text. 1973 edition.
Author : John H. Conway
Publisher : Springer Science & Business Media
ISBN 13 : 1461240727
Total Pages : 313 pages
Book Rating : 4.4/5 (612 download)
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
