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Author : Jean E. Cunningham,Orest J. Fiume
Publisher : Jcc Press
Page : 200 pages
File Size : 52,7 Mb
Release : 2017-09-30
Category : Business & Economics
ISBN : 0999380109
How management accounting evolved with Lean principles.
Author : Ethan D. Bloch
Publisher : Springer Science & Business Media
Page : 577 pages
File Size : 52,9 Mb
Release : 2011-05-27
Category : Mathematics
ISBN : 9780387721767
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 : Jonathan Borwein
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 50,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461585107
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 Stillwell
Publisher : Springer Science & Business Media
Page : 253 pages
File Size : 44,6 Mb
Release : 2013-10-16
Category : Mathematics
ISBN : 9783319015774
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 : John Harrison
Publisher : Springer Science & Business Media
Page : 193 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781447115915
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 : P. Ehrlich
Publisher : Springer Science & Business Media
Page : 313 pages
File Size : 43,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401582483
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 : James Roy Newman
Publisher : Courier Corporation
Page : 632 pages
File Size : 52,9 Mb
Release : 2000-09-18
Category : Mathematics
ISBN : 0486411516
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 (booknews.com).
Author : Claude W. Burrill
Publisher : Unknown
Page : 182 pages
File Size : 53,5 Mb
Release : 1967
Category : Arithmetic
ISBN : STANFORD:36105033263794
Author : John M. H. Olmsted
Publisher : Courier Dover Publications
Page : 241 pages
File Size : 46,8 Mb
Release : 2018-09-12
Category : Mathematics
ISBN : 9780486827643
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 : Phil Pine
Publisher : Peterson's
Page : 850 pages
File Size : 53,7 Mb
Release : 2009-06-15
Category : Juvenile Nonfiction
ISBN : 9780768927917
For students, this updated guide teaches test-taking strategies and tests all the skills needed to do well on the SAT. For parents, there is a 24-page Parent's Guide that provides information on financial aid and scholarships.
Author : J. B. Roberts
Publisher : Courier Dover Publications
Page : 160 pages
File Size : 52,6 Mb
Release : 2018-03-21
Category : Mathematics
ISBN : 9780486829869
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 : C.H.Jr. Edwards
Publisher : Springer Science & Business Media
Page : 363 pages
File Size : 53,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461262305
The calculus has served for three centuries as the principal quantitative language of Western science. In the course of its genesis and evolution some of the most fundamental problems of mathematics were first con fronted and, through the persistent labors of successive generations, finally resolved. Therefore, the historical development of the calculus holds a special interest for anyone who appreciates the value of a historical perspective in teaching, learning, and enjoying mathematics and its ap plications. My goal in writing this book was to present an account of this development that is accessible, not solely to students of the history of mathematics, but to the wider mathematical community for which my exposition is more specifically intended, including those who study, teach, and use calculus. The scope of this account can be delineated partly by comparison with previous works in the same general area. M. E. Baron's The Origins of the Infinitesimal Calculus (1969) provides an informative and reliable treat ment of the precalculus period up to, but not including (in any detail), the time of Newton and Leibniz, just when the interest and pace of the story begin to quicken and intensify. C. B. Boyer's well-known book (1949, 1959 reprint) met well the goals its author set for it, but it was more ap propriately titled in its original edition-The Concepts of the Calculus than in its reprinting.
Author : Elliott Mendelson
Publisher : Dover Books on Mathematics
Page : 0 pages
File Size : 53,8 Mb
Release : 2008
Category : Mathematics
ISBN : 0486457923
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 : Frank Arntzenius,Cian Seán Dorr
Publisher : Oxford University Press
Page : 297 pages
File Size : 55,5 Mb
Release : 2012-01-19
Category : Philosophy
ISBN : 9780199696604
Frank Arntzenius presents a series of radical ideas about the structure of space and time, and establishes a new metaphysical position which holds that the fundamental structure of the physical world is purely geometrical structure. He argues that we should broaden our conceptual horizons and accept that spaces other than spacetime may exist.
Author : Andreas Löffler,Lutz Kruschwitz
Publisher : Springer
Page : 125 pages
File Size : 49,7 Mb
Release : 2019-07-03
Category : Business & Economics
ISBN : 9783030201036
This open access textbook is the first to provide Business and Economics Ph.D. students with a precise and intuitive introduction to the formal backgrounds of modern financial theory. It explains Brownian motion, random processes, measures, and Lebesgue integrals intuitively, but without sacrificing the necessary mathematical formalism, making them accessible for readers with little or no previous knowledge of the field. It also includes mathematical definitions and the hidden stories behind the terms discussing why the theories are presented in specific ways.
