Download or read book Irrational Numbers and Limits written by Sophia Foster Richardson and published by . This book was released on 1914 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Elements of the Mathematical Theory of Limits written by John Gaston Leathem and published by . This book was released on 1925 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Irrational Numbers and Their Representation by Sequences and Series written by Henry Parker Manning and published by . This book was released on 1906 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A History of the Conceptions of Limits and Fluxions in Great Britain from Newton to Woodhouse written by Florian Cajori and published by . This book was released on 1919 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Irrational Numbers written by Ivan Niven and published by American Mathematical Soc.. This book was released on 1985-12-31 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, Ivan Niven provides a masterful exposition of some central results on irrational, transcendental, and normal numbers. He gives a complete treatment by elementary methods of the irrationality of the exponential, logarithmic, and trigonometric functions with rational arguments. The approximation of irrational numbers by rationals, up to such results as the best possible approximation of Hurwitz, is also given with elementary techniques. The last third of the monograph treats normal and transcendental numbers, including the transcendence of p and its generalization in the Lindermann theorem, and the Gelfond-Schneider theorem. Most of the material in the first two thirds of the book presupposes only calculus and beginning number theory. The book is almost wholly self-contained. The results needed from analysis and algebra are central and well-known theorems, and complete references to standard works are given to help the beginner. The chapters are, for the most part, independent. There is a set of notes at the end of each chapter citing the main sources used by the author and suggesting further reading.
Download or read book The Teaching of Mathematics in the Elementary and the Secondary School written by Jacob William Albert Young and published by . This book was released on 1924 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Irrational Numbers and Their Representation by Sequences and Series written by Henry Parker Manning and published by Createspace Independent Publishing Platform. This book was released on 2016-06-24 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dr. Manning's book on irrational numbers contains a presentation in a simple form of another field of mathematical inquiry, such as is also eminently_ suited for placing in the hands of the ordinary schoolmaster. We have decided that the geometry of proportion shall be taught to schoolboys without reference to irrational quantities, but we have not yet eliminated a spirit of reckless extravagance in the quite unnecessary use of infinite series, often with total disregard for their convergency. In Dr. Manning's treatment an irrational number is defined as forming a point of separation between rational numbers of two classes, the numbers of one class being less than those of the other. This definition appears to involve the assumption (pp. 7, 10, &c.) that the point of separation is unique, in other words, that there cannot be two irrational numbers which have not some rational number separating them. Perhaps this assumption may be regarded as a definition of equality of irrational numbers; in any case, the inquiring reader would find it necessary to examine more fully the references to Dedekind's and Cantor's writings given on p. 56. Once the assumption or definition is made, the representation of numbers by sequences readily follows. The theory of limits is discussed on p. 57, and in the following chapter the notion of a sequence is shown to give rise to that of a series. The remaining portion of the book is mainly devoted to the study of convergence, and includes the well-known multiplication theorem and applications to the still better-known binomial and exponential series. -Nature, Vol. 75
Download or read book Irrational Numbers written by Ivan Niven and published by Cambridge University Press. This book was released on 2005-08-18 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, Ivan Niven provides a masterful exposition of some central results on irrational, transcendental, and normal numbers. He gives a complete treatment by elementary methods of the irrationality of the exponential, logarithmic, and trigonometric functions with rational arguments. The approximation of irrational numbers by rationals, up to such results as the best possible approximation of Hurwitz, is also given with elementary technique. The last third of the monograph treats normal and transcendental numbers, including the Lindemann theorem, and the Gelfond-Schneider theorem. The book is wholly self-contained. The results needed from analysis and algebra are central. Well-known theorems, and complete references to standard works are given to help the beginner. The chapters are for the most part independent. There are notes at the end of each chapter citing the main sources used by the author and suggesting further reading.
Download or read book The Principles of Mathematics written by Bertrand Russell and published by . This book was released on 1903 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Limits Limits Everywhere written by David Applebaum and published by OUP Oxford. This book was released on 2012-03-01 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: A quantity can be made smaller and smaller without it ever vanishing. This fact has profound consequences for science, technology, and even the way we think about numbers. In this book, we will explore this idea by moving at an easy pace through an account of elementary real analysis and, in particular, will focus on numbers, sequences, and series. Almost all textbooks on introductory analysis assume some background in calculus. This book doesn't and, instead, the emphasis is on the application of analysis to number theory. The book is split into two parts. Part 1 follows a standard university course on analysis and each chapter closes with a set of exercises. Here, numbers, inequalities, convergence of sequences, and infinite series are all covered. Part 2 contains a selection of more unusual topics that aren't usually found in books of this type. It includes proofs of the irrationality of e and π, continued fractions, an introduction to the Riemann zeta function, Cantor's theory of the infinite, and Dedekind cuts. There is also a survey of what analysis can do for the calculus and a brief history of the subject. A lot of material found in a standard university course on "real analysis" is covered and most of the mathematics is written in standard theorem-proof style. However, more details are given than is usually the case to help readers who find this style daunting. Both set theory and proof by induction are avoided in the interests of making the book accessible to a wider readership, but both of these topics are the subjects of appendices for those who are interested in them. And unlike most university texts at this level, topics that have featured in popular science books, such as the Riemann hypothesis, are introduced here. As a result, this book occupies a unique position between a popular mathematics book and a first year college or university text, and offers a relaxed introduction to a fascinating and important branch of mathematics.
Download or read book Principles of Mathematics written by Bertrand Russell and published by Routledge. This book was released on 2020-02-25 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which Principia Mathematica provided the detailed proof, and introduced the work of Frege to a wider audience. In addition to the new introduction by John Slater, this edition contains Russell's introduction to the 1937 edition in which he defends his position against his formalist and intuitionist critics.
Download or read book Understanding the Infinite written by Shaughan Lavine and published by Harvard University Press. This book was released on 1998-01-13 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: How can the infinite, a subject so remote from our finite experience, be an everyday tool for the working mathematician? Blending history, philosophy, mathematics, and logic, Shaughan Lavine answers this question with exceptional clarity. Making use of the mathematical work of Jan Mycielski, he demonstrates that knowledge of the infinite is possible, even according to strict standards that require some intuitive basis for knowledge.
Download or read book A Concept of Limits written by Donald W. Hight and published by Courier Corporation. This book was released on 1977-01-01 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: An exploration of conceptual foundations and the practical applications of limits in mathematics, this text offers a concise introduction to the theoretical study of calculus. It analyzes the idea of a generalized limit and explains sequences and functions to those for whom intuition cannot suffice. Many exercises with solutions. 1966 edition.
Download or read book Functions Limits and Continuity written by Paulo Ribenboim and published by New York : Wiley. This book was released on 1964 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Theory of Functions of a Real Variable and the Theory of Fourier s Series written by Ernest William Hobson and published by . This book was released on 1907 with total page 791 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Iterated Limits in General Analysis written by Ralph Eugene Root and published by . This book was released on 1914 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sir Asutosh Mookerjee written by and published by . This book was released on 1921 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt:
