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Author : Saitoh Saburou
Publisher : Unknown
Page : 128 pages
File Size : 43,5 Mb
Release : 2021-11
Category : Electronic
ISBN : 1649972245
Author : Saburou Saitoh
Publisher : Scientific Research Publishing, Inc. USA
Page : 333 pages
File Size : 50,9 Mb
Release : 2021-11-29
Category : Antiques & Collectibles
ISBN : 9781649972255
This is based on the record of how I have been discovering and pioneering a new world by breaking the first of the Ten Commandments of Mathematics, which has been 2300 years since Aristotle and must not be divided by zero. I am involved in the basic issues of humankind involved in mathematical physics, philosophy, and worldview. What is eternity and what is infinity? What is the significance of human existence?
Author : SABUROU SAITOH
Publisher : Scientific Research Publishing, Inc. USA
Page : 203 pages
File Size : 40,9 Mb
Release : 2021-02-04
Category : Mathematics
ISBN : 9781649970893
The common sense on the division by zero with the long and mysterious history is wrong and our basic idea on the space around the point at infinity is also wrong since Euclid. On the gradient or on differential coefficients we have a great missing since tan(π/2) = 0. Our mathematics is also wrong in elementary mathematics on the division by zero. In this book in a new and definite sense, we will show and give various applications of the division by zero 0/0 = 1/0 = z/0 = 0. In particular, we will introduce several fundamental concepts in calculus, Euclidean geometry, analytic geometry, complex analysis and differential equations. We will see new properties on the Laurent expansion, singularity, derivative, extension of solutions of differential equations beyond analytical and isolated singularities, and reduction problems of differential equations. On Euclidean geometry and analytic geometry, we will find new fields by the concept of the division by zero. We will collect many concrete properties in mathematical sciences from the viewpoint of the division by zero. We will know that the division by zero is our elementary and fundamental mathematics.
Author : Carl B. Boyer
Publisher : Courier Corporation
Page : 431 pages
File Size : 52,5 Mb
Release : 2012-10-09
Category : Mathematics
ISBN : 9780486175386
Fluent description of the development of both the integral and differential calculus — its early beginnings in antiquity, medieval contributions, and a consideration of Newton and Leibniz.
Author : Anonim
Publisher : BRILL
Page : 787 pages
File Size : 40,6 Mb
Release : 2024-03-11
Category : Philosophy
ISBN : 9789004691568
Zero has been axial in human development, but the origin and discovery of zero has never been satisfactorily addressed by a comprehensive, systematic and above all interdisciplinary research program. In this volume, over 40 international scholars explore zero under four broad themes: history; religion, philosophy & linguistics; arts; and mathematics & the sciences. Some propose that the invention/discovery of zero may have been facilitated by the prior evolution of a sophisticated concept of Nothingness or Emptiness (as it is understood in non-European traditions); and conversely, inhibited by the absence of, or aversion to, such a concept of Nothingness in the West. But not all scholars agree. Join the debate.
Author : Roger Herz-Fischler
Publisher : Wilfrid Laurier Univ. Press
Page : 208 pages
File Size : 51,6 Mb
Release : 1987
Category : Geometry
ISBN : 9780889201521
Author : Saburou Saitoh,Yoshihiro Sawano
Publisher : Springer
Page : 452 pages
File Size : 44,8 Mb
Release : 2016-10-14
Category : Mathematics
ISBN : 9789811005305
This book provides a large extension of the general theory of reproducing kernels published by N. Aronszajn in 1950, with many concrete applications.In Chapter 1, many concrete reproducing kernels are first introduced with detailed information. Chapter 2 presents a general and global theory of reproducing kernels with basic applications in a self-contained way. Many fundamental operations among reproducing kernel Hilbert spaces are dealt with. Chapter 2 is the heart of this book.Chapter 3 is devoted to the Tikhonov regularization using the theory of reproducing kernels with applications to numerical and practical solutions of bounded linear operator equations.In Chapter 4, the numerical real inversion formulas of the Laplace transform are presented by applying the Tikhonov regularization, where the reproducing kernels play a key role in the results.Chapter 5 deals with ordinary differential equations; Chapter 6 includes many concrete results for various fundamental partial differential equations. In Chapter 7, typical integral equations are presented with discretization methods. These chapters are applications of the general theories of Chapter 3 with the purpose of practical and numerical constructions of the solutions.In Chapter 8, hot topics on reproducing kernels are presented; namely, norm inequalities, convolution inequalities, inversion of an arbitrary matrix, representations of inverse mappings, identifications of nonlinear systems, sampling theory, statistical learning theory and membership problems. Relationships among eigen-functions, initial value problems for linear partial differential equations, and reproducing kernels are also presented. Further, new fundamental results on generalized reproducing kernels, generalized delta functions, generalized reproducing kernel Hilbert spaces, andas well, a general integral transform theory are introduced.In three Appendices, the deep theory of Akira Yamada discussing the equality problems in nonlinear norm inequalities, Yamada's unified and generalized inequalities for Opial's inequalities and the concrete and explicit integral representation of the implicit functions are presented.
Author : Denise Gaskins
Publisher : Tabletop Academy Press
Page : 288 pages
File Size : 55,8 Mb
Release : 2012-09-04
Category : Education
ISBN : 9781892083241
Author : Judith V. Grabiner
Publisher : Courier Corporation
Page : 274 pages
File Size : 54,5 Mb
Release : 2012-05-11
Category : Mathematics
ISBN : 9780486143743
This text examines the reinterpretation of calculus by Augustin-Louis Cauchy and his peers in the 19th century. These intellectuals created a collection of well-defined theorems about limits, continuity, series, derivatives, and integrals. 1981 edition.
Author : Anonim
Publisher : Oxford University Press, USA
Page : 238 pages
File Size : 55,5 Mb
Release : 2000
Category : Mathematics
ISBN : 9780195128420
In the tradition of "Longitude, " a small and engagingly written book on the history and meaning of zero--a "tour de force" of science history that takes us through the hollow circle that leads to infinity. 32 illustrations.
Author : David Crowley,Paul Heyer
Publisher : Routledge
Page : 337 pages
File Size : 50,9 Mb
Release : 2015-09-30
Category : Language Arts & Disciplines
ISBN : 9781317349402
Updated in a new 6th edition, Communication in History reveals how media has been influential in both maintaining social order and as powerful agents of change. With revised new readings, this anthology continues to be, as one reviewer wrote, "the only book in the sea of History of Mass Communication books that introduces readers to a more expansive, intellectually enlivening study of the relationship between human history and communication history". From print to the Internet, this book encompasses a wide-range of topics, that introduces readers to a more expansive, intellectually enlivening study of the relationship between human history and communication history.
Author : Peter Urquhart,Paul Heyer
Publisher : Routledge
Page : 348 pages
File Size : 48,8 Mb
Release : 2018-09-03
Category : Language Arts & Disciplines
ISBN : 9781351747325
Now in its 7th edition, Communication in History reveals how media has been influential in both maintaining social order and as powerful agents of change. Thirty-eight contributions from a wide range of voices offer instructors the opportunity to customize their courses while challenging students to build upon their own knowledge and skill sets. From stone-age symbols and early writing to the Internet and social media, readers are introduced to an expansive, intellectually enlivening study of the relationship between human history and communication media.
Author : Ekkehard Kopp
Publisher : Open Book Publishers
Page : 280 pages
File Size : 42,6 Mb
Release : 2020-10-23
Category : Mathematics
ISBN : 9781800640979
Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject.
Author : John Stillwell
Publisher : Springer Nature
Page : 400 pages
File Size : 46,9 Mb
Release : 2020-11-07
Category : Mathematics
ISBN : 9783030551933
This textbook provides a unified and concise exploration of undergraduate mathematics by approaching the subject through its history. Readers will discover the rich tapestry of ideas behind familiar topics from the undergraduate curriculum, such as calculus, algebra, topology, and more. Featuring historical episodes ranging from the Ancient Greeks to Fermat and Descartes, this volume offers a glimpse into the broader context in which these ideas developed, revealing unexpected connections that make this ideal for a senior capstone course. The presentation of previous versions has been refined by omitting the less mainstream topics and inserting new connecting material, allowing instructors to cover the book in a one-semester course. This condensed edition prioritizes succinctness and cohesiveness, and there is a greater emphasis on visual clarity, featuring full color images and high quality 3D models. As in previous editions, a wide array of mathematical topics are covered, from geometry to computation; however, biographical sketches have been omitted. Mathematics and Its History: A Concise Edition is an essential resource for courses or reading programs on the history of mathematics. Knowledge of basic calculus, algebra, geometry, topology, and set theory is assumed. From reviews of previous editions: “Mathematics and Its History is a joy to read. The writing is clear, concise and inviting. The style is very different from a traditional text. I found myself picking it up to read at the expense of my usual late evening thriller or detective novel.... The author has done a wonderful job of tying together the dominant themes of undergraduate mathematics.” Richard J. Wilders, MAA, on the Third Edition "The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century.... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community." European Mathematical Society, on the Second Edition
Author : Sigurd Angenent
Publisher : Unknown
Page : 134 pages
File Size : 55,6 Mb
Release : 2014-11-26
Category : Electronic
ISBN : 1505204844
MATH 221 FIRST Semester CalculusBy Sigurd Angenent