Book Of Lemmas

Author : Archimedes
Publisher : Unknown
Page : 524 pages
File Size : 54,6 Mb
Release : 1897
Category : Geometry
ISBN : UOMDLP:abw0362:0001.001

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The Works of Archimedes by Archimedes Pdf

Author : Thomas F. Glick,Steven John Livesey,Faith Wallis
Publisher : Psychology Press
Page : 632 pages
File Size : 50,9 Mb
Release : 2005
Category : History
ISBN : 0415969301

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Medieval Science, Technology, and Medicine by Thomas F. Glick,Steven John Livesey,Faith Wallis Pdf

Demonstrates that the millennium from the fall of the Roman Empire to the flowering of the Renaissance was a period of great intellectual and practical achievement and innovation. This reference work will be useful to scholars, students, and general readers researching topics in many fields of study, including medieval studies and world history.

Author : Richard J. Rossi
Publisher : John Wiley & Sons
Page : 338 pages
File Size : 48,6 Mb
Release : 2011-10-05
Category : Mathematics
ISBN : 9781118030578

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Theorems, Corollaries, Lemmas, and Methods of Proof by Richard J. Rossi Pdf

A hands-on introduction to the tools needed for rigorous and theoretical mathematical reasoning Successfully addressing the frustration many students experience as they make the transition from computational mathematics to advanced calculus and algebraic structures, Theorems, Corollaries, Lemmas, and Methods of Proof equips students with the tools needed to succeed while providing a firm foundation in the axiomatic structure of modern mathematics. This essential book: Clearly explains the relationship between definitions, conjectures, theorems, corollaries, lemmas, and proofs Reinforces the foundations of calculus and algebra Explores how to use both a direct and indirect proof to prove a theorem Presents the basic properties of real numbers/li> Discusses how to use mathematical induction to prove a theorem Identifies the different types of theorems Explains how to write a clear and understandable proof Covers the basic structure of modern mathematics and the key components of modern mathematics A complete chapter is dedicated to the different methods of proof such as forward direct proofs, proof by contrapositive, proof by contradiction, mathematical induction, and existence proofs. In addition, the author has supplied many clear and detailed algorithms that outline these proofs. Theorems, Corollaries, Lemmas, and Methods of Proof uniquely introduces scratch work as an indispensable part of the proof process, encouraging students to use scratch work and creative thinking as the first steps in their attempt to prove a theorem. Once their scratch work successfully demonstrates the truth of the theorem, the proof can be written in a clear and concise fashion. The basic structure of modern mathematics is discussed, and each of the key components of modern mathematics is defined. Numerous exercises are included in each chapter, covering a wide range of topics with varied levels of difficulty. Intended as a main text for mathematics courses such as Methods of Proof, Transitions to Advanced Mathematics, and Foundations of Mathematics, the book may also be used as a supplementary textbook in junior- and senior-level courses on advanced calculus, real analysis, and modern algebra.

Author : Matt Kaufmann,Panagiotis Manolios,J Strother Moore
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 49,8 Mb
Release : 2013-04-17
Category : Computers
ISBN : 9781475731880

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Computer-Aided Reasoning by Matt Kaufmann,Panagiotis Manolios,J Strother Moore Pdf

Computer-Aided Reasoning: ACL2 Case Studies illustrates how the computer-aided reasoning system ACL2 can be used in productive and innovative ways to design, build, and maintain hardware and software systems. Included here are technical papers written by twenty-one contributors that report on self-contained case studies, some of which are sanitized industrial projects. The papers deal with a wide variety of ideas, including floating-point arithmetic, microprocessor simulation, model checking, symbolic trajectory evaluation, compilation, proof checking, real analysis, and several others. Computer-Aided Reasoning: ACL2 Case Studies is meant for two audiences: those looking for innovative ways to design, build, and maintain hardware and software systems faster and more reliably, and those wishing to learn how to do this. The former audience includes project managers and students in survey-oriented courses. The latter audience includes students and professionals pursuing rigorous approaches to hardware and software engineering or formal methods. Computer-Aided Reasoning: ACL2 Case Studies can be used in graduate and upper-division undergraduate courses on Software Engineering, Formal Methods, Hardware Design, Theory of Computation, Artificial Intelligence, and Automated Reasoning. The book is divided into two parts. Part I begins with a discussion of the effort involved in using ACL2. It also contains a brief introduction to the ACL2 logic and its mechanization, which is intended to give the reader sufficient background to read the case studies. A more thorough, textbook introduction to ACL2 may be found in the companion book, Computer-Aided Reasoning: An Approach. The heart of the book is Part II, where the case studies are presented. The case studies contain exercises whose solutions are on the Web. In addition, the complete ACL2 scripts necessary to formalize the models and prove all the properties discussed are on the Web. For example, when we say that one of the case studies formalizes a floating-point multiplier and proves it correct, we mean that not only can you read an English description of the model and how it was proved correct, but you can obtain the entire formal content of the project and replay the proofs, if you wish, with your copy of ACL2. ACL2 may be obtained from its home page. The results reported in each case study, as ACL2 input scripts, as well as exercise solutions for both books, are available from this page.

Author : Wim van den Dungen
Publisher : Lulu.com
Page : 354 pages
File Size : 53,7 Mb
Release : 2016-12-16
Category : Education
ISBN : 9781365540448

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Book of Lemmas by Wim van den Dungen Pdf

The 'Book of Lemmas' presents the outlines of an immanent and transcendent metaphysics. The latter is introduced by a survey of epistemology, in particular criticism, demarcating between valid and invalid propositions and between science and metaphysics. Immanent metaphysics does not move beyond the limitations of conceptual reason and is a heuristic of science. The ontological principal of the proposed process-ontology is the actual occasion, defined by its two state vectors: material efficiency and scalar finality (information and consciousness).

Author : Nathan Sidoli,Glen Van Brummelen
Publisher : Springer Science & Business Media
Page : 584 pages
File Size : 48,8 Mb
Release : 2013-10-30
Category : Mathematics
ISBN : 9783642367366

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From Alexandria, Through Baghdad by Nathan Sidoli,Glen Van Brummelen Pdf

This book honors the career of historian of mathematics J.L. Berggren, his scholarship, and service to the broader community. The first part, of value to scholars, graduate students, and interested readers, is a survey of scholarship in the mathematical sciences in ancient Greece and medieval Islam. It consists of six articles (three by Berggren himself) covering research from the middle of the 20th century to the present. The remainder of the book contains studies by eminent scholars of the ancient and medieval mathematical sciences. They serve both as examples of the breadth of current approaches and topics, and as tributes to Berggren's interests by his friends and colleagues.

Author : Roshdi Rashed
Publisher : Routledge
Page : 760 pages
File Size : 50,6 Mb
Release : 2013-06-26
Category : History
ISBN : 9781135072544

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Ibn al-Haytham's Theory of Conics, Geometrical Constructions and Practical Geometry by Roshdi Rashed Pdf

Theory of Conics, Geometrical Constructions and Practical Geometry: A History of Arabic Sciences and Mathematics Volume 3, provides a unique primary source on the history and philosophy of mathematics and science from the mediaeval Arab world. The present text is complemented by two preceding volumes of A History of Arabic Sciences and Mathematics, which focused on founding figures and commentators in the ninth and tenth centuries, and the historical and epistemological development of ‘infinitesimal mathematics’ as it became clearly articulated in the oeuvre of Ibn al-Haytham. This volume examines the increasing tendency, after the ninth century, to explain mathematical problems inherited from Greek times using the theory of conics. Roshdi Rashed argues that Ibn al-Haytham completes the transformation of this ‘area of activity,’ into a part of geometry concerned with geometrical constructions, dealing not only with the metrical properties of conic sections but with ways of drawing them and properties of their position and shape. Including extensive commentary from one of world’s foremost authorities on the subject, this book contributes a more informed and balanced understanding of the internal currents of the history of mathematics and the exact sciences in Islam, and of its adaptive interpretation and assimilation in the European context. This fundamental text will appeal to historians of ideas, epistemologists and mathematicians at the most advanced levels of research.

Author : S. A. Paipetis,Marco Ceccarelli
Publisher : Springer Science & Business Media
Page : 499 pages
File Size : 41,8 Mb
Release : 2010-05-25
Category : Technology & Engineering
ISBN : 9789048190911

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The Genius of Archimedes -- 23 Centuries of Influence on Mathematics, Science and Engineering by S. A. Paipetis,Marco Ceccarelli Pdf

Archimedes is held in high esteem by mathematicians, physicists and engineers as one of the most brilliant scientists of all time. These proceedings contain original, unpublished papers with the primary emphasis on the scientific work of Archimedes and his influence on the fields of mathematics, science, and engineering. There are also papers dealing with archaeological aspects and the myths and legends about Archimedes and about the Archimedes Palimpsest. Papers on the following subjects form part of the book: Hydrostatics (buoyancy, fluid pressure and density, stability of floating bodies); Mechanics (levers, pulleys, centers of gravity, laws of equilibrium); Pycnometry (measurement of volume and density); Integral Calculus (Archimedes as the father of the integral calculus, method of exhaustion, approximation of pi, determination of areas and volumes); Mathematical Physics (Archimedes as the father of mathematical physics, Law of the Lever, Law of Buoyancy, Axiomatization of Physics); History of Mathematics and Mechanics (Archimedes’ influence in antiquity, the middle ages, the Renaissance, and modern times; his influence on Leonado da Vinci, Galileo, Newton, and other giants of science and mathematics); Ancient Machines and Mechanisms (catapults, water screws, iron hands, compound pulleys, planetaria, water clocks, celestial globes, the Antikythera Mechanism); Archimedean Solids (their rediscovery in the Rennaisance and their applications in materials science and chemistry); Archimedean Legends (how stories of golden crowns, eureka moments, naked runs, burning mirrors, steam cannons, etc., have influenced us through the ages, whether true or not); The Cattle Problem (how its 18th century rediscovery inspired the study of equations with integer solutions); Teaching the Ideas of Archimedes (how his life and works have influenced the teaching of science, mathematics, and engineering).

Author : Archimedes
Publisher : Unknown
Page : 524 pages
File Size : 49,9 Mb
Release : 1897
Category : Geometry
ISBN : UOM:39015065510326

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The Works of Archimedes by Archimedes Pdf

Author : Alexander Jones
Publisher : Springer Science & Business Media
Page : 764 pages
File Size : 44,8 Mb
Release : 2013-11-09
Category : Mathematics
ISBN : 9781461249085

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Pappus of Alexandria Book 7 of the Collection by Alexander Jones Pdf

The seventh book of Pappus's Collection, his commentary on the Domain (or Treasury) of Analysis, figures prominently in the history of both ancient and modern mathematics: as our chief source of information concerning several lost works of the Greek geometers Euclid and Apollonius, and as a book that inspired later mathematicians, among them Viete, Newton, and Chasles, to original discoveries in their pursuit of the lost science of antiquity. This presentation of it is concerned solely with recovering what can be learned from Pappus about Greek mathematics. The main part of it comprises a new edition of Book 7; a literal translation; and a commentary on textual, historical, and mathematical aspects of the book. It proved to be convenient to divide the commentary into two parts, the notes to the text and translation, and essays about the lost works that Pappus discusses. The first function of an edition of this kind is, not to expose new discoveries, but to present a reliable text and organize the accumulated knowledge about it for the reader's convenience. Nevertheless there are novelties here. The text is based on a fresh transcription of Vat. gr. 218, the archetype of all extant manuscripts, and in it I have adopted numerous readings, on manuscript authority or by emendation, that differ from those of the old edition of Hultsch. Moreover, many difficult parts of the work have received little or no commentary hitherto.

Author : Jacob Perkins
Publisher : Packt Publishing Ltd
Page : 530 pages
File Size : 55,5 Mb
Release : 2014-08-26
Category : Computers
ISBN : 9781782167860

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Python 3 Text Processing with NLTK 3 Cookbook by Jacob Perkins Pdf

This book is intended for Python programmers interested in learning how to do natural language processing. Maybe you’ve learned the limits of regular expressions the hard way, or you’ve realized that human language cannot be deterministically parsed like a computer language. Perhaps you have more text than you know what to do with, and need automated ways to analyze and structure that text. This Cookbook will show you how to train and use statistical language models to process text in ways that are practically impossible with standard programming tools. A basic knowledge of Python and the basic text processing concepts is expected. Some experience with regular expressions will also be helpful.

Author : Roshdi Rashed,Athanase Papadopoulos
Publisher : Walter de Gruyter GmbH & Co KG
Page : 888 pages
File Size : 44,7 Mb
Release : 2017-10-23
Category : Philosophy
ISBN : 9783110569872

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Menelaus' ›Spherics‹ by Roshdi Rashed,Athanase Papadopoulos Pdf

Despite its importance in the history of Ancient science, Menelaus’ Spherics is still by and large unknown. This treatise, which lies at the foundation of spherical geometry, is lost in Greek but has been preserved in its Arabic versions. The reader will find here, for the first time edited and translated into English, the essentials of this tradition, namely: a fragment of an early Arabic translation and the first Arabic redaction of the Spherics composed by al-Māhānī /al-Harawī, together with a historical and mathematical study of Menelaus’ treatise. With this book, a new and important part of the Greek and Arabic legacy to the history of mathematics comes to light. This book will be an indispensable acquisition for any reader interested in the history of Ancient geometry and science and, more generally, in Greek and Arabic science and culture.

Author : Thomas L. Heath
Publisher : Cambridge University Press
Page : 447 pages
File Size : 48,9 Mb
Release : 2015-02-12
Category : History
ISBN : 9781107480421

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The Thirteen Books of Euclid's Elements by Thomas L. Heath Pdf

First published in 1926, this book contains the first volume of a three-volume English translation of the thirteen books of Euclid's Elements.

Author : Euclid
Publisher : Courier Corporation
Page : 468 pages
File Size : 46,6 Mb
Release : 1956-01-01
Category : Mathematics
ISBN : 9780486600888

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The Thirteen Books of Euclid's Elements by Euclid Pdf

Contains the complete English text of all thirteen books of the "Elements," along with critical analysis of each definition, postulate, and proposition.

Author : George Murray Paterson
Publisher : Unknown
Page : 140 pages
File Size : 44,5 Mb
Release : 1826
Category : Electronic
ISBN : BL:A0026576467

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Sacred Lemmas, Or Analyses of Scriptures Historical, Prophetical, and Evangelical, According to the Science of Analogies by George Murray Paterson Pdf