On Which Are Founded the Mathematical Theories of Logic and Probabilities
Author: George Boole
Publisher: Createspace Independent Publishing Platform
View: 7292An Investigation of the Laws of Thought: On Which are Founded the Mathematical Theories of Logic and Probabilities by George Boole. The design of the following treatise is to investigate the fundamental laws of those operations of the mind by which reasoning is performed; to give expression to them in the symbolical language of a Calculus, and upon this foundation to establish the science of Logic and construct its method; to make that method itself the basis of a general method for the application of the mathematical doctrine of Probabilities; and, finally, to collect from the various elements of truth brought to view in the course of these inquiries some probable intimations concerning the nature and constitution of the human mind. The following work is not a republication of a former treatise by the Author, entitled, "The Mathematical Analysis of Logic." Its earlier portion is indeed devoted to the same object, and it begins by establishing the same system of fundamental laws, but its methods are more general, and its range of applications far wider. It exhibits the results, matured by some years of study and reflection, of a principle of investigation relating to the intellectual operations, the previous exposition of which was written within a few weeks after its idea had been conceived.
Author: George 1815-1864 Boole
Publisher: Wentworth Press
View: 8512This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Author: George Boole
Category: Difference equations
View: 2782Written by the founder of symbolic logic (and Boolean algebra), this classic treatise on the calculus of finite differences offers a thorough discussion of the basic principles of the subject, covering nearly all the major theorems and methods with clarity and rigor. Includes more than 200 problems. 1872 edition.
The Growth of Scientific Knowledge
Author: Karl Popper
View: 6750Conjectures and Refutations is one of Karl Popper's most wide-ranging and popular works, notable not only for its acute insight into the way scientific knowledge grows, but also for applying those insights to politics and to history. It provides one of the clearest and most accessible statements of the fundamental idea that guided his work: not only our knowledge, but our aims and our standards, grow through an unending process of trial and error.
Being an Essay Towards a Calculus of Deductive Reasoning
Author: George Boole
Publisher: Cambridge University Press
View: 7734In The Mathematical Analysis of Logic, mathematician George Boole persuasively argues that logic should be aligned with mathematics, not philosophy.
Language, Literature, and Social Context : Essays in Honor of David W. Johnson
Author: D. W Johnson
Publisher: CUA Press
View: 8097With increasing interest in early Egyptian (Coptic) Christianity, this volume offers an important collection of essays about Coptic language, literature, and social history by the very finest authors in the field. The essays explore a wide range of topics and offer much to the advancement of Coptic studies
Author: James Clerk Maxwell
Publisher: CUP Archive
View: 3594This is a comprehensive edition of Maxwell's manuscript papers published virtually complete and largely for the first time. Maxwell's work was of central importance in establishing and developing the major themes of the physics of the nineteenth century: his theory of the electromagnetic field and the electromagnetic theory of light and his special place in the history of physics. His fecundity of imagination and the sophistication of his examination of the foundations of physics give particular interest and importance to his writings. Volume II: 1862-1873 contains texts which illuminate Maxwell's scientific maturity. In this period he wrote the classic works on field physics and statistical molecular theory which established his unique status in the history of science. His important correspondence with Thomson and Tait provides remarkable insight into the major themes of his physics and the writing of his seminal Treatise on Electricity and Magnetism (1873).
Author: Mario Livio
Publisher: Simon and Schuster
View: 8455Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world. Nobel Laureate Eugene Wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that—mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. Is mathematics ultimately invented or discovered? If, as Einstein insisted, mathematics is “a product of human thought that is independent of experience,” how can it so accurately describe and even predict the world around us? Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.
Author: Ivan Oliveira,Roberto Sarthour Jr.,Tito Bonagamba,Eduardo Azevedo,Jair C. C. Freitas
View: 7927Quantum Computation and Quantum Information (QIP) deals with the identification and use of quantum resources for information processing. This includes three main branches of investigation: quantum algorithm design, quantum simulation and quantum communication, including quantum cryptography. Along the past few years, QIP has become one of the most active area of research in both, theoretical and experimental physics, attracting students and researchers fascinated, not only by the potential practical applications of quantum computers, but also by the possibility of studying fundamental physics at the deepest level of quantum phenomena. NMR Quantum Computation and Quantum Information Processing describes the fundamentals of NMR QIP, and the main developments which can lead to a large-scale quantum processor. The text starts with a general chapter on the interesting topic of the physics of computation. The very first ideas which sparkled the development of QIP came from basic considerations of the physical processes underlying computational actions. In Chapter 2 it is made an introduction to NMR, including the hardware and other experimental aspects of the technique. In Chapter 3 we revise the fundamentals of Quantum Computation and Quantum Information. The chapter is very much based on the extraordinary book of Michael A. Nielsen and Isaac L. Chuang, with an upgrade containing some of the latest developments, such as QIP in phase space, and telecloning. Chapter 4 describes how NMR generates quantum logic gates from radiofrequency pulses, upon which quantum protocols are built. It also describes the important technique of Quantum State Tomography for both, quadrupole and spin 1/2 nuclei. Chapter 5 describes some of the main experiments of quantum algorithm implementation by NMR, quantum simulation and QIP in phase space. The important issue of entanglement in NMR QIP experiments is discussed in Chapter 6. This has been a particularly exciting topic in the literature. The chapter contains a discussion on the theoretical aspects of NMR entanglement, as well as some of the main experiments where this phenomenon is reported. Finally, Chapter 7 is an attempt to address the future of NMR QIP, based in very recent developments in nanofabrication and single-spin detection experiments. Each chapter is followed by a number of problems and solutions. * Presents a large number of problems with solutions, ideal for students * Brings together topics in different areas: NMR, nanotechnology, quantum computation * Extensive references
A Survey Course
Author: William Johnston,Alex McAllister
Publisher: Oxford University Press
View: 5791A Transition to Advanced Mathematics: A Survey Course promotes the goals of a "bridge'' course in mathematics, helping to lead students from courses in the calculus sequence (and other courses where they solve problems that involve mathematical calculations) to theoretical upper-level mathematics courses (where they will have to prove theorems and grapple with mathematical abstractions). The text simultaneously promotes the goals of a ``survey'' course, describing the intriguing questions and insights fundamental to many diverse areas of mathematics, including Logic, Abstract Algebra, Number Theory, Real Analysis, Statistics, Graph Theory, and Complex Analysis. The main objective is "to bring about a deep change in the mathematical character of students -- how they think and their fundamental perspectives on the world of mathematics." This text promotes three major mathematical traits in a meaningful, transformative way: to develop an ability to communicate with precise language, to use mathematically sound reasoning, and to ask probing questions about mathematics. In short, we hope that working through A Transition to Advanced Mathematics encourages students to become mathematicians in the fullest sense of the word. A Transition to Advanced Mathematics has a number of distinctive features that enable this transformational experience. Embedded Questions and Reading Questions illustrate and explain fundamental concepts, allowing students to test their understanding of ideas independent of the exercise sets. The text has extensive, diverse Exercises Sets; with an average of 70 exercises at the end of section, as well as almost 3,000 distinct exercises. In addition, every chapter includes a section that explores an application of the theoretical ideas being studied. We have also interwoven embedded reflections on the history, culture, and philosophy of mathematics throughout the text.
A Hands-on Approach
Author: Michael R. W. Dawson
Publisher: John Wiley & Sons
View: 1338Connectionism is a “hands on” introduction to connectionist modeling through practical exercises in different types of connectionist architectures. explores three different types of connectionist architectures – distributed associative memory, perceptron, and multilayer perceptron provides a brief overview of each architecture, a detailed introduction on how to use a program to explore this network, and a series of practical exercises that are designed to highlight the advantages, and disadvantages, of each accompanied by a website at http://www.bcp.psych.ualberta.ca/~mike/Book3/ that includes practice exercises and software, as well as the files and blank exercise sheets required for performing the exercises designed to be used as a stand-alone volume or alongside Minds and Machines: Connectionism and Psychological Modeling (by Michael R.W. Dawson, Blackwell 2004)
How George Boole and Claude Shannon Created the Information Age
Author: Paul J. Nahin
Publisher: Princeton University Press
View: 1268Examines how mathematician and philosopher George Boole and electrical engineer Claude Shannon became the fathers of the information age by advancing Boolean logic, and looks at the influence of other factors, including the Turing machine.
Author: Mircea Pitici,David Mumford
Publisher: Princeton University Press
View: 8568Collects essays on mathematics, from the mathematical aspects of origami and the mathematics of dating to the frequency and distribution of prime numbers and a ball in five dimensions.
Recent and Classical Studies in the Logic of George Boole
Author: James Gasser
Publisher: Springer Science & Business Media
View: 5563Modern mathematical logic would not exist without the analytical tools first developed by George Boole in The Mathematical Analysis of Logic and The Laws of Thought. The influence of the Boolean school on the development of logic, always recognised but long underestimated, has recently become a major research topic. This collection is the first anthology of works on Boole. It contains two works published in 1865, the year of Boole's death, but never reprinted, as well as several classic studies of recent decades and ten original contributions appearing here for the first time. From the programme of the English Algebraic School to Boole's use of operator methods, from the problem of interpretability to that of psychologism, a full range of issues is covered. The Boole Anthology is indispensable to Boole studies and will remain so for years to come.
A Critical Exposition from the Standpoint of Contemporary Algebra, Logic and Probability Theory
Author: T. Hailperin
View: 1605Since the publication of the first edition in 1976, there has been a notable increase of interest in the development of logic. This is evidenced by the several conferences on the history of logic, by a journal devoted to the subject, and by an accumulation of new results. This increased activity and the new results - the chief one being that Boole's work in probability is best viewed as a probability logic - were influential circumstances conducive to a new edition. Chapter 1, presenting Boole's ideas on a mathematical treatment of logic, from their emergence in his early 1847 work on through to his immediate successors, has been considerably enlarged. Chapter 2 includes additional discussion of the ``uninterpretable'' notion, both semantically and syntactically. Chapter 3 now includes a revival of Boole's abandoned propositional logic and, also, a discussion of his hitherto unnoticed brush with ancient formal logic. Chapter 5 has an improved explanation of why Boole's probability method works. Chapter 6, Applications and Probability Logic, is a new addition. Changes from the first edition have brought about a three-fold increase in the bibliography.