## Elements of Logic via Numbers and Sets

Author: D.L. Johnson

Publisher: Springer Science & Business Media

ISBN: 1447106032

Category: Mathematics

Page: 188

View: 7908

In mathematics we are interested in why a particular formula is true. Intuition and statistical evidence are insufficient, so we need to construct a formal logical proof. The purpose of this book is to describe why such proofs are important, what they are made of, how to recognize valid ones, how to distinguish different kinds, and how to construct them. This book is written for 1st year students with no previous experience of formulating proofs. Dave Johnson has drawn from his considerable experience to provide a text that concentrates on the most important elements of the subject using clear, simple explanations that require no background knowledge of logic. It gives many useful examples and problems, many with fully-worked solutions at the end of the book. In addition to a comprehensive index, there is also a useful `Dramatis Personae` an index to the many symbols introduced in the text, most of which will be new to students and which will be used throughout their degree programme.
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## Sets, Logic and Categories

Author: Peter J. Cameron

Publisher: Springer Science & Business Media

ISBN: 1447105893

Category: Mathematics

Page: 182

View: 8910

Set theory, logic and category theory lie at the foundations of mathematics, and have a dramatic effect on the mathematics that we do, through the Axiom of Choice, Gödel's Theorem, and the Skolem Paradox. But they are also rich mathematical theories in their own right, contributing techniques and results to working mathematicians such as the Compactness Theorem and module categories. The book is aimed at those who know some mathematics and want to know more about its building blocks. Set theory is first treated naively an axiomatic treatment is given after the basics of first-order logic have been introduced. The discussion is su pported by a wide range of exercises. The final chapter touches on philosophical issues. The book is supported by a World Wibe Web site containing a variety of supplementary material.
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## Symmetries

Author: D.L. Johnson

Publisher: Springer Science & Business Media

ISBN: 9781852332709

Category: Mathematics

Page: 198

View: 4296

" ... many eminent scholars, endowed with great geometric talent, make a point of never disclosing the simple and direct ideas that guided them, subordinating their elegant results to abstract general theories which often have no application outside the particular case in question. Geometry was becoming a study of algebraic, differential or partial differential equations, thus losing all the charm that comes from its being an art." H. Lebesgue, Ler;ons sur les Constructions Geometriques, Gauthier Villars, Paris, 1949. This book is based on lecture courses given to final-year students at the Uni versity of Nottingham and to M.Sc. students at the University of the West Indies in an attempt to reverse the process of expurgation of the geometry component from the mathematics curricula of universities. This erosion is in sharp contrast to the situation in research mathematics, where the ideas and methods of geometry enjoy ever-increasing influence and importance. In the other direction, more modern ideas have made a forceful and beneficial impact on the geometry of the ancients in many areas. Thus trigonometry has vastly clarified our concept of angle, calculus has revolutionised the study of plane curves, and group theory has become the language of symmetry.
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## The British National Bibliography

Author: Arthur James Wells

Publisher: N.A

ISBN: N.A

Category: English literature

Page: N.A

View: 5944

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## New Scientist

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Science

Page: N.A

View: 4723

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## American Book Publishing Record

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 7470

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## Introduction to Calculus and Classical Analysis

Author: O. Hijab

Publisher: Springer Science & Business Media

ISBN: 9780387949260

Category: Mathematics

Page: 313

View: 5044

As an excellent, easy-to-understand introduction to analysis, this book involves rigorous analysis, computational dexterity, and a breadth of applications, making it ideal for undergraduate majors. The book contains many remarkable features, including a heavy emphasis on computational problems and applications from many parts of analysis. The work completely avoids treating complex numbers. Nearly 350 problems with solutions are included in the back of the book.
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## Bookseller

Author: N.A

Publisher: N.A

ISBN: N.A

Category: English imprints

Page: N.A

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## American Book Publishing Record

BPR cumulative

Author: Bowker Staff

Publisher: R. R. Bowker

ISBN: 9780835240857

Category: Reference

Page: 17426

View: 5799

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## Metric Spaces

Author: Mícheál O'Searcoid

Publisher: Springer Science & Business Media

ISBN: 9781846286278

Category: Mathematics

Page: 304

View: 2237

The abstract concepts of metric spaces are often perceived as difficult. This book offers a unique approach to the subject which gives readers the advantage of a new perspective on ideas familiar from the analysis of a real line. Rather than passing quickly from the definition of a metric to the more abstract concepts of convergence and continuity, the author takes the concrete notion of distance as far as possible, illustrating the text with examples and naturally arising questions. Attention to detail at this stage is designed to prepare the reader to understand the more abstract ideas with relative ease.
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## Naive Mengenlehre

Author: Paul R. Halmos

Publisher: Vandenhoeck & Ruprecht

ISBN: 9783525405277

Category: Arithmetic

Page: 132

View: 9414

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## Theorem Proving with the Real Numbers

Author: John Robert Harrison

Publisher: N.A

ISBN: N.A

Category: Automatic theorem proving

Page: 147

View: 7407

Abstract: "This thesis discusses the use of the real numbers in theorem proving. Typically, 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 floating 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 describe 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. We aim to show that a theory of real numbers is useful in practice and interesting in theory, and that the 'LCF style' of theorem proving is well suited to the kind of work we describe. We hope also to convince the reader that the kind of mathematics needed for applications is well within the abilities of current theorem proving technology."
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## Bulletin of the Belgian Mathematical Society, Simon Stevin

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

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## Mathematica®: A Problem-Centered Approach

Author: Roozbeh Hazrat

Publisher: Springer Science & Business Media

ISBN: 1849962510

Category: Mathematics

Page: 180

View: 5405

Mathematica®: A Problem-Centered Approach introduces the vast array of features and powerful mathematical functions of Mathematica using a multitude of clearly presented examples and worked- out problems. Each section starts with a description of a new topic and some basic examples. The author then demonstrates the use of new commands through three categories of problems - the first category highlights those essential parts of the text that demonstrate the use of new commands in Mathematica whilst solving each problem presented; - the second comprises problems that further demonstrate the use of commands previously introduced to tackle different situations; and - the third presents more challenging problems for further study. The intention is to enable the reader to learn from the codes, thus avoiding long and exhausting explanations. While based on a computer algebra course taught to undergraduate students of mathematics, science, engineering and finance, the book also includes chapters on calculus and solving equations, and graphics, thus covering all the basic topics in Mathematica. With its strong focus upon programming and problem solving, and an emphasis on using numerical problems that do not need any particular background in mathematics, this book is also ideal for self-study and as an introduction to researchers who wish to use Mathematica as a computational tool. Mathematica®: A Problem-Centered Approach comes with a free 30 day trial of the Wolfram Mathematica(R) software'
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## Choice

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Best books

Page: N.A

View: 461

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## Journal of Economic Literature

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Economics

Page: N.A

View: 2434

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## Mathematical Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 9707

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## Professor Stewarts mathematische Schätze

Author: Ian Stewart

Publisher: Rowohlt Verlag GmbH

ISBN: 3644017115

Category: Mathematics

Page: 432

View: 6136

Was war noch mal die Catalan’sche Vermutung? Und woher kommt eigentlich das Wurzelsymbol? Was hat die Zahl Pi mit dem Sternenhimmel zu tun? Wer erfand das Gleichheitszeichen? Der britische Matheguru Ian Stewart breitet in diesem Band Schätze aus, die er in Jahrzehnten gesammelt hat: über 180 interessante Matherätsel, Lösungen, Spiele, Tricks, Geschichten, Anekdoten und Logeleien. Zudem ist Stewarts Schatztruhe mit interessanten historischen Exkursen angereichert, zum Beispiel einer kurzen Einführung in das Rechnen der Maya und der alten Ägypter und auch in die Vergangenheit unseres eigenen Rechnens: Wer erfand das Gleichheitszeichen – und warum? Ein Buch zum Blättern und Stöbern, zum Spaßhaben und Dazulernen, für Laien und für Fortgeschrittene.
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