كتب رياضيات mathmatic

M. B. Monagan K. O. Geddes K. M. Heal G. Labahn S. M. Vorkoetter J. McCarron P. DeMarco,
"Maple 9 Command the Brillance of a Thousand Mathematicians Advanced Programing Guide"
maplesof; 1 edition (2003) | ISBN:1894511441 | 444 pages | PDF | 2,2 Mb

Wenpeng Zhang , Yoshio Tanigawa, "Number Theory: Tradition and Modernization"
Springer; 1 edition (January 13, 2006) | ISBN:0387304142 | 242 pages | PDF | 11,7 Mb



Number Theory: Tradition and Modernization is a collection of survey and research papers on various topics in number theory. Though the topics and descriptive details appear varied, they are unified by two underlying principles: first, making everything readable as a book, and second, making a smooth transition from traditional approaches to modern ones by providing a rich array of examples.

The chapters are presented in quite different in depth and cover a variety of descriptive details, but the underlying editorial principle enables the reader to have a unified glimpse of the developments of number theory. Thus, on the one hand, the traditional approach is presented in great detail, and on the other, the modernization of the methods in number theory is elaborated. The book emphasizes a few common features such as functional equations for various zeta-functions, modular forms, congruence conditions, exponential sums, and algorithmic aspects.

Yu Animov, " Differential Geometry and Topology of Curves"
CRC (January 11, 2001) | ISBN:9056990918 | 216 pages | 8,5 Mb


Differential geometry is an actively developing area of modern mathematics. This volume presents a classical approach to the general topics of the geometry of curves, including the theory of curves in n-dimensional Euclidean space. The author investigates problems for special classes of curves and gives the working method used to obtain the conditions for closed polygonal curves. The proof of the Bakel-Werner theorem in conditions of boundedness for curves with periodic curvature and torsion is also presented. This volume also highlights the contributions made by great geometers. past and present, to differential geometry and the topology of curves.

Book Info
Text devoted to the general topics of the geometry of curves as well as some particular results in that area. Introduces basic notions by using accessible language, beginning with important definitions, including the definition of a curve. Investigates problems for special classes of curves, and proves certain theorems.

Martin Lorenz, "Multiplicative Invariant Theory"
Springer; 1 edition (April 19, 2005) | ISBN:3540243232 | 177 pages | PDF | 12,4 Mb



Multiplicative invariant theory, as a research area in its own right within the wider spectrum of invariant theory, is of relatively recent vintage. The present text offers a coherent account of the basic results achieved thus far..

Multiplicative invariant theory is intimately tied to integral representations of finite groups. Therefore, the field has a predominantly discrete, algebraic flavor. Geometry, specifically the theory of algebraic groups, enters through Weyl groups and their root lattices as well as via character lattices of algebraic tori.

Throughout the text, numerous explicit examples of multiplicative invariant algebras and fields are presented, including the complete list of all multiplicative invariant algebras for lattices of rank 2.

The book is intended for graduate and postgraduate students as well as researchers in integral representation theory, commutative algebra and, mostly, invariant theory.

Imme van den Berg , Vitor Neves, "The Strength of Nonstandard Analysis"
Springer; 1 edition (April 24, 2007) | ISBN:3211499040 | 401 pages | Djvu | 1,6 Mb


Nonstandard Analysis enhances mathematical reasoning by introducing new ways of expression and deduction. Distinguishing between standard and nonstandard mathematical objects, its inventor, the eminent mathematician Abraham Robinson, settled in 1961 the centuries-old problem of how to use infinitesimals correctly in analysis. Having also worked as an engineer, he saw not only that his method greatly simplified mathematically proving and teaching, but also served as a powerful tool in modelling, analyzing and solving problems in the applied sciences, among others by effective rescaling and by infinitesimal discretizations.

This book reflects the progress made in the forty years since the appearance of Robinsons revolutionary book Nonstandard Analysis: in the foundations of mathematics and logic, number theory, statistics and probability, in ordinary, partial and stochastic differential equations and in education. The contributions are clear and essentially self-contained.

Matthias Beck , Sinai Robins, "Computing the Continuous Discretely Integer-point Enumeration in Polyhedra "
Springer; 1st ed. 2007. Corr. printing edition (July 1, 2007) | ISBN:0387291393 | 226 pages | PDF | 2,3 Mb


This much-anticipated textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. The authors have weaved a unifying thread through basic yet deep ideas in discrete geometry, combinatorics, and number theory. Because there is no other book that puts together all of these ideas in one place, this text is truly a service to the mathematical community.

We encounter here a friendly invitation to the field of "counting integer points in polytopes," also known as Ehrhart theory, and its various connections to elementary finite Fourier analysis, generating functions, the Frobenius coin-exchange problem, solid angles, magic squares, Dedekind sums, computational geometry, and more. With 250 exercises and open problems, the reader feels like an active participant, and the authors' engaging style encourages such participation. The many compelling pictures that accompany the proofs and examples add to the inviting style.

For teachers, this text is ideally suited as a capstone course for undergraduate students or as a compelling text in discrete mathematical topics for beginning graduate students. For scientists, this text can be utilized as a quick tooling device, especially for those who want a self-contained, easy-to-read introduction to these topics.

Gerard van der Geer, Ben Moonen, René Schoof, "Number Fields and Function Fields: Two Parallel Worlds"
Birkhäuser Boston; 1 edition (September 14, 2005) | ISBN:0817643974 | 318 pages | PDF | 2,2 Mb



Ever since the analogy between number fields and function fields was discovered, it has been a source of inspiration for new ideas, and a long history has not in any way detracted from the appeal of the subject.

As a deeper understanding of this analogy could have tremendous consequences, the search for a unified approach has become a sort of Holy Grail. The arrival of Arakelov's new geometry that tries to put the archimedean places on a par with the finite ones gave a new impetus and led to spectacular success in Faltings' hands. There are numerous further examples where ideas or techniques from the more geometrically-oriented world of function fields have led to new insights in the more arithmetically-oriented world of number fields, or vice versa.

These invited articles by leading researchers in the field explore various aspects of the parallel worlds of function fields and number fields. Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and t-motives.

This volume is aimed at a wide audience of graduate students, mathematicians, and researchers interested in geometry and arithmetic and their connections.

Contributors: G. Böckle; T. van den Bogaart; H. Brenner; F. Breuer; K. Conrad; A. Deitmar; C. Deninger; B. Edixhoven; G. Faltings; U. Hartl; R. de Jong; K. Köhler; U. Kühn; J.C. Lagarias; V. Maillot; R. Pink; D. Roessler; and A. Werner.

Dominic Jordan, Peter Smith, " Nonlinear Ordinary Differential Equations An Introduction for Scientists and Engineers"
Oxford University Press, USA; 4 edition (September 21, 2007) | ISBN:0199208255 | 560 pages | PDF | 5,6 Mb


Review
`Review from previous edition "...classic book...The book succeeds as an exceptionally well written test fot its intended audience...No doubt one of its strongest features is over 500 problems...throughout the entire book only important physical processes are described... The new edition is greatly enhanced...I strongly recommend that you take a look. The presentation is exquisitely straightforward with numerous physically interesting examples, and it is carefully and well written"' SIAM

Book Description
This is a thoroughly updated and expanded 4th edition of the classic text em/Nonlinear Ordinary Differential Equations/em by Dominic Jordan and Peter Smith. Including numerous worked examples and diagrams, further exercises have been incorporated into the text and answers are provided at the back of the book. Topics include phase plane analysis, nonlinear damping, small parameter expansions and singular perturbations, stability, Liapunov methods, Poincare sequences, homoclinic bifurcation and Liapunov exponents. Over 500 end-of-chapter problems are also included and as an additional resource fully-worked solutions to these are provided in the accompanying text em/Nonlinear Ordinary Differential Equations: Problems and Solutions/em, (OUP, 2007). Both texts cover a wide variety of applications whilst keeping mathematical prequisites to a minimum making these an ideal resource for students and lecturers in engineering, mathematics and the sciences.

Jurgen Appell, Espedito De Pascale, Alfonso Vignoli , "Nonlinear Spectral Theory"
Walter de Gruyter (April 2004) | ISBN:3110181436 | 408 pages | PDF | 1,7 Mb

Karl-Heinz Förster , Peter Jonas , Heinz Langer , Carsten Trunk , "Operator Theory in Inner Product Spaces"
Birkhäuser Basel; 1 edition (April 19, 2007) | ISBN:3764382694 | 240 pages | PDF | 2 Mb

This volume contains contributions written by participants of the 4th Workshop on Operator Theory in Krein Spaces and Applications, which was held at the TU Berlin, Germany, December 17 to 19, 2004. The workshop covered topics from spectral, perturbation and extension theory of linear operators and relations in inner product spaces, including spectral analysis of differential operators, the theory of generalized Nevanlinna functions and related classes of functions, spectral theory of matrix polynomials, and problems from scattering theory.

Luigi Ambrosio, Luis Caffarelli , Michael G. Crandall , Lawrence C. Evans, Nicola Fusco, "Calculus of Variations and Nonlinear Partial Differential Equations:
Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 27 - July ... Mathematics"
Springer; 1 edition (January 2008) | ISBN-10: 3540759131 | 204 pages | PDF | 1,3 Mb


This volume provides the texts of lectures given by L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco at the Summer course held in Cetraro (Italy) in 2005. These are introductory reports on current research by world leaders in the fields of calculus of variations and partial differential equations. The topics discussed are transport equations for nonsmooth vector fields, homogenization, viscosity methods for the infinite Laplacian, weak KAM theory and geometrical aspects of symmetrization. A historical overview of all CIME courses on the calculus of variations and partial differential equations is contributed by Elvira Mascolo

Adrian I. Ban, Sorin G. Gal , " Defects of Properties in Mathematics"
World Scientific Publishing Company; 1st edition (June 15, 2002) | ISBN:9810249241 | 364 pages | PDF | 10,3 Mb

Seymour Lipschutz / Marc Lipson, Schaum's Outline of Discrete Mathematics, 3rd Ed.
McGraw-Hill | ISBN10: 0071470387 | 3 edition (June 21, 2007) | 474 pages | PDF | 7 MB

This is a topic that becomes increasingly important every year as the digital age extends and grows more encompassing in every facet of life. Discrete mathematics, the study of finite systems has become more important as the computer age has advanced, as computer arithmetic, logic, and combinatorics have become standard topics in the discipline. For mathematics majors it is one of the core required courses. This new edition will bring the outline into sync with Rosen, McGraw-Hill's bestselling textbook in the field as well as up to speed in the current curriculum. New material will include expanded coverage of logic, the rules of inference and basic types of proofs in mathematical reasoning. This will give students a better understanding of proofs of facts about sets and functions.There will be increased emphasis on discrete probability and aspects of probability theory, and greater accessibility to counting techniques. This new edition features: a counting chapter which will have new material on generalized combinations; a new chapter on computer arithmetic, with binary and hexagon addition and multiplication; and, a new Cryptology chapter including substitution and RSA method. This outline is the perfect supplement to any course in discrete math and can also serve as a stand-alone textbook.

Joaquim M. Domingos, "Geometrical Properties of Vectors and Covectors: An Introductory Survey of Differentiable Manifolds, Tensors and Forms"
World Scientific Publishing Company (October 9, 2006) | ISBN:9812700447 | 84 pages | PDF | 2,3 Mb



Geometrical Properties of Vectors and Covectors: An Introductory Survey of Differentiable Manifolds, Tensors and Forms

Philippe Flajolet and Robert Sedgewick, "Analytic Combinatorics"
Web Edition. Ninth Printing (Valentine's) | February 14, 2007 | no ISBN | PDF | 760 pages | 10,9 Mb

Analytic Combinatorics aims at predicting precisely the properties of large structured combinatorial configurations, through an approach based extensively on analytic methods. Generating functions are the central objects of the theory.

Analytic Combinatorics starts from an exact enumerative description of combinatorial structures by means of generating functions, which make their first appearance as purely formal algebraic objects. Next, generating functions are interpreted as analytic objects, that is, as mappings of the complex plane into itself. Singularities determine a function’s coefficients in asymptotic form and lead to precise estimates for counting sequences. This chain applies to a large number of problems of discrete mathematics relative to words, trees, permutations, graphs, and so on. A suitable adaptation of the methods also opens the way to the quantitative analysis of characteristic parameters of large random structures, via a perturbational approach.

This book is meant to be reader-friendly. Each major method is abundantly illustrated by means of concrete examples treated in detail -- there are scores of them, spanning froma fraction of a page to several pages -- offering a complete treatment of a specific problem. These are borrowed not only from combinatorics itself but also from neighbouring areas of science. With a view of addressing not only mathematicians of varied profiles but also scientists of other disciplines, Analytic Combinatorics is self contained, including ample appendices that recapitulate the necessary background in combinatorics and complex function theory. A rich set of short Notes -- there are more than 250 of them -- are inserted in the text and can provide exercises meant for self study or for students' practice, as well as introductions to the vast body of literature that is available. We have also made every effort to focus on core ideas rather than technical details, supposing a certain amount of mathematical maturity but only basic prerequisites on the part of our gentle readers. The book is also meant to be strongly problem-oriented, and indeed it can be regarded as amanual, or even a huge algorithm, guiding the reader to the solution of a very large variety of problems regarding discrete mathematical models of varied origins. In this spirit, many of our developments connect nicely with computer algebra and symbolic manipulation systems.

Christian A. Schenk, Gerhart I. Schuëller, "Uncertainty Assessment of Large Finite Element Systems"
Springer; 1 edition (August 5, 2005) | ISBN:3540253432 | 165 pages | 4,9 Mb

The treatment of uncertainties in the analysis of engineering structures remains one of the premium challenges in modern structural mechanics. It is only in recent years that the developments in stochastic and deterministic computational mechanics began to be synchronized. To foster these developments, novel computational procedures for the uncertainty assessment of large finite element systems are presented in this monograph. The stochastic input is modeled by the so-called Karhunen-Loève expansion, which is formulated in this context both for scalar and vector stochastic processes as well as for random fields. Particularly for strongly non-linear structures and systems the direct Monte Carlo simulation technique has proven to be most advantageous as method of solution. The capabilities of the developed procedures are demonstrated by showing some practical applications.

Shoshichi Kobayashi , Katsumi Nomizu, "Foundations of Differential Geometry, Vol. 1"
Wiley-Interscience; New Ed edition (February 8, 1996) | ISBN: 0471157333 | 329 pages | Djvu | 6,6 Mb

Review:

The Definitive Reference for Four Decades

The two-volume set by Kobayashi and Nomizu has remained the definitive reference for differential geometers since their appearance in 1963(volume 1) and 1969 (volume 2). Over the decades, many readers have developed a love/hate relationship with these difficult, challenging texts. For example, in a 2006 edition of a competing text, the author remarked that "every differential geometer must have a copy of these tomes," but followed this judgment by observing that "their effective usefulness had probably passed away," comparing them to the infamously difficult texts of Bourbaki.

As a practicing differential geometer, I would argue that Kobayashi and Nomizu remains an essential reference even today, for a number of reasons.
Volume 1 still remains unrivalled for its concise, mathematically rigorous presentation of the theory of connections on a principal fibre bundle---material that is absolutely essential to the reader who desires to understand gauge theories in modern physics. The essential core of Volume 1 is the development of connections on a principal fibre bundle, linear and affine connections, and the special case of Riemannian connections, where a connection must be "fitted" to the geometry that results from a pre-existing metric tensor on the underlying manifold, M.
Volume 2 offers thorough introductions to a number of classical topics, including submanifold theory, Morse index theory, homogeneous and symmetric spaces, characteristic classes, and complex manifolds.

The influence of the texts by Kobayashi and Nomizu can be seen in most of the subsequent differential geometry texts, both in organization and content, and especially in the adoption of notation. If there was a particularly fine point in your favorite introductory differential geometry text that you never completely understood, the odds are good that you will find the answer, fully developed and presented at an entirely different mathematical level, in Kobayashi and Nomizu. It is not an unreasonable analogy to say that learning differential geometry without having your own copy of Kobayashi/Nomizu is like studying literature in the complete ignorance of Shakespeare.

Let there be no mistake about the advanced level of these texts. The Preface to Volume 1 clearly states that the authors presume the reader to be familiar with differentiable manifolds, Lie groups, and fibre bundles, as developed in the (now classical) texts by Chevalley, Montgomery-Zippin, Pontrjagin, and Steenrod. Today's reader is far more likely to have studied these subject from more recent books like those by Boothby, Hall, and Husemoller, but whatever the source, a familiarity IS presumed. The "lightning review" provided in Chapter I of Volume 1 will be extremely tough going for the reader who is new to these topics. It should also be noted that in 329 pages of Volume 1 and 470 pages of Volume 2, not a single diagram or picture is to be found! Those drawn to geometry for its visual aspects will find Kobayashi/Nomizu totally lacking in visual aids.

As with so many classic references in mathematics, the hardbound edition of Kobayashi and Nomizu is no longer in print. Copies appear sporadically on the used book market at absolutely obscene prices. The Classics Library paperback edition is still available, but the serious student will find that the paperbacks simply do not fare well under serious, sustained use.

Shoshichi Kobayashi , Katsumi Nomizu, "Foundations of Differential Geometry, Vol. 2"
Wiley-Interscience; New Ed edition (February 8, 1996) | ISBN: 0471157325 | 488 pages | Djvu | 4,6 Mb

Review:

The Definitive Reference for Four Decades

The two-volume set by Kobayashi and Nomizu has remained the definitive reference for differential geometers since their appearance in 1963(volume 1) and 1969 (volume 2). Over the decades, many readers have developed a love/hate relationship with these difficult, challenging texts. For example, in a 2006 edition of a competing text, the author remarked that "every differential geometer must have a copy of these tomes," but followed this judgment by observing that "their effective usefulness had probably passed away," comparing them to the infamously difficult texts of Bourbaki.

As a practicing differential geometer, I would argue that Kobayashi and Nomizu remains an essential reference even today, for a number of reasons.
Volume 1 still remains unrivalled for its concise, mathematically rigorous presentation of the theory of connections on a principal fibre bundle---material that is absolutely essential to the reader who desires to understand gauge theories in modern physics. The essential core of Volume 1 is the development of connections on a principal fibre bundle, linear and affine connections, and the special case of Riemannian connections, where a connection must be "fitted" to the geometry that results from a pre-existing metric tensor on the underlying manifold, M.
Volume 2 offers thorough introductions to a number of classical topics, including submanifold theory, Morse index theory, homogeneous and symmetric spaces, characteristic classes, and complex manifolds.

The influence of the texts by Kobayashi and Nomizu can be seen in most of the subsequent differential geometry texts, both in organization and content, and especially in the adoption of notation. If there was a particularly fine point in your favorite introductory differential geometry text that you never completely understood, the odds are good that you will find the answer, fully developed and presented at an entirely different mathematical level, in Kobayashi and Nomizu. It is not an unreasonable analogy to say that learning differential geometry without having your own copy of Kobayashi/Nomizu is like studying literature in the complete ignorance of Shakespeare.

Let there be no mistake about the advanced level of these texts. The Preface to Volume 1 clearly states that the authors presume the reader to be familiar with differentiable manifolds, Lie groups, and fibre bundles, as developed in the (now classical) texts by Chevalley, Montgomery-Zippin, Pontrjagin, and Steenrod. Today's reader is far more likely to have studied these subject from more recent books like those by Boothby, Hall, and Husemoller, but whatever the source, a familiarity IS presumed. The "lightning review" provided in Chapter I of Volume 1 will be extremely tough going for the reader who is new to these topics. It should also be noted that in 329 pages of Volume 1 and 470 pages of Volume 2, not a single diagram or picture is to be found! Those drawn to geometry for its visual aspects will find Kobayashi/Nomizu totally lacking in visual aids.

As with so many classic references in mathematics, the hardbound edition of Kobayashi and Nomizu is no longer in print. Copies appear sporadically on the used book market at absolutely obscene prices. The Classics Library paperback edition is still available, but the serious student will find that the paperbacks simply do not fare well under serious, sustained use.

Julian Lowell Coolidge, " The elements of non-Euclidean geometry"
Cornell University Library (January 1, 1909) | ISBN:1429704462 | 312 pages | PDF | 15,3 Mb


This volume is produced from digital images from the Cornell University Library Historical Mathematics Monographs collection.

Isaiah Leslie Miller, "An Introduction To Mathematics - With Applications To Science And Agriculture"
Mellon Press (March 15, 2007) | ISBN:140671819X | 312 pages | PDF | 8,8 Mb


AN INTRODUCTION TO MATHEMATICS With Applications to Science and Agriculture BY ISATAII LESLIE MILLER Professor of Mathematics, South Dakota State College of Agriculture and Mechanic Arts F. S. CROFTS CO. NEW YORK ----MCMXXX COPYRIGHT, 1930, BY F. S. CROITS Co., INC. MANUFACTURED IN THE UNITED STATES OF AMERICA BY BRAUNWORTH CO., INC., BROOKLYN, NEW YORK PREFACE AFTER some fourteen years of teaching in American colleges and universities the author finds that the average high school graduate has not developed in himself a mathematical type of reasoning. lie therefore hopes that this treatment may in some measure accomplish this purpose. The first few chapters are devoted to a thorough review of high school algebra, for the author is convinced that most college freshmen need considerable drill on the fundamental processes of algebra before attempting a very extensive study of mathematics. In preparing this book the author has kept in mind two types of students first, those who will never take additional work in mathematics, and second, those who will continue the work in science or agriculture for advanced degrees and will doubtless desire to pursue additional courses in mathematics. He has therefore attempted to write a book basic in the fundamental principles of mathematics and at the same time has endeavored to make practical applications to the fields of science and agri culture, wherever possible. He feels that a thorough knowledge of the material covered in this work will enable the second type of student to successfully pursue a course in analytical geometry followed by a course in the calculus. The author gratefully acknowledges his indebtedness to his colleagues, Professor Win. Asker for preparing the chapter on statistics, and Mr. H. B. MacDougal for checking much of the material, to Professor I. W. Smith of the North Dakota Agri cultural College for using the material in mimeographed form and offering many valuable suggestions, to Dean D. A. Roth VI PREFACE rock of Indiana University for reading most of the manuscript and to Professor Wm. Marshall of Purdue University for encouraging him in the work. The author also desires to thank Professor E. S. Crawley of the University of Pennsylvania for his generous permission to use the greater part of his Tables of Logarithms as a portion of this book.

A. Zygmund, "Contributions To Fourier Analysis"
Zygmund Press (March 15, 2007) | ISBN:1406760439 | 200 pages | PDF | 6,4 Mb


In the theory of convergence and summability whether for ordinary Fourier series or other expansions emphasis is placed on the phenomenon of localization whenever such occurs, and in the present paper a certain aspect of this phenomenon will be studied for the problem of best approximation as well.

John C. Sparks, "Calculus Without Limits Almost"
AuthorHouse; 3rd Updated edition (June 21, 2004) | ISBN:1418441244 | 392 pages | PDF | 1,5 Mb


John C. Sparks is a senior staff engineer at Wright-Patterson Air Force Base in Dayton, Ohio with approximately thirty-one years of engineering and management experience. In addition to his Air Force career, Sparks has taught mathematics at Sinclair Community College for over twenty years. In late 2003, Sparks received the Ohio Association of Two-Year Colleges' 2002-2003 Adjunct Teacher of the Year award. He and his wife, Carolyn (photo), have celebrated thirty-five years of marriage and have two sons, Robert and Curtis, who are both married. Sparks is a lifelong resident of Xenia, Ohio. Sparks has written and published three volumes of poetry, Rhyme for All Seasons, Mixed Images, and Gold, Hay and Stubble: One Journeyman's Poetic Diary. Calculus without Limits is his first full-length mathematics work; and, with its publication, a thirty-year old dream is realized.

By Bruce Hughes, Andrew Ranicki, "Ends of Complexes (Cambridge Tracts in Mathematics)"
Cambridge University Press | ISBN: 0521576253 | 1996 | 379 pages | PDF | 2.4 MB

The ends of a topological space are the directions in which it becomes noncompact by tending to infinity. The tame ends of manifolds are particularly interesting, both for their own sake, and for their use in the classification of high-dimensional compact manifolds. The book is devoted to the related theory and practice of ends, dealing with manifolds and CW complexes in topology and chain complexes in algebra. The first part develops a homotopy model of the behavior at infinity of a noncompact space. The second part studies tame ends in topology. The authors show tame ends to have a uniform structure, with a periodic shift map. They use approximate fibrations to prove that tame manifold ends are the infinite cyclic covers of compact manifolds. The third part translates these topological considerations into an appropriate algebraic context, relating tameness to homological properties and algebraic K- and L-theory. This book will appeal to researchers in topology and geometry

Bob Connell, " Basic Math for Process Control"
Instrumentation Systems and Automation Societ (October 2002) | ISBN:1556178131 | 176 pages | PDF | 5,5 Mb


A practical tutorial on the mathematics essential to the process control field, written by an experienced process control engineer for practicing engineers and students. A quick-and-easy review of the mathematics common to the field, including chapters on frequency response analysis, transfer functions and block diagrams, and the Z-N approximation. A handy desk reference for process control engineers - a helpful aid to students in mathematics courses.

Richard Bornat, " Proof and Disproof in Formal Logic: An Introduction for Programmers"
Oxford University Press, USA (September 2, 2005) | ISBN: 0198530277 | 264 pages | PDF | 2,7 Mb

iProof and Disproof in Formal Logic/i is a lively and entertaining introduction to formal logic providing an excellent insight into how a simple logic works. Formal logic allows you to check a logical claim without considering what the claim means. This highly abstracted idea is an essential and practical part of computer science. The idea of a formal system--a collection of rules and axioms which define a universe of logical proofs--is what gives us programming languages and modern-day programming. This book concentrates on using logic as a tool: making and using formal proofs and disproofs of particular logical claims. The logic it uses--natural deduction--is very small and very simple; working with it helps you see how large mathematical universes can be built on small foundations. The book is divided into four parts: DT Part I "Basics" gives an introduction to formal logic with a short history of logic and explanations of some technical words. DT Part II "Formal syntactic proof" show you how to do calculations in a formal system where you are guided by shapes and never need to think about meaning. Your experiments are aided by Jape, which can operate as both inquisitor and oracle. DT Part III "Formal semantic disproof" shows you how to construct mathematical counterexamples to show that proof is impossible. Jape can check the counterexamples you build. DT Part IV "Program specification and proof" describes how to apply your logical understanding to a real computer science problem, the accurate description and verification of programs. Jape helps, as far as arithmetic allows. Aimed at undergraduates and graduates in computer science, logic, mathematics, and philosophy, the text includes reference to and exercises based on the computer software package Jape, an interactive teaching and research tool designed and hosted by the author that is freely available on the web.