Mathematical Structures for Computer Science

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A good reference.......2005-07-25

I used this book in my Data Structures class. It has sample problems with solutions in the back of the book so you understand what they were talking about (unfortunately, I cannot say the same for a lot of data structures texts) The sample problems were also good for review for an exam. This was one of the few Computer Science textbooks that I have actually kept as a reference.

CS Professors Love This Book. CS Students Hate It........2005-05-04

If you are seasoned in the ways of computer science and mathematics, you will probably love this book. However if you are new to the concepts presented in the pages of this book, you will probably hate it. It is particularly bad once you really start getting into the meat of things, around chapter three. The examples and explanations are utterly terse.

Here is how the book defines "cardinality": "...The number of elements in a finite set is the cardinality of the set, so this would be a set of cardinality k." That is the best explanation the book offers as to the meaning of the word cardinality, a word my professor used close to fifty times every lecture, a word that really deserves better explanation than a single sentence, especially with regard to sets.

If I were providing something constructive the author, I would probably say that definitions should be much easier to find and much more detailed and examples of definitions should cover all the angles. I suppose my largest complaint with the book would simply be that if you are a CS student and you REALLY NEED a strong foundation in the concepts of discrete math, this book doesn't quite get there. The book misses its target audience.

Not quite the best, but close.......2005-02-19

Although there is now consensus over the coverage in a first course in discrete mathematics, the level of difficulty one finds in books for this audience has a wide range. Some opt for the basic approach, with very little rigor, and anything labeled as a proof is either trivial or an advanced waving of the hands. Notational complexity is kept to a minimum, which is fine for the beginner, but limits the value as the student goes on into more advanced courses. On the other end, there are those where rigorous proofs abound, it reads more like a book for traditional math majors rather than one largely designed for computer science majors.
While Gersting is somewhere in the middle, the slant is more towards the advanced. The first four chapters cover logic, the fundamentals of proofs, set theory and relations and functions respectively. This order is in complete agreement with my beliefs. I would not give any book that does not start with these basic topics a second look much less consider adopting it. Graphs are covered in chapters five and six; Boolean algebra in seven and the theory of computation is covered in chapter eight. The treatment is on the high end, but still within the bounds of a first course in discrete mathematics. Worked examples are everywhere and a large number of exercises are at the end of each section. Practice problems are embedded inside the chapters and solutions to all the practice problems are found in an appendix.
While I believe I have found a better book to use in my discrete class, this one is my second choice. In fact I successfully used it for two years, until I replaced it. The primary reasons for the change was that the new book has biographical sketches of mathematicians (something I adore), the font is larger and there are more solutions to the exercises.

A very valuable book!!.......2003-04-20

With all due respect to some of the other reviewers, I found this book extremely helpful and extremely well written. Much of the polarity in the reviews may stem from the fact that different people have different learning models and corresponding expectations. As a career changer with several degrees in other engineering disciplines, I found many of the explanations very helpful and very appropriate relative to my current learning/retraining objectives. With the examples and practice problems, this book provides what I believe to be an excellent introduction to a wide range of topics relating to the mathematical basis for computer science. I find that I typically consult this book first before moving to other more rigorous (and often more obscure) treatments of the same topics.

Nice book!.......2003-01-07

I've been studying this book for a semester and I found this a good one. However there are too much helpful exercises, I think the book should have all the answers and be more thorough. Because most of time it's hard to understand it when studying alone.

Advanced Topics, Volume 2, Non-Linear Finite Element Analysis of Solids and Structures

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Excellent Study
Non-linear FEM for mere mortals.

Advanced Topics, Volume 2, Non-Linear Finite Element Analysis of Solids and Structures
M. A. Crisfield
Manufacturer: Wiley
ProductGroup: Book
Binding: Hardcover

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ASIN: 047195649X

Book Description

Non-linear Finite Element Analysis of Solids and Structures Volume 2: Advanced Topics M. A. Crisfield Imperial College of Science, Technology and Medicine, London, UK In such fields as aeronautical, civil, mechanical and structural engineering, non-linear analysis techniques are becoming widely used for the solution of practical engineering problems. Taking an engineering rather than a mathematical bias, this comprehensive book builds on the fundamental ideas explained in Volume One, introducing the reader to more detailed, advanced topics. Large strains and large rotations, plasticity with a range of yield criteria and hardening rules, stability theory and advanced solution procedures including branch-switching techniques, contact and friction, and nonlinear dynamics, are covered in depth. Examples from a non-linear finite element computer program incorporating the advanced solution procedures are included. The computer program is available on the Internet via anonymous ftp, using the URL ftp://ftp.cc.ic.ac.uk/pub/depts/aero/nonlin2/.

Customer Reviews:

Excellent Study.......2004-08-05

Crisfield's first and second books are excellent sources for anyone from different disiplines. His success can be attributed to explaining the materials in their simple forms and to his notations that is easy to follow. Starting from 1D nonlinear truss elements to 3D beam-column elements, all concepts are explained in a similar way so once you are into it, it is easy to follow the text. I mostly studied his work on finite rotations, and arc-length algorithms.

Non-linear FEM for mere mortals........2000-07-17

Very elegantly written with excellent notation. Brings the implementaion of things like co-rotational FEM programming within the grasp of people with a mere engineering background. I especially liked the chapter on large rotations.

Non-Linear Finite Element Analysis of Solids and Structures

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Excellent book - fills a long standing gap

Non-Linear Finite Element Analysis of Solids and Structures
M. A. Crisfield
Manufacturer: Wiley
ProductGroup: Book
Binding: Paperback

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ASIN: 047197059X

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Non-linear Finite Element Analysis of Solids and Structures Volume 1 : Essentials M.A. Crisfield Imperial College of Science, Technology and Medicine, London, UK Taking an engineering rather than a mathematical bias, this comprehensive book details the fundamentals of non-linear finite element analysis. The author explains how non-linear techniques can be used to solve practical problems. The main ideas of geometric non-linearity, continuum mechanics, plasticity, element technology and stability theory are explored in detail. The reader is also introduced to the recent research in this developing field. The computer programs in the text are available on the Internet via anonymous ftp, using the URL ftp://cc.ic.ac.uk, directory /pub/depts/aero/nonlin. These useful finite element computer programs illustrate many of the ideas considered in the book. The logic can also be followed without these finer details since these computer programs and subroutines are also represented by examples and flowcharts. The second volume will address advanced topics such as large strains and large rotations, plasticity with a range of yield criteria and hardening rules, stability theory and advanced solution procedures including branch-switching techniques, contact and friction, and non-linear dynamics. It will also include examples from an up-dated non-linear finite element computer program incorporating the advanced solution procedures.

Customer Reviews:

Excellent book - fills a long standing gap.......2000-04-07

I feel the book really fills a long standing gap in this field, since nonlinear analysis (especially geometric nonlinear analysis) is always treated slightly ambiguously by other authors. The book is extremely clear and consistent in its manner of explanation. However, at some places, the author has used excessive mathematical derivations which may not contribute so much to understanding.

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Topology Optimization
M.P. Bendsoe , and O. Sigmund
Manufacturer: Springer
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Binding: Hardcover

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ASIN: 3540429921

Book Description

The topology optimization method solves the basic engineering problem of distributing a limited amount of material in a design space. The first edition of this book has become the standard text on optimal design, which is concerned with the optimization of structural topology, shape and material. This edition has been substantially revised and updated to reflect progress made in modelling and computational procedures. It also encompasses a comprehensive and unified description of the state of the art of the so-called material distribution method, based on the use of mathematical programming and finite elements. Applications treated include not only structures but also MEMS and materials.

Nonlinear Analysis of Thin-Walled Structures: Statics, Dynamics, and Stability (Mechanical Engineering Series)

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Nonlinear Analysis of Thin-Walled Structures: Statics, Dynamics, and Stability (Mechanical Engineering Series)
James F. Doyle
Manufacturer: Springer
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Binding: Hardcover

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ASIN: 0387952160

Book Description

This book deals with the computational analysis of thin-walled structures such as aircraft, ships, and containment vessels. Building on the author's earlier book Static and Dynamic Analysis of Structures, it shows how to use computational methods to tackle some of the fundamental problems of structural mechanics, with particular emphasis on nonlinear phenomena. Where the earlier book dealt with linear systems, the central theme running through this volume is the notion that unstable equilibria are associated with motions and large displacements and therefore require a full nonlinear analysis. The discussion begins with an overview of the basic mechanics of deformable bodies, including variational formulations, and then considers the large deflection behavior of shell and frame structures using a finite-element analysis. The second part of the book begins with a summary of linear vibrations of structures, including an introduction to modal analysis; it continues with computational formulations of nonlinear dynamic analyses of structures and refines the concept of dynamic equilibrium in the context of large deflections. The book concludes with a discussion of stability, including the difficult problem of stability of motions in the large. By describing the methods on which commercial software pakckages are based, this book allows an engineer to evaluate the results these computations produce. It therefore should be useful to practicing engineers and graduate students.

Interaction And Non-Linear Effects In Structural Equation

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An excellent book for applied researchers in SEM

Interaction And Non-Linear Effects In Structural Equation

Manufacturer: Lawrence Erlbaum
ProductGroup: Book
Binding: Paperback

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ASIN: 0805829512

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This volume provides a comprehensive presentation of the various procedures currently available for testing interaction and nonlinear effects in structural equation modeling. By focusing on various software applications, the reader should quickly be able to incorporate one of the procedures into testing interaction or nonlinear effects in their own model. Although every attempt is made to keep mathematical details to a minimum, it is assumed that the reader has mastered the equivalent of a graduate-level multivariate statistics course which includes adequate coverage of structural equation modeling. This book will be of interest to researchers and practitioners in education and the social sciences. br

Customer Reviews:

An excellent book for applied researchers in SEM.......2000-04-03

This is an excellent reference book for applied researchers who use advanced structural equation modeling (SEM) in social, psychological, and biomedical studies. The authors are well-known experienced experts in SEM, and the contents of this book are practical. Researcher who use different software in SEM can find their practical examples and related theoretical bases.

Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces (Lecture Notes in Mathematics)

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Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces (Lecture Notes in Mathematics)
L. Molnár
Manufacturer: Springer
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Binding: Paperback

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Over the past several decades, the territory of preserver problems has been continuously enlarging within the frame of linear analysis. The aim of this work is to present a sort of cross-section of the modern theory of preservers on infinite dimensional spaces (operator spaces and function spaces) through the author's corresponding results. Special emphasis is put on preserver problems concerning some structures of Hilbert space operators which appear in quantum mechanics. Moreover, local automorphisms and local isometries of operator algebras and function algebras are discussed in details.

The Structure of Compact Groups: A Primer for Students - a Handbook for the Expert (De Gruyter Studies in Mathematics)

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The Structure of Compact Groups: A Primer for Students - a Handbook for the Expert (De Gruyter Studies in Mathematics)
Karl Heinrich Hofmann , and Sidney A. Morris
Manufacturer: Walter de Gruyter
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Binding: Hardcover

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ASIN: 3110190060

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Dealing with subject matter of compact groups that is frequently cited in fields like algebra, topology, functional analysis, and theoretical physics, this book has been conceived with the dual purpose of providing a text book for upper level graduate courses or seminars, and of serving as a source book for research specialists who need to apply the structure and representation theory of compact groups.

After a gentle introduction to compact groups and their representation theory, the book presents self-contained courses on linear Lie groups, on compact Lie groups, and on locally compact abelian groups. However, the thrust of book points in the direction of the structure theory of infinite dimensional, not necessarily commutative compact groups, unfettered by weight restrictions or dimensional bounds. In the process it utilizes infinite dimensional Lie algebras and the exponential function of arbitrary compact groups.

Book Description

This volume in matrix structural analysis is written for senior undergraduate students. Matrix structural analysis is presented in the various chapters for structures modeled as beams, plane frames, grid frames, space frames, plane trusses, and space trusses. An introduction to the related topic of the finite element method is also given. A CD-ROM accompanying this book contains not only the student version of SAP 2000 but also user manuals and numerous sample problems and examples. Throughout the book, illustrative examples are given with detailed solutions derived from hand calculations and from using the computer program. Long mathematical proofs have been relegated to a section on analytical problems at the end of each chapter. Appendices give the equivalent end forces for typical loading needed in matrix structural analysis. An extensive glossary is also included; this serves as a convenient reference for the student to locate definitions, concepts, and formulae. This text is essential for undergraduate civil engineering students. Professional civil engineers interested in a simple presentation of matrix structural analysis will also find the book useful.

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Linear Syntax
Andreas Kathol
Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Paperback

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ASIN: 019823872X

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iLinear Syntax/i makes a case for a critical reassessment of the widespread view that syntax can be reduced to tree structures. It argues that clausal syntax should instead be based on concepts that are defined in terms of linear order. By connecting the descriptive tools of modern phrase-structure grammar with traditional descriptive scholarship, Andreas Kathol offers a new perspective on many long-standing problems in syntactic theory.

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