Finite Mathematics and Its Applications

Book Description

This self-teaching volume provides extremely readable coverage of the principles of finite mathematics and their applications in business, social science, and the life sciences. Topics are presented in a straight-forward, interesting manner (with topics from elementary mathematics reviewed as the need for them arises), and an abundance of worked examples with computational details, practice problems, exercises, chapter self-assessment tests, and reviews of fundamental concepts allow readers to work through the material confidently at their own pace. Contains many examples similar to those found on CPA, GMAT, and GRE Economics exams. Features optional, explicitly detailed use of graphing calculators, electronic spreadsheets, and mathematical software, wherever relevant. Linear Equations and Straight Lines. Matrices. Linear Programming, A Geometric Approach. The Simplex Method. Sets and Counting. Probability. Probability and Statistics. Markov Processes. The Theory of Games. The Mathematics of Finance. Difference Equations and Mathematical Models. Logic. Graphs. For anyone who needs to get up to speed with the applications of mathematics in business, social sciences, or life sciences.

Customer Reviews:

Better than the one I use, but not by enough to change.......2005-10-20

I recently evaluated this book as a possible textbook for the finite mathematics class that I teach. A great deal of space is devoted to the use of technology using a TI-83 graphing calculator and Microsoft Excel spreadsheets. Images of the calculator and computer screens are used to demonstrate the solutions. While I don't use either technology in my class, the presence of the technology solutions had no affect on my opinion of the book.
I would have little difficulty using the book and my students would have no difficulty reading it. The explanations are easy to follow and at a level suitable for the background we require of our students. There are a large number of exercises and the coverage is ordinary. By ordinary, I mean that the covered topics are the standard ones in a college level course in finite mathematics and the order of presentation is a natural one.
In the end, I chose to stick with the book that I have been using. As a general rule, I change books only when I find one that is significantly better and in this case I did not. This book is a good one and even slightly better than the one I am currently using. I just don't believe that the difference is enough to justify the change.

Great Choice.......2005-09-20

I was very satisfied with my results and the sender got my book sent to me extremely quick.

I'm glad I'm the teacher and not the student!!!.......2005-02-10

Wow. This book is bad. I have to use this book -- chosen by the department -- for a class I'm teaching. The fact that the book is a bad choice for this class is not the fault of the book -- I was given the text with instructions to teach chapters 1 - 4, 10, and 11, and then to use extra material for topics not covered in the book -- clearly, this text does not fit the class, and either the course should be redesigned, or a different text should be chosen.

Anyway, a first glance was enough to see how miserably this book is organized. The first chapter covers:
1.1 Coordinate Systems and Graphs
1.2 Linear Inequalities
1.3 The Intersection Point of a Pair of Lines
1.4 The Slope of a Straight Line
1.5 The Method of Least Squares

So, section 1.2 is dependent on 1.3 which is dependent on 1.4 -- isn't the order a bit backwards? And then in 1.5, you're on to a topic which is a huge leap in difficulty from learning how to plot a point on Cartesian coordinates from 1.1. Unbelievable.

This type of interdependence carries on through all of the sections of the book that I've looked at (admittedly not all). It seems that one must already know the material from further ahead in the book in order to use the book to learn the material in the given chapter.

I believe that by this Eighth Edition of the book, the authors should be removed from it -- it should be given to students using this text without already knowing it all, and let those students revise and edit the continuity of the material.

Matrix notation is introduced, virtually without explanation of either how to use it or why. Examples are given that attempt to show how to perform some operations on a TI-83 (or similar) calculator, but these efforts fail miserably.

Frankly, I'm having a hard time even figuring out what it is that this book is trying to teach -- and I already understand the material! If, however, the goal of the book is to confuse students such that they should hate and fear all math courses, then the authors have achieved their goals.

Finite Element Model Updating in Structural Dynamics (Solid Mechanics and Its Applications)

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Finite Element Model Updating in Structural Dynamics (Solid Mechanics and Its Applications)
M. Friswell , and J.E. Mottershead
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0792334310

Book Description

Finite element model updating has emerged in the 1990s as a subject of immense importance to the design, construction and maintenance of mechanical systems and civil engineering structures. This book, the first on the subject, sets out to explain the principles of model updating, not only as a research text, but also as a guide for the practising engineer who wants to get acquainted with, or use, updating techniques. It covers all aspects of model preparation and data acquisition that are necessary for updating. The various methods for parameter selection, error localisation, sensitivity and parameter estimation are described in detail and illustrated with examples. The examples can be easily replicated and expanded in order to reinforce understanding. The book is aimed at researchers, postgraduate students and practising engineers.

Finite Mathematics and Its Applications (9th Edition)

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Nothing to differentitate it from the other finite textbooks

Finite Mathematics and Its Applications (9th Edition)
Larry J Goldstein , David I Schneider , and Martha J Siegel
Manufacturer: Prentice Hall
ProductGroup: Book
Binding: Hardcover

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ASIN: 0131873644

Book Description

A âtried and trueâ favorite of both students and instructors alike, this text offers extremely readable coverage of the principles of finite mathematics and their applications in business, social science, and the life sciences. Topics are presented in a straightforward, interesting manner, with considerable attention given to the applications of the mathematics. The goal is for the students' mathematical maturity and appreciation for the usefulness of mathematics to grow simultaneously. Many sections contain specially designed technology exercises.

Customer Reviews:

Nothing to differentitate it from the other finite textbooks.......2006-02-25

I am always trolling for a new and better textbook for my finite mathematics class. In my search, I have found a repetitive sameness to the books that are available. The only constant and real differentiating factors to the books are the order of the material and the quality of the writing. Occasionally, a book will cover a topic that the others don't, but often when that is done; it is a liability rather than an asset.
This book is like all the others in topics of coverage, the number of exercises is not excessive and there is a larger project at the end of each chapter. As is typical of nearly every math book, solutions to the odd exercises are included. Some day, a rebel will include solutions to the even numbered problems just to be different. I currently use "Finite Mathematics: An Applied Approach 9th Edition" by Sullivan and Mizrahi in my class. Since I am happy with this text and there are no fundamental differences between Sullivan and Mizrahi and this one, I will not be changing what I use. However, I have no doubt that if I were to change to this one, it would introduce no significant problems.

Introduction to Vertex Operator Superalgebras and Their Modules (Mathematics and Its Applications)

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Introduction to Vertex Operator Superalgebras and Their Modules (Mathematics and Its Applications)
Xiaoping Xu
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0792352424

Book Description

This book presents a systematic study on the structures of vertex operator superalgebras and their modules. Related theories of self-dual codes and lattices are included, as well as recent achievements on classifications of certain simple vertex operator superalgebras and their irreducible twisted modules, constructions of simple vertex operator superalgebras from graded associative algebras and their anti-involutions, self-dual codes and lattices.
Audience: This book is of interest to researchers and graduate students in mathematics and mathematical physics.

Handbook of Computational Group Theory (Discrete Mathematics and Its Applications)

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Important Text on CGT

Handbook of Computational Group Theory (Discrete Mathematics and Its Applications)
Derek F. Holt , Bettina Eick , and Eamonn A. O'Brien
Manufacturer: Chapman & Hall/CRC
ProductGroup: Book
Binding: Hardcover

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ASIN: 1584883723

Book Description

The origins of computation group theory (CGT) date back to the late 19th and early 20th centuries. Since then, the field has flourished, particularly during the past 30 to 40 years, and today it remains a lively and active branch of mathematics. The Handbook of Computational Group Theory offers the first complete treatment of all the fundamental methods and algorithms in CGT presented at a level accessible even to advanced undergraduate students. It develops the theory of algorithms in full detail and highlights the connections between the different aspects of CGT and other areas of computer algebra. While acknowledging the importance of the complexity analysis of CGT algorithms, the authors' primary focus is on algorithms that perform well in practice rather than on those with the best theoretical complexity. Throughout the book, applications of all the key topics and algorithms to areas both within and outside of mathematics demonstrate how CGT fits into the wider world of mathematics and science. The authors include detailed pseudocode for all of the fundamental algorithms, and provide detailed worked examples that bring the theorems and algorithms to life.

Customer Reviews:

Important Text on CGT.......2005-05-12

Handbook of Computational Group Theory by Derek F. Holt (Discrete Mathematics and Its Applications: Chapman & Hall/CRC) is about computational group theory, which we shall frequently abbreviate to CGT. The origins of this lively and active branch of mathematics can he traced back to the nineteenth and early twentieth centuries, but it has been flourishing particularly during the past 30 to 40 years. The aim of this book is to provide as complete a treatment as possible of all of the fundamental methods and algorithms in CGT, without straying above a level suitable for a beginning postgraduate student.
The most basic algorithms in CGT tend to be representation specific; that is, there are separate methods for groups given as permutation or matrix groups, groups defined by means of polycyclic presentations, and groups that are defined using a general finite presentation. The author has devoted separate chapters to algorithms that apply to groups in these different types of repre¬sentations, but there are other chapters that cover important methods involving more than one type. For example, Chapter 6 is about finding presentations of permutation groups and the connections between coset enumeration and methods for finding the order of a finite permutation group.
There is also included a chapter (Chapter 11) on the increasing number of precomputed stored libraries and databases of groups, character tables, etc. that are now publicly available. They have been playing a major rôle in CGT in recent years, both as an invaluable resource for the general mathematical public, and as components for use in some advanced algorithms in CGT. The library of all finite groups of order up to 2000 (except for order 1024) has proved to be particularly popular with the wider community.
It is inevitable that our choice of topics and treatment of the individual topics will reflect the authors' personal expertise and preferences to some extent. On the positive side, the final two chapters of the book cover appli¬cations of string-rewriting techniques to CGT (which is, however, treated in much greater detail, and the application of finite state automata to the computation of automatic structures of finitely presented groups. On the other hand, there may be some topics for which our treatment is more superficial than it would ideally be.
One such area is the complexity analysis of the algorithms of CGT. During the 1980s and 1990s some, for the most part friendly and respectful, rivalry developed between those whose research in CGT was principally directed to-wards producing better performance of their code, and those who were more interested in proving theoretical results concerning the complexity of the al¬gorithms. This study of complexity began with the work of Eugene Luks, who established a connection in his 1982 article between permutation group algorithms and the problem of testing two finite graphs for isomorphism. Our emphasis in this book will be more geared towards algorithms that per-form well in practice, rather than those with the best theoretical complexity. Fortunately, Seress' book includes a very thorough treatment of com¬plexity issues, and so we can safely refer the interested reader there. In any case, as machines become faster, computer memories larger, and bigger and bigger groups come within the range of practical computation, it is becom¬ing more and more the case that those algorithms with the more favourable complexity will also run faster when implemented.
The important topic of computational group representation theory and computations with group characters is perhaps not treated as thoroughly as it might be in this book. Some of the basic material is covered in Chapter 7, but there is unfortunately no specialized book on this topic.
One of the most active areas of research in CGT at the present time, both from the viewpoint of complexity and of practical performance, is the development of effective methods for computing with large finite groups of matrices. Much of this material is beyond the scope of this book. It is, in any case, developing and changing too rapidly to make it sensible to attempt to cover it properly here. Some pointers to the literature will of course be provided, mainly in Section 7.8.
Yet another topic that is beyond the scope of this book, but which is of increasing importance in CGT, is computational Lie theory. This includes computations with Coxeter groups, reflection groups, and groups of Lie type and their representations. It also connects with computations in Lie algebras, which is an area of independent importance. The article by Cohen, Murray, and Taylor provides a possible starting point for the interested reader.
The author firmly believes that the correct way to present a mathematical algorithm is by means of pseudocode, since a textual description will generally lack precision, and will usually involve rather vague instructions like "carry on in a similar manner". So we have included pseudocode for all of the most basic algorithms, and it is only for the more advanced procedures that we have occasionally lapsed into sketchy summaries. We are very grateful to Thomas Cormen who has made his LATEX package `clrscode' for displaying algorithms publicly available. This was used by him and his coauthors in the well-known textbook on algorithms.
Although working through all but the most trivial examples with procedures that are intended to be run on a computer can be very tedious, the author attempted to include illustrative examples for as many algorithms as is practical.
At the end of each chapter, or sometimes section, the reader's attention directed to some applications of the techniques developed in that chapter either to other areas of mathematics or to other sciences. It is generally difficult to do this effectively. Although there are many important and interesting applications of CGT around, the most significant of them will typically use methods of CGT as only one of many components, and so it not possible to do them full justice without venturing a long way outside of the main topic of the book.
The author assumes that the reader is familiar with group theory up to an advanced undergraduate level, and has a basic knowledge of other topics in algebra, such as ring and field theory. Chapter 2 includes a more or less complete survey of the required background material in group theory, but we shall assume that at least most of the topics reviewed will be already familiar to readers. Chapter 7 assumes some basic knowledge of group representation theory, such as the equivalence between matrix representations of a group G over a field K and KG-modules, but it is interesting to note that many of the most fundamental algorithms in the area, such as the `Meataxe', use only rather basic linear algebra.

Graph Theory As I Have Known It (Oxford Lecture Series in Mathematics and Its Applications , No 11)

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An introduction to some advanced theorems on graphs
Inside the mind of a great mathematician

Graph Theory As I Have Known It (Oxford Lecture Series in Mathematics and Its Applications , No 11)
W. T. Tutte
Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Hardcover

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ASIN: 0198502516

Book Description

This book provides a unique and unusual introduction to graph theory by one of the founding fathers, and will be of interest to all researchers in the subject. It is not intended as a comprehensive treatise, but rather as an account of those parts of the theory that have been of special interest to the author. Professor Tutte details his experience in the area, and provides a fascinating insight into how he was led to his theorems and the proofs he used. As well as being of historical interest it provides a useful starting point for research, with references to further suggested books as well as the original papers. The book starts by detailing the first problems worked on by Professor Tutte and his colleagues during his days as an undergraduate member of the Trinity Mathematical Society in Cambridge. It covers subjects such as comnbinatorial problems in chess, the algebraicization of graph theory, reconstruction of graphs, and the chromatic eigenvalues. In each case fascinating historical and biographical information about the author's research is provided.

Customer Reviews:

An introduction to some advanced theorems on graphs.......2001-01-03

The author has spent most of his professional life pondering some of the more substantial problems in graph theory. This book is not a comprehensive treatise on the subject but an organized collection of a series of lectures that he delivered in 1984. The lectures were just as much an attempt to provide insight into the process that led to some advanced theorems as about the theorems themselves. For this reason, the book is best suited for the beginning graduate student with some experience in the field.
Some of the problems covered in the book are: the knight's tour problem as an exercise in graph theory, subgraphs and Hamiltonian circuits; algebra in graph theory, symmetry in graphs and graphs on spheres. Throughout the explanations of the problems and the solution strategies, it is impossible not to appreciate the effort that was put forward to solve them. Tutte is clearly one of the leading authorities in graph theory and good at explaining what graph theory is all about.
This is not an easy book to read, yet it is readable. It would be ideal as the material for a graduate seminar in graph theory or a text in advanced topics.

Inside the mind of a great mathematician.......2000-07-06

It is unquestionably that W. T. Tutte is today one the greatest mathematicians in the world. I read this book with great enthusiasm because the author explains, with the work that made his fame, the most difficult part of the discovery of mathematics: The creativity involved.

The students will find in this book a great motivation to thinking in mathematics. For the experimented mathematician this book will make clear the born procces of some classic results in graph theory.

Book Description

The theory of finite fields is a branch of algebra with diverse applications in such areas as combinatorics, coding theory and the mathematical study of switching circuits. This updated second edition is devoted entirely to the theory of finite fields, and it provides comprehensive coverage of the literature. Bibliographical notes at the end of each chapter give a historical survey of the development of the subject. Worked examples and lists of exercises throughout the book make it useful as a text for advanced level courses for students of algebra.

Customer Reviews:

An excellent and thorough reference.......2007-07-06

This book is an excellent reference on finite fields. Chapter 1 covers the necessary background material at the right level for someone with a good knowledge of mathematics, but little algebra. Chapter 2 covers the basics of finite fields and chapter 3 goes into more detail on polynomials. The later chapters treat special topics and some applications. The proofs are clear, not over detailed and not overly terse either. If you just want to know the basics then there may be more in this book than you will ever need, but if you want a thorough reference it is recommended.

2-nd edition = 1-st edition.......2001-02-13

Undoubtedly an excellent book, but comprehensive ... only up to 1983, as this is essentially an IDENTICAL reprint by CUP of the original 1983 book by Addison-Wesley. Don't be misled by the 1997 edition date; second edition = first edition, not a single result from 1983 - 1997.

Book for professional mathematician.......2001-01-06

This is the best book on Galois (Finite) Fields, written by Austrian and Australian professors can be recomended as the most complete reference in the field. It is amazing how helpful it has been to me since time I wrote my MS diploma. Though an instance I was using was borrowed from library, I'd recomend everybody, who is related to deescrete math to have one.

Codes and Algebraic Curves (Oxford Lecture Series in Mathematics and Its Applications, 8)

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Best Book on Goppa Codes

Codes and Algebraic Curves (Oxford Lecture Series in Mathematics and Its Applications, 8)
Oliver Pretzel
Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Hardcover

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Book Description

The geometry of curves has fascinated mathematicians for 2500 years, and the theory has become highly abstract. Recently links have been made with the subject of error correction, leading to the creation of geometric Goppa codes, a new and important area of coding theory. This book is an updated and extended version of the last part of the successful book Error-Correcting Codes and Finite Fields. It provides an elementary introduction to Goppa codes, and includes many examples, calculations, and applications. The book is in two parts with an emphasis on motivation, and applications of the theory take precedence over proofs of theorems. The formal theory is, however, provided in the second part of the book, and several of the concepts and proofs have been simplified without sacrificing rigour.

Customer Reviews:

Best Book on Goppa Codes.......2000-05-07

This is the best book I've seen explaining Goppa codes and their mathematical background. The explanation of algebraic curves is much easier to follow than the other two books I know of on this topic, "Algebraic Function Fields and Codes" by Stichtenoth and "Algebraic Curves over Finite Fields" by Moreno. In fact, even if you aren't especially interested in Goppa codes, this would be a good book from which to learn the basics of algebraic curves.

Book Description

This book gives a comprehensive overview of central themes of finite model theory – expressive power, descriptive complexity, and zero-one laws – together with selected applications relating to database theory and artificial intelligence, especially constraint databases and constraint satisfaction problems. The final chapter provides a concise modern introduction to modal logic, emphasizing the continuity in spirit and technique with finite model theory. This underlying spirit involves the use of various fragments of and hierarchies within first-order, second-order, fixed-point, and infinitary logics to gain insight into phenomena in complexity theory and combinatorics.

The book emphasizes the use of combinatorial games, such as extensions and refinements of the Ehrenfeucht-Fraissé pebble game, as a powerful way to analyze the expressive power of such logics, and illustrates how deep notions from model theory and combinatorics, such as o-minimality and treewidth, arise naturally in the application of finite model theory to database theory and AI.

Students of logic and computer science will find here the tools necessary to embark on research into finite model theory, and all readers will experience the excitement of a vibrant area of the application of logic to computer science.

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