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Investigations in Algebra departs from a preoccupation with calculus as the ultimate goal of and the universal introduction to advanced mathematics by using Logo to explore combinatorics, number theory, the study of discrete functions, and other topics that are not on the traditional path to calculus.

This approach encourages students to participate actively in exciting mathematics, developing in them a facility for abstraction and an appreciation for the power of mathematical methods. Most of the projects in the first two parts of the book have been worked through by students at Woburn High School, often without assistance from a teacher.

In three parts, Investigations in Algebra emphasizes the treatment of functions as concrete objects modeled as Logo procedures, applies the techniques of induction and recursion to combinatorial problems, and takes up topics in number theory (including unique factorization congruence, and multiplicative functions). Integral to the presentation are numerous carefully constructed problems routine exercises, long term projects, and open ended experiments—developed in twenty years of classroom use. ... Read more

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Well organized, concise, to-the point.
"Learning Linear Algebra Through Derive" by Brian Denton

This book is a good example of how all college level math textbooks should be written. It focuses on understanding the concepts of linear algebra byfollowing a basic form of presenting a theorem and then working through theproof combined with exercises focusing on both methods and proofs ofproperties along with independent exploratory exercises for use with Derive(PC math program). This method of presentation is excellent forunderstanding the basic fundamentals and developing thinking skills toheighten knowledge of the material. The text covers the following areas oflinear algebra:

1. The Idea of a Matrix (basic operations) 2. TheDeterminant 3. Vectors 4. More Matrices (properties, finding inversematrices, solving systems of eqs.) 5. Systems of Linear Equations (moresolution methods, error checking, perturbations) 6. Vector Spaces andLinear Transformations 7. Eigenvalues and Eigenvectors 8. OrthogonalMatrices 9. Applications

This book would easily get five stars if it didnot omit basic proofs in some of the later chapters, saying that they canbe found in any traditional linear algebra text. This necessitates the useof a secondary text and hence reduces the completeness of this book. Byusing this book I have learned the material covered in a semester-longcourse in greater depth in under a month. I believe this book is a veryuseful tool for anyone learning linear algebra. ... Read more

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Computer Simulation and Computer Algebra. Starting from simple examples in classical mechanics, these introductory lectures proceed to simulations in statistical physics (using FORTRAN) and then explain in detail the use of computer algebra (by means of Reduce). This third edition takes into account the most recent version of Reduce (3.4.1) and updates the description of large-scale simulations to subjects such as the 170000 X 170000 Ising model. Furthermore, an introduction to both vector and parallel computing is given. ... Read more

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The book deals with computer arithmetic in a more general sense than usual. Advanced computer arithmetic requires that all computer approximations of arithmetic operations - in particular those in the usual vector and matrix spaces - differ from the correct result by at most one rounding. The implementation of advanced computer arithmetic by fast hardware is examined in the book. The new expanded computational capability is gained at modest cost. It increases both, the speed of a computation and the accuracy of the computed result. Fast multiple precision arithmetic can be easily provided with it. All this strongly supports the case for implementing advanced computer arithmetic on every CPU. It is also shown in the book that on superscalar processors interval operations can be made as fast as simple floating-point operations with only very modest additional hardware costs. ... Read more

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Numerical linear algebra is far too broad a subject to treat in a single introductory volume. Stewart has chosen to treat algorithms for solving linear systems, linear least squares problems, and eigenvalue problems involving matrices whose elements can all be contained in the high-speed storage of a computer. By way of theory, the author has chosen to discuss the theory of norms and perturbation theory for linear systems and for the algebraic eigenvalue problem. These choices exclude, among other things, the solution of large sparse linear systems by direct and iterative methods, linear programming, and the useful Perron-Frobenious theory and its extensions. However, a person who has fully mastered the material in this book should be well prepared for independent study in other areas of numerical linear algebra. ... Read more

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A new model-theoretic approach to universal algebra is offered in this book. Written for computer scientists, it presents a systematic development of the methods and results of universal algebra that are useful in a variety of applications in computer science. The notation is simple and the concepts are clearly presented. The book concerns the algebraic characterization of axiomatic classes of algebras (equational, implicational, and universal Horn classes) by closure operators generalizing the famous Birkhoff Variety Theorem, and the algebraic characterization of the related theories. The book also presents a thorough study of term rewriting systems. Besides basic notions, the Knuth-Bendix completion procedure and termination proof methods are considered. A third main topic is that of fixpoint techniques and complete ordered algebras. Algebraic specifications of abstract data types and algebraic semantics of recursive program schemes are treated as applications. The book is self-contained and suitable both as a textbook for graduate courses and as a reference for researchers. ... Read more

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Network Algebra considers the algebraic study of networks and their behaviour. It contains general results on the algebraic theory of networks, recent results on the algebraic theory of models for parallel programs, as well as results on the algebraic theory of classical control structures. The results are presented in a unified framework of the calculus of flownomials, leading to a sound understanding of the algebraic fundamentals of the network theory. Network Algebra will be of interest to anyone interested in network theory or its applications and provides them with the results needed to put their work on a firm basis. Graduate students will also find the material within this book useful for their studies. ... Read more

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The aim of this book is to teach the reader the topics in algebra which are useful in the study of computer science. In a clear, concise style, the author present the basic algebraic structures, and their applications to such topics as the finite Fourier transform, coding, complexity, and automata theory. The book can also be read profitably as a course in applied algebra for mathematics students. ... Read more

Customer Reviews (1)

Very Dense
Unless you have extensive mathematical background avoid this book.I used it for a graduate class and needed two other books just to understand what this one said. ... Read more

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Process algebra, also known as the Algebra of Communicating Processes (ACP), is a mathematical theory or model of computer processes, particularly concurrent systems.In this introduction to ACP, the authors describe an algebraic formalism that can be used to specify, apply logic to, and improve parallel systems. Their axiomatic approach permits intensive calculations to be performed and establishes a uniform framework in which a range of models can be investigated. The book addresses issues such as parallelism, communication, abstraction, non-determinism, and fairness and provides many examples, so it should appeal to computer scientists and mathematicians alike.It is a unique introduction to this model of concurrent programming and will be essential reading for all computer scientists interested in parallel processing and algebraic methods in computer science. ... Read more

Customer Reviews (1)

Great introduction to the theory of concurrency
This book is a wonderful introduction to the theory behind concurrency.All the given proofs are explained well (but references to some of the steps would be nice).The only problems I had with the book is the lack of some references in the proofs and no answers to the exercises. ... Read more

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This second edition of Compact Numerical Methods for Computers presents reliable yet compact algorithms for computational problems. As in the previous edition, the author considers specific mathematical problems of wide applicability, develops approaches to a solution and the consequent algorithm, and provides the program steps. He emphasizes useful applicable methods from various scientific research fields, ranging from mathematical physics to commodity production modeling. While the ubiquitous personal computer is the particular focus, the methods have been implemented on computers as small as a programmable pocket calculator and as large as a highly parallel supercomputer.

New to the Second Edition

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Algorithmic Algebra studies some of the main algorithmic tools of computer algebra, covering such topics as Gröbner bases, characteristic sets, resultants and semialgebraic sets. The main purpose of the book is to acquaint advanced undergraduate and graduate students in computer science, engineering and mathematics with the algorithmic ideas in computer algebra so that they could do research in computational algebra or understand the algorithms underlying many popular symbolic computational systems: Mathematica, Maple or Axiom, for instance. Also, researchers in robotics, solid modeling, computational geometry and automated theorem proving community may find it useful as symbolic algebraic techniques have begun to play an important role in these areas. The book, while being self-contained, is written at an advanced level and deals with the subject at an appropriate depth. The book is accessible to computer science students with no previous algebraic training. Some mathematical readers, on the other hand, may find it interesting to see how algorithmic constructions have been used to provide fresh proofs for some classical theorems. The book also contains a large number of exercises with solutions to selected exercises, thus making it ideal as a textbook or for self-study. ... Read more

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One of the Best in Computer Algebra Text
Anyone need to use algorithms in polynomials should have a copy of this! This is definitely one of the best! It covers almost everything anyone need in computation with systems of polynomial equations: Grobner Basis,Resultants, Characteristic Set, Real Solutions of Polynomials... and also abit of Data Structure. ... Read more

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Process algebra is a widely accepted and much used technique in the specification and verification of parallel and distributed software systems. This book sets the standard for the field. It assembles the relevant results of most process algebras currently in use, and presents them in a unified framework and notation. The authors describe the theory underlying the development, realization and maintenance of software that occurs in parallel or distributed systems. A system can be specified in the syntax provided, and the axioms can be used to verify that a composed system has the required external behavior. As examples, two protocols are completely specified and verified in the text: the Alternating-Bit Protocol for Data Communication, and Fischer's Protocol of Mutual Exclusion. The book serves as a reference text for researchers and graduate students in computer science, offering a complete overview of the field and referring to further literature where appropriate. ... Read more

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This volume asssembles papers describing the present state of development of practical parallelism for computer algebra. Subjects covered include vectorization, loosely couple systems and a variety of algorithmic developments and software tools, with an emphasis on finding solutions to real problems and producing usable algebra systems. ... Read more

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This is the sixth in a series of conference proceedings of international conferences on computer algebra held in Europe. All the preceding ones have also been published as Lecture Notes in Computer Science. They contain original research material not published elsewhere, and a few invited lectures summarising the state of the art. Computer algebra is the science of using computers to do algebraic calculations, rather than the purely arithmetic calculations which we all know computers can do. These calculations may be polynomial-like calculations - one thread of the conference was devoted to polynomial algorithms - or may relate to other areas of mathematics such as integration, the solution of differential equations, or geometry - a second thread was devoted to those topics. The calculations can be applied in a wide range of scientific and engineering subjects, and in branches of mathematics. Physics has benefitted especially from these calculations, and the proceedings contain many papers on this, and also papers on applications in computer aided design and robotics, to name but a few other applications. The third thread of the proceedings was devoted to these applications and to the computer algebra systems which perform these calculations. ... Read more

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Esiste oggi un potente strumento didattico che può essere utile per rinnovare contenuti e metodi dell'insegnamento: ora che la COMUPTER ALGEBRA è disponibile su calcolatrici di piccole dimensioni, l'insegnante e lo studente hanno l`opportunità di rendere il proprio insegnamento-apprendimento più efficace. Questo libro mostra percorsi didattici, provati in classe nell'ambito della sperimentazione LABCLASS del M.P.I., che, partendo da attività di ricerca sperimentale, hanno lo scopo di rafforzare la valenza semantica degli oggetti matematici e innestare su un terreno più solido definizioni e teoremi. Il volume è destinato ai docenti delle scuole medie superiori e dell'università e agli studenti curiosi di 'fare' matematica non solo con carta e penna. ... Read more

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This volume presents the proceedings of the Joint Summer Research Conference on $q$-series, combinatorics, and computer algebra held at Mount Holyoke College (South Hadley, MA). All of the papers were contributed by participants and offer original research on topics of current interest. Articles in the book reflect the diversity of areas that overlap with $q$-series, as well as the usefulness of $q$-series across the mathematical sciences. The conference was held in honor of Richard Askey on the occasion of his 65th birthday and the proceedings contain an article about Askey's contributions to special functions. ... Read more

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The book consists of state-of-the-art chapters on Nevanlinnatheory, Fatou--Julia theory, entire and meromorphic functions,several complex variables, computer applications to complex analysis,line bundles, and collocation methods. Audience: Researchers working in the field as well as scientistsinterested in the applications. ... Read more