Research in Scientific Computing in Undergraduate Education

13. Books

Introduction To Computational Mathematics, Xin-she Yang (Editor)


Product Details

* Hardcover: 260 pages

* Publisher: World Scientific Publishing Company (August 30, 2008 )

* Language: English

* ISBN-10: 9812818170

* ISBN-13: 978-9812818171

* Product Dimensions: 9.2 x 6.2 x 1 inches


Computational Science (Mathematics), D. Kiryanov (Author), E. Kiryanova (Author)


Editorial Review

This applications-oriented book teaches students and engineers how to employ mathematical techniques for simulation and data processing using Mathcad. It is designed as a reference for practicing engineers or for use as a standard university course text, illustrating practical examples from computational science (such as optics, environmental science, chemistry, biology, tomography, economics, etc). The authors describe the most popular classical algorithms and modern techniques with all of the examples computed in Mathcad (on CD-ROM). Brief Table of Contents PART 1. EXPERIMENT PROCESSING Chapter 1. Data Processing Chapter 2. Inverse Problems PART 2. MODELLING Chapter 3. Ordinary Differential Equations: Cauchy Problems Chapter 4. Nonlinear Dynamics Chapter 5. Boundary-Value Problems Chapter 6. Partial Differential Equations Appendix A. References Appendix B. CD-ROM. Index

About the Author

Dmitry Kiryanov is a researcher at the Keldysh Institute of Applied Mathematics and head of the multimedia courseware laboratory at the Moscow University. He received his Ph.D. in physics from Moscow University. Elena Kiryanova is a researcher at the Keldysh Institute of Applied Mathematics with a Masters of Science in cybernetics and mathematics.

Product Details

* Hardcover: 400 pages

* Publisher: Infinity Science Press (September 15, 2006)

* Language: English

* ISBN-10: 0977858227

* ISBN-13: 978-0977858224

* Product Dimensions: 9.3 x 7.5 x 1.4 inches


Computational Mathematics, K. Thangavel (Editor), P. Balasubramaniam (Editor)


Book Description

Computational Mathematics presents a real life system, which is always challenging for scientists and engineers. Concerned with the design and control of continuum systems and processes, it emphasizes the solution of a general class of inverse/design problems and presents methodologies for dynamic coupling between experiments and computation. The book reviews computational design models that can be used to point to the field variables that are best to measure as well as the most effective control mechanisms having major impact on the physical phenomena one is interested to control. The field of computational mathematics also concerns algorithmic developmental approach for mathematically driven data mining and reduced-order modeling of continuum systems.

Product Details

* Hardcover: 266 pages

* Publisher: Alpha Science International, Ltd (February 2005)

* Language: English

* ISBN-10: 8173196192

* ISBN-13: 978-8173196195

* Product Dimensions: 9.7 x 7.2 x 0.8 inches


Scientific Computing: An Introductory Survey, Michael T. Heath

This book presents a broad overview of numerical methods for solving all the major problems in scientific computing, including linear and nonlinear equations, least squares, eigenvalues, optimization, interpolation, integration, ordinary and partial differential equations, fast Fourier transforms, and random number generators. The treatment is comprehensive yet concise, software-oriented yet compatible with a variety of software packages and programming languages. The book features more than 160 examples, 500 review questions, 240 exercises, and 200 computer problems.

Changes for the second edition include

* expanded motivational discussions and examples* formal statements of all major algorithms* expanded discussions of existence, uniqueness, and conditioning for each type of problem so that students can recognize “good” and “bad” problem formulations and understand the corresponding quality of results produced* expanded coverage of several topics, particularly eigenvalues and constrained optimization

The book contains a wealth of material and can be used in a variety of one- or two-term courses in computer science, mathematics, or engineering. Its comprehensiveness and modern perspective, as well as the software pointers provided, also make it a highly useful reference for practicing professionals who need to solve computational problems.

Publisher: McGraw-Hill

Address: New York

Edition: Second

Copyright Date: 2002

Current Printing: Fifth

Pages: 563 + xii

ISBN: 0-07-239910-4


Experimentation in Mathematics: Computational Paths to Discovery, Jonathan Borwein (Author), David Bailey (Author), Roland Girgensohn (Author)


Product Description

…addresses the current state of experimental research supplement it with intriguing historical facts, and chart a road for future development.

Book Info

Explains experimental mathematics and offers accessible examples of the ‘new paradigm’ in action. Addresses the role of computer-based experimental research for the formulation of new hypotheses and the discovery of new results. For researchers and practitioners. DLC: Mathematics–Research.

Product Details

* Hardcover: 300 pages

* Publisher: AK Peters; 1st edition (March 31, 2004)

* Language: English

* ISBN-10: 1568811365

* ISBN-13: 978-1568811369

* Product Dimensions: 9.2 x 6.2 x 1.1 inches

Most Helpful Customer Reviews

2 of 2 people found the following review helpful:

4 out of 5 stars using computers in pure maths, September 20, 2006

By W Boudville (Terra, Sol 3) – See all my reviews

The book is an advanced text in computational maths. It requires a solid undergraduate background in real analysis. Typically, you’d have this if you are a maths major. Or possibly a theoretical physics major. The level of rigour is unlike most undergrad texts on numerical analysis. The authors strive to demonstrate that even in pure maths, it can be fruitful to have a computer perform computations. The chapters show that often when there are what appear to be pure maths derivations, a context might appear where you can, or perhaps need to, crunch some numbers. There are many problems; some quite challenging. Not all the computations are numerical. Several involve symbolic algebra. The text leaves it to you to use whatever maths packages you prefer.

9 of 18 people found the following review helpful:

5 out of 5 stars Advanced numerical techniques, and mathematical experiments, June 4, 2004

By Midwest Book Review (Oregon, WI USA) – See all my reviews

The collaboration of Jonathan Borwein, David Bailey, and Roland Girgensohn, Experimentation In Mathematics: Computational Paths To Discovery is a scholarly, college and graduate-studies text discussing the role of computer-based experimental research in the formulation of new hypotheses. Extensive equations, advanced numerical techniques, and mathematical experiments explained in meticulous, step-by-step detail reveal the “new paradigm” in mathematic research, in this solid text especially for expert students and field professionals in cutting-edge mathematical studies.


Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica ®, Sriram Pemmaraju (Author), Steven Skiena (Author)


Editorial Review

“This book is the definitive reference guide to Combinatorica — an extension of the popular computer software, Mathematica — with examples of the 450 combinatorics functions. The authors developed the newest version of this software that has dramatic improvements in graphical processing performance, representation, visualization, and many brand new functions…This book is highly recommended. It is a well organized and readable textbook for beginners and intermediate students.” Leonardo

Product Description

With examples of all 450 functions in action plus tutorial text on the mathematics, this book is the definitive guide to Experimenting with Combinatorica, a widely used software package for teaching and research in discrete mathematics. Three interesting classes of exercises are provided–theorem/proof, programming exercises, and experimental explorations–ensuring great flexibility in teaching and learning the material. The Combinatorica user community ranges from students to engineers, researchers in mathematics, computer science, physics, economics, and the humanities. Recipient of the EDUCOM Higher Education Software Award, Combinatorica is included with every copy of the popular computer algebra system Mathematica.

Product Details

* Hardcover: 494 pages

* Publisher: Cambridge University Press (December 8, 2003)

* Language: English

* ISBN-10: 0521806860

* ISBN-13: 978-0521806862

* Product Dimensions: 9.4 x 8.7 x 1.1 inches


A Computational Introduction to Number Theory and Algebra (Hardcover) by Victor Shoup (Download: computational_introduction-to-number_theory_and_algebra)

Editorial Reviews


“This is an outstanding and well-written book whose aim is to introduce the reader to a broad range of material — ranging from basic to relatively advanced — without requiring any prior knowledge on the part of the reader other than calculus and mathematical maturity. That the book succeeds at this goal is quite an accomplishment! …this book is a must-read for anyone interested in computational number theory or algebra and especially applications of the latter to cryptography. I would not hesitate, though, to recommend this book even to students ‘only’ interested in the algebra itself (and not the computational aspects thereof); especially for computer science majors, this book is one of the best available introductions to that subject.”


“As computer science students have very likely not previously mastered probability theory, linear algebra, or basic abstract algebra, Shoup packages crash courses in each. Despite taking time for so many basics, Shoup climaxes with careful treatment of the late-breaking, ingenious, polynomial-time deterministic primality test of Agrawal, Kayal, and Saxena. Apart from number theory, one could easily build a fine discrete mathematics course on this book. Highly recommended.”


Product Description

Number theory and algebra play an increasingly significant role in computing and communications, as evidenced by the striking applications of these subjects to such fields as cryptography and coding theory. This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The mathematical prerequisites are minimal: nothing beyond material in a typical undergraduate course in calculus is presumed, other than some experience in doing proofs – everything else is developed from scratch. Thus the book can serve several purposes. It can be used as a reference and for self-study by readers who want to learn the mathematical foundations of modern cryptography. It is also ideal as a textbook for introductory courses in number theory and algebra, especially those geared towards computer science students.

Most Helpful Customer Reviews

8 of 11 people found the following review helpful:

5.0 out of 5 stars The background you really need, clear and sweet, November 6, 2005

By Jonathan Poritz (Zurich, Switzerland)

This book is a marvel. It is clear and concise yet thorough. The author is obviously a bit of an obsessive compulsive, he has found the shortest paths from the clearest definitions to the most important results, each given with the cleanest, most insight-inducing proofs … the results (and definitions) he gives are the ones any student (practitioner!) of modern computer science (especially cryptology) *needs* to know — having this book on your shelves (and its contents in your head) should be a requirement for any degree, at any level, in computer science.

[Caveat: I know the author and have read his book in draft form. I also required my students to get it and read it, in a computer science course I taught.]


A Course in Computational Number Theory (Textbooks in Mathematical Sciences) (Hardcover)
by David Bressoud (Author), Stan Wagon (Author)

# Hardcover: 367 pages
# Publisher: Key College; 1 edition (May 11, 2000)
# Language: English
# ISBN-10: 1930190107
# ISBN-13: 978-1930190108
# Product Dimensions: 9.5 x 7.2 x 1.1 inches



Computational Homology (Applied Mathematical Sciences)by Tomasz Kaczynski, Konstantin Mischaikow & Marian Mrozek

Editorial Reviews

“…This is an interesting and unusual book written with the intention of serving several purposes. One of them is to demonstrate that methods of algebraic topology, in particular homology theory, that have proved remarkably successful in several areas of pure mathematics can provide powerful, and in some cases indispensable, tools in a number of areas of applied mathematics and science. The second is to provide the necessary theory and “technology” for such applications. This means on the one hand providing all the necessary mathematical foundations of the subject, including definitions and theorems, and on the other hand efficient computational techniques capable of dealing with real life situations. Thus, the book stresses algorithmic and computational approaches; and in fact includes computer code written in a programming language specially designed for this purpose. It is addressed to a varied audience of computer scientists, experimental scientists and engineers while at the same time trying to retain the interest of mathematicians. With this in mind the authors have attempted to produce a modular book, which allows a number of different reading approaches. The basic subdivision of the book is into three parts. The last part contains all the basic pre-requisites from algebra and topology: the most essential facts about Euclidean spaces, point set topology, abelian groups, vector spaces and matrix algebras. This part also contains a description of the programming language used to describe the algorithms found in the book…” –MATHEMATICAL REVIEWS

“This book provides the conceptual background for computational homology – a powerful tool used to study the properties of spaces and maps that are insensitive to small perturbations. The material presented here is a unique combination of current research and classical rigor, computation and application.” (Corina Mohorianu, Zentralblatt Mathematik, Vol. 1039 (8), 2004)

“In addition to developing a computational homology theory which produces efficient algorithms, the authors demonstrate how these algorithms can be applied to a variety of problems … . I certainly recommend Computational Homology to mathematicians and applied scientists who wish to learn about the potential of algebraic topological methods. … this book is the first comprehensive effort to describe the computational aspects of homology theory … . It is written at a level that is suitable for advanced undergraduate and early graduate courses … .” (Thomas Wanner, SIAM Review, Vol. 48 (1). 2006)

“This is the first textbook on what is necessarily a mixture of classical mathematics, computer science, and applications. … it is a unique feature of Computational Homology that every geometric step, however conceptually simple, is broken down into elementary operations. … The book offers a reliable yet practical introduction to (cubical homology), with a strong emphasis on computational aspects. Hands-on experience can be gained through the many problems within the book and also by means of the software packages … .” (Arno Berger, Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 86 (4). 2006)

Product Description

Homology is a powerful tool used by mathematicians to study the properties of spaces and maps that are insensitive to small perturbations. This book uses a computer to develop a combinatorial computational approach to the subject. The core of the book deals with homology theory and its computation. Following this is a section containing extensions to further developments in algebraic topology, applications to computational dynamics, and applications to image processing. Included are exercises and software that can be used to compute homology groups and maps. The book will appeal to researchers and graduate students in mathematics, computer science, engineering, and nonlinear dynamics.

  • 480 pages
  • Springer (January 9, 2004)
  • ISBN-10: 0387408533
  • ISBN-13: 978-0387408538
  • $75


Topology for Computing (Cambridge Monographs on Applied and Computational Mathematics) by Afra J. Zomorodian.

Product Description
Written by a computer scientist for computer scientists, this book teaches topology from a computational point of view, and shows how to solve real problems that have topological aspects involving computers. Such problems arise in many areas, such as computer graphics, robotics, structural biology, and chemistry. The author starts from the basics of topology, assuming no prior exposure to the subject, and moves rapidly up to recent advances in the area, including topological persistence and hierarchical Morse complexes. Algorithms and data structures are presented when appropriate.

  • 243 pages
  • Cambridge University Press(January 10, 2005)
  • ISBN-10: 0521836662
  • ISBN-13: 978-0521836661
  • $51

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