Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3rd Edition

Algebraic Geometry is the study of systems of polynomial equations in one or more variables, asking such questions as: Does the system have finitely many solutions, and if so how can one find them? And if there are infinitely many solutions, how can they be described and manipulated?

The solutions of a system of polynomial equations form a geometric object called a variety; the corresponding algebraic object is an ideal. There is a close relationship between ideals and varieties which reveals the intimate link between algebra and geometry. Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory.

The algorithms to answer questions such as those posed above are an important part of algebraic geometry. Although the algorithmic roots of algebraic geometry are old, it is only in the last forty years that computational methods have regained their earlier prominence. New algorithms, coupled with the power of fast computers, have led to both theoretical advances and interesting applications, for example in robotics and in geometric theorem proving.

In addition to enhancing the text of the second edition, with over 200 pages reflecting changes to enhance clarity and correctness, this third edition of Ideals, Varieties and Algorithms includes: A significantly updated section on Maple in Appendix C; Updated information on AXIOM, CoCoA, Macaulay 2, Magma, Mathematica and SINGULAR; A shorter proof of the Extension Theorem presented in Section 6 of Chapter 3.

“I consider the book to be wonderful. … The exposition is very clear, there are many helpful pictures, and there are a great many instructive exercises, some quite challenging … offers the heart and soul of modern commutative and algebraic geometry.”
–The American Mathematical Monthly

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Algorithms and Computation: 15th International Symposium

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Computer Vision: Algorithms and Applications

The book emphasizes basic techniques that work under real-world conditions, not the esoteric mathematics that has intrinsic elegance but less practical applicability. The text is suitable for teaching a senior-level undergraduate course in computer vision to students in computer science and electrical engineering.

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Once you’ve learned to program, you run into real-world problems that require more than a programming language alone to solve. Data Structures and Algorithms in Java is a gentle immersion into the most practical ways to make data do what you want it to do. Lafore’s relaxed mastery of the techniques comes through as though he’s chatting with the reader over lunch, gesturing toward appealing graphics. The book starts at the very beginning with data structures and algorithms, but assumes the reader understands a language such as Java or C++. Examples are given in Java to keep them free of explicit pointers.

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Beginning Algorithms
Publisher: Wrox | ISBN: 0764596748 | edition 2005 | PDF | 608 pages | 9,22 Mb

A good understanding of algorithms, and the knowledge of when to apply them, is crucial to producing software that not only works correctly, but also performs efficiently. This is the only book to impart all this essential information-from the basics of algorithms, data structures, and performance characteristics to the specific algorithms used in development and programming tasks.

Packed with detailed explanations and instructive examples, the book begins by offering you some fundamental data structures and then goes on to explain various sorting algorithms. You’ll then learn efficient practices for storing and searching by way of hashing, trees, sets, and maps. The authors also share tips on optimization techniques and ways to avoid common performance pitfalls. In the end, you’ll be prepared to build the algorithms and data structures most commonly encountered in day-to-day software development.
What you will learn from this book
* The basics of algorithms, such as iteration and recursion
* Elementary data structures such as lists, stacks, and queues
* Basic and advanced sorting algorithms including insertion sort, quicksort, and shell sort
* Advanced data structures such as binary trees, ternary trees, and heaps
* Algorithms for string searching, string matching, hashing, and computational geometry
* How to use test-driven development techniques to ensure your code works as intended
* How to dramatically improve the performance of your code with hands-on techniques for profiling and optimization
Who this book is for
This book is for anyone who develops applications, or is just beginning to do so, and is looking to understand algorithms and data structures. An understanding of computer programming is beneficial.
Wrox Beginning guides are crafted to make learning programming languages and technologies easier than you think, providing a structured, tutorial format that will guide you through all the techniques involved.

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Experimental Algorithms

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Logic and Theory of Algorithms

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This book constitutes the refereed proceedings of the 4th International Conference on Computability in Europe, CiE 2008, held in Athens, Greece, in June 2008.

The 36 revised full papers presented together with 25 invited tutorials and lectures were carefully reviewed and selected from 108 submissions. Among them are papers of 6 special sessions entitled algorithms in the history of mathematics, formalising mathematics and extracting algorithms from proofs, higher-type recursion and applications, algorithmic game theory, quantum algorithms and complexity, and biology and computation.

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There are books on algorithms that are rigorous but incomplete and others that cover masses of material but lack rigor. Introduction to Algorithms combines rigor and comprehensiveness. The book covers a broad range of algorithms in depth, yet makes their design and analysis accessible to all levels of readers. Each chapter is relatively self-contained and can be used as a unit of study. The algorithms are described in English and in a pseudocode designed to be readable by anyone who has done a little programming. The explanations have been kept elementary without sacrificing depth of coverage or mathematical rigor. The first edition became the standard reference for professionals and a widely used text in universities worldwide. The second edition features new chapters on the role of algorithms, probabilistic analysis and randomized algorithms, and linear programming, as well as extensive revisions to virtually every section of the book. In a subtle but important change, loop invariants are introduced early and used throughout the text to prove algorithm correctness. Without changing the mathematical and analytic focus, the authors have moved much of the mathematical foundations material from Part I to an appendix and have included additional motivational material at the beginning.

Product Details

• Hardcover: 1184 pages
• Publisher: The MIT Press; 2nd edition (September 1, 2001)
• Language: English
• ISBN-10: 0262032937
• ISBN-13: 978-0262032933
• Product Dimensions: 9.1 x 8.1 x 2 inches

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The design of algorithms for problem-solving lies at the heart of computer science. Concise yet authoritative, Algorithms: A Functional Programming Approach teaches the skills needed to master this essential subject. The authors challenge more traditional methods of teaching algorithms by using a functional programming context, with Haskell as the implementation language. This leads to smaller, clearer and more elegant programs which enable the programmer to understand the algorithm itself more quickly and to use that understanding to explore alternative solutions.

Placing the emphasis on program development rather than the mathematical properties of algorithms, the book uses a succession of practical programming examples to develop in the reader problem-solving skills which can be easily transferred to other language paradigms. Key features of this innovative text include: Unmatched collection of functional programming algorithms A wealth of practical examples, bringing the algorithms into clear focus. For computer science students taking algorithms and/or functional programming courses, Algorithms: A Functional Programming Approach represents the ideal textbook. It is also an invaluable reference source of functional programs for practitioners.
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Too often the problem sets in standard algorithm texts are composed of small, idiosyncratic units of busy-work and irrelevant questions — forcing instructors into the time-consuming task of finding or composing additional problems. Designed to fill that gap, this supplement provides an extensive and varied collection of useful, practical problems on the design, analysis, and verification of algorithms.

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There is a considerable, satisfying and underappreciated depth in the science of computing, it offers so much more than simply a driving licence for using a computer. The author of this book is a top researcher working on the fundamentals of informatics, and he has considerable experience teaching complex subjects in a simple manner. In this book he invites the reader to explore the science of computing, convinced that a good explanation of even the most basic techniques can demonstrate the power and magic of the underlying principles.

The author starts with the development of computer science, algorithms and programming, and then explains and shows how to exploit the concepts of infinity, computability, computational complexity, nondeterminism and randomness. Finally, he offers some insight into emerging computing paradigms such as biological computing and quantum computing.

This book is a fascinating read for students of all levels, and for those curious to learn about the science and magic of algorithmics and its role in other scientific disciplines.

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Research on algorithms and applications of stochastic programming, the study of procedures for decision making under uncertainty over time, has been very active in recent years and deserves to be more widely known. This is the first book devoted to the full scale of applications of stochastic programming and also the first to provide access to publicly available algorithmic systems. The 32 contributed papers in this volume are written by leading stochastic programming specialists and reflect the high level of activity in recent years in research on algorithms and applications. The book introduces the power of stochastic programming to a wider audience and demonstrates the application areas where this approach is superior to other modeling approaches. Applications of Stochastic Programming consists of two parts. The first part presents papers describing publicly available stochastic programming systems that are currently operational. All the codes have been extensively tested and developed and will appeal to researchers and developers who want to make models without extensive programming and other implementation costs. The codes are a synopsis of the best systems available, with the requirement that they be user-friendly, ready to go, and publicly available. The second part of the book is a diverse collection of application papers in areas such as production, supply chain and scheduling, gaming, environmental and pollution control, financial modeling, telecommunications, and electricity. It contains the most complete collection of real applications using stochastic programming available in the literature. The papers show how leading researchers choose to treat randomness when making planning models, with an emphasis on modeling, data, and solution approaches. Contents Preface: Part I: Stochastic Programming Codes; Chapter 1: Stochastic Programming Computer Implementations, Horand I. Gassmann, SteinW.Wallace, and William T. Ziemba; Chapter 2: The SMPS Format for Stochastic Linear Programs, Horand I. Gassmann; Chapter 3: The IBM Stochastic Programming System, Alan J. King, Stephen E.Wright, Gyana R. Parija, and Robert Entriken; Chapter 4: SQG: Software for Solving Stochastic Programming Problems with Stochastic Quasi-Gradient Methods, Alexei A. Gaivoronski; Chapter 5: Computational Grids for Stochastic Programming, Jeff Linderoth and Stephen J.Wright; Chapter 6: Building and Solving Stochastic Linear Programming Models with SLP-IOR, Peter Kall and János Mayer; Chapter 7: Stochastic Programming from Modeling Languages, Emmanuel Fragnière and Jacek Gondzio; Chapter 8: A Stochastic Programming Integrated Environment (SPInE), P. Valente, G. Mitra, and C. A. Poojari; Chapter 9: Stochastic Modelling and Optimization Using Stochastics™ , M. A. H. ! Dempster, J. E. Scott, and G.W. P. Thompson; Chapter 10: An Integrated Modelling Environment for Stochastic Programming, Horand I. Gassmann and David M. Gay; Part II: Stochastic Programming Applications; Chapter 11: Introduction to Stochastic Programming Applications Horand I. Gassmann, Sandra L. Schwartz, SteinW.Wallace, and William T. Ziemba Chapter 12: Fleet Management, Warren B. Powell and Huseyin Topaloglu; Chapter 13: Modeling Production Planning and Scheduling under Uncertainty, A. Alonso-Ayuso, L. F. Escudero, and M. T. Ortuño; Chapter 14: A Supply Chain Optimization Model for the Norwegian Meat Cooperative, A. Tomasgard and E. Høeg; Chapter 15: Melt Control: Charge Optimization via Stochastic Programming, Jitka Dupaˇcová and Pavel Popela; Chapter 16: A Stochastic Programming Model for Network Resource Utilization in the Presence of Multiclass Demand Uncertainty, Julia L. Higle and Suvrajeet Sen; Chapter 17: Stochastic Optimization and Yacht Racing, A. B. Philpott; Chapter 18: Stochastic Approximation, Momentum, and Nash Play, H. Berglann and S. D. Flåm; Chapter 19: Stochastic Optimization for Lake Eutrophication Management, Alan J. King, László Somlyódy, and Roger J

Book Description
This is the first book devoted to the full scale of applications of stochastic programming and also the first to provide access to publicly available algorithmic systems. The 32 contributed papers are written by leading stochastic programming specialists and reflect recent advanced research on algorithms and applications.

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Book Description:

According to Webster’s Dictionary, a fascicle is “one of the division of a bookpublished in parts.”This material represents a first look at material from the long-anticipated andmuch-discussed Volume 4 of Donald Knuth’s The Art of ComputerProgramming.Knuth’s fascicle philosophy is as follows: “The material will first appear in betatestform as fascicles of approximately 128 pages each, issued approximatelytwice per year. These fascicles will represent my best attempt to write acomprehensive account, but computer science has grown to the point where Icannot hope to be an authority on all the material covered in these books.Therefore I’ll need feedback from readers in order to prepare the officialvolumes later.”

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This book presents the concepts, methods, and results that are fundamental to the science of computing. The book begins with the basic ideas of algorithms such as the structure and the methods of data manipulation, and then moves on to demonstrate how to design an accurate and efficient algorithm. Inherent limitations to algorithmic design are also discussed throughout the second part of the text. The third edition features an introduction to the object-oriented paradigm along with new approaches to computation. Anyone interested in being introduced to the theory of computer science.

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Practical Algorithms in C++
By Bryan Flamig

• Publisher: John Wiley & Sons
• Number Of Pages: 464
• Publication Date: 1995-02-16
• ISBN-10 / ASIN: 0471009555
• ISBN-13 / EAN: 9780471009559
• Binding: Paperback

Book Description:

A practical guide to implementing algorithms in C++.

Have you been looking for a C++ book that not only talks about some of the most popular algorithms of today, but also implements them? Then look no further. This book presents algorithms from a practical point of view, clearly explaining how the algorithms work, as well as fully implementing them in C++. Written to the intermediate C++ programmer, this book covers a wide range of subjects, from sorting and searching algorithms, to graph traversal algorithms, hashing algorithms, priority queues, finite state machines, and “algorithmic generators,” a unique, object-oriented way of implementing algorithms.

Includes theory and practice, with emphasis on practice.

• Builds from the basics to the most advanced techniques.
• Backs each algorithm with full source code provided on disk-no misleading code fragments.
• Includes high quality code, written specifically for C++, and not simply ported from some other language.
• All code fully tested in Borland and Microsoft versions of C++.

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Algorithms in C++, Parts 1-4: Fundamentals, Data Structure, Sorting, Searching (3rd Edition) (Pts. 1-4)
By Robert Sedgewick

• Publisher: Addison-Wesley Professional
• Number Of Pages: 752
• Publication Date: 1998-07-23
• ISBN-10 / ASIN: 0201350882
• ISBN-13 / EAN: 9780201350883

Product Description:

Robert Sedgewick has thoroughly rewritten and substantially expanded andupdated his popular work to provide current and comprehensive coverage ofimportant algorithms and data structures. Christopher Van Wyk and Sedgewickhave developed new C++ implementations that both express the methods in aconcise and direct manner, and also provide programmers with the practicalmeans to test them on real applications. Many new algorithms are presented, and the explanations of each algorithmare much more detailed than in previous editions. A new text design anddetailed, innovative figures, with accompanying commentary, greatly enhancethe presentation. The third edition retains the successful blend of theory andpractice that has made Sedgewick’s work an invaluable resource for more than250,000 programmers! This particular book, Parts 1-4, represents the essential first half of Sedgewick’scomplete work. It provides extensive coverage of fundamental data structuresand algorithms for sorting, searching, and related applications. Although thesubstance of the book applies to programming in any language, theimplementations by Van Wyk and Sedgewick also exploit the natural matchbetween C++ classes and ADT implementations. Highlights

Expanded coverage of arrays, linked lists, strings, trees, and other basic

data structures Greater emphasis on abstract data types (ADTs), modular programming, object-oriented programming, and C++ classes than in previous editions

Over 100 algorithms for sorting, selection, priority queue ADT implementations, and symbol table ADT (searching) implementations

New implementations of binomial queues, multiway radix sorting, randomized BSTs, splay trees, skip lists, multiway tries, B trees, extendible hashing, and much more Increased quantitative information about the algorithms, giving you a

basis for comparing them Over 1000 new exercises to help you learn the properties of algorithms Whether you are learning the algorithms for the first time or wish to have up-to-date reference material that incorporates new programming styles with classic and new algorithms, you will find a wealth of useful information in this book.

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Randomized Algorithms
By Rajeev Motwani, Prabhakar Raghavan

• Publisher: Cambridge University Press
• Number Of Pages: 492
• Publication Date: 1995-08-25
• ISBN-10 / ASIN: 0521474655
• ISBN-13 / EAN: 9780521474658

Product Description:

For many applications, a randomized algorithm is either the simplest or the fastest algorithm available, and sometimes both. This book introduces the basic concepts in the design and analysis of randomized algorithms. The first part of the text presents basic tools such as probability theory and probabilistic analysis that are frequently used in algorithmic applications. Algorithmic examples are also given to illustrate the use of each tool in a concrete setting. In the second part of the book, each chapter focuses on an important area to which randomized algorithms can be applied, providing a comprehensive and representative selection of the algorithms that might be used in each of these areas. Although written primarily as a text for advanced undergraduates and graduate students, this book should also prove invaluable as a reference for professionals and researchers.

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Algorithms are at the heart of every nontrivial computer application, and algorithmics is a modern and active area of computer science. Every computer scientist and every professional programmer should know about the basic algorithmic toolbox: structures that allow efficient organization and retrieval of data, frequently used algorithms, and basic techniques for modeling, understanding and solving algorithmic problems.
This book is a concise introduction addressed to students and professionals familiar with programming and basic mathematical language. Individual chapters cover arrays and linked lists, hash tables and associative arrays, sorting and selection, priority queues, sorted sequences, graph representation, graph traversal, shortest paths, minimum spanning trees, and optimization. The algorithms are presented in a modern way, with explicitly formulated invariants, and comment on recent trends such as algorithm engineering, memory hierarchies, algorithm libraries and certifying algorithms. The authors use pictures, words and high-level pseudocode to explain the algorithms, and then they present more detail on efficient implementations using real programming languages like C++ and Java.
The authors have extensive experience teaching these subjects to undergraduates and graduates, and they offer a clear presentation, with examples, pictures, informal explanations, exercises, and some linkage to the real world. Most chapters have the same basic structure: a motivation for the problem, comments on the most important applications, and then simple solutions presented as informally as possible and as formally as necessary. For the more advanced issues, this approach leads to a more mathematical treatment, including some theorems and proofs. Finally, each chapter concludes with a section on further findings, providing views on the state of research, generalizations and advanced solutions.

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“…well equipped with exercises and with procedures which are helpful in implementing the coders…” (Zentralblatt Math, Vol.1041, No.16, 2004)

Description
* Speech coding is a highly mature branch of signal processing deployed in products such as cellular phones, communication devices, and more recently, voice over internet protocol
* This book collects many of the techniques used in speech coding and presents them in an accessible fashion
* Emphasizes the foundation and evolution of standardized speech coders, covering standards from 1984 to the present
* The theory behind the applications is thoroughly analyzed and proved

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