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Unlike most texts on logic and mathematics, this book is about how to prove theorems rather than proof of specific results. We give our answers to such questions as: - When should induction be used? - How does one invent an appropriate induction argument? - When should a definition be expanded?

This well-accepted introduction to computational geometry is a textbook for high-level undergraduate and low-level graduate courses. The focus is on algorithms and hence the book is well suited for students in computer science and engineering. Motivation is provided from the application areas: all solutions and techniques from computational geometry are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. For students this motivation will be especially welcome. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement. All the basic techniques and topics from computational geometry, as well as several more advanced topics, are covered. The book is largely self-contained and can be used for self-study by anyone with a basic background in algorithms. In the second edition, besides revisions to the first edition, a number of new exercises have been added.

Computational Fluid Dynamics (CFD) and structural analysis play a significant role in the development of technical devices, building construction, weather predictions, biochemistry processes modeling, and in many other fields. With regard to increase computational power increase and improvements in computer modeling techniques, it is expected that the numerical simulations will prevail the traditional methods, such as the experiments and analytical solutions, in the near future. Behind computer modeling, there are complex mathematical apparatuses, physical theories, chemical reactions, etc. Together, these factors make it difficult to understand and use CFD and structural analysis. This book attempts to systematize and provide an easy explanation of computer modeling.

COMPUTATIONAL METHODS IN CIRCUIT SIMULATION INCUDES THEORY, NUMERICAL TECHNIQUES, AND RECIPES ON HOW TO BUILD A SIMULATOR FOR THE ANALYSIS OF VERY LARGE CIRCUITS WITH COMPLEX DEVICE AND COMPONENT MODELS This book provides theoretical basis of circuit simulation with special emphasis on the simulation of very large circuits and systems. The results are presented in algorithmic form and recipes that can be easily translated into computer code. The book: · Explains the theoretical basis of circuit formulation and describes the Extended Nodal Analysis, which is a generalization of the traditional nodal and modified nodal analysis that allows the inclusion of complex device models. · Describes how to build the circuit equations from the input netlist using the stamp approach. · Presents the solution of large linear equations using sparse matrix techniques, partitioning, iterative and projection methods. · Covers DC solution or the solution of nonlinear algebraic equations, including variations of Newton method and piecewise-linear techniques. · Covers transient analysis or solution of algebraic-differential equations, including integration formulas, stability, error estimation and step-size control. · Explains reduced-order modeling for the simulation of very large dynamic circuits and systems. · Includes sensitivity analysis.

Thoroughly updated to include the latest developments in the field, this classic text on finite-difference and finite-volume computational methods maintains the fundamental concepts covered in the first edition. As an introductory text for advanced undergraduates and first-year graduate students, Computational Fluid Mechanics and Heat Transfer, Third Edition provides the background necessary for solving complex problems in fluid mechanics and heat transfer. Divided into two parts, the book first lays the groundwork for the essential concepts preceding the fluids equations in the second part. It includes expanded coverage of turbulence and large-eddy simulation (LES) and additional material included on detached-eddy simulation (DES) and direct numerical simulation (DNS). Designed as a valuable resource for practitioners and students, new homework problems have been added to further enhance the student’s understanding of the fundamentals and applications.

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Phase diagrams are used in materials research and engineering to understand the interrelationship between composition, microstructure and process conditions. In complex systems, computational methods such as CALPHAD are employed to model thermodynamic properties for each phase and simulate multicomponent phase behavior. Written by recognized experts in the field, this is an introductory guide to the CALPHAD method, providing a theoretical and practical approach. Building on core thermodynamic principles, this 2007 book applies crystallography, first principles methods and experimental data to computational phase behavior modeling using the CALPHAD method. With a chapter dedicated to creating thermodynamic databases, the reader will be confident in assessing, optimizing and validating complex thermodynamic systems alongside database construction and manipulation. Several case studies put the methods into a practical context, making this suitable for use on advanced materials design and engineering courses and an invaluable reference to those using thermodynamic data in their research or simulations.

"The second volume of the authors’ ‘Computational commutative algebra’...covers on its 586 pages a wealth of interesting material with several unexpected applications. ... an encyclopedia on computational commutative algebra, a source for lectures on the subject as well as an inspiration for seminars. The text is recommended for all those who want to learn and enjoy an algebraic tool that becomes more and more relevant to different fields of applications." --ZENTRALBLATT MATH

Given the explosion of interest in mathematical methods for solving problems in finance and trading, a great deal of research and development is taking place in universities, large brokerage firms, and in the supporting trading software industry. Mathematical advances have been made both analytically and numerically in finding practical solutions. This book provides a comprehensive overview of existing and original material, about what mathematics when allied with Mathematica can do for finance. Sophisticated theories are presented systematically in a user-friendly style, and a powerful combination of mathematical rigor and Mathematica programming. Three kinds of solution methods are emphasized: symbolic, numerical, and Monte-- Carlo. Nowadays, only good personal computers are required to handle the symbolic and numerical methods that are developed in this book. Key features: * No previous knowledge of Mathematica programming is required * The symbolic, numeric, data management and graphic capabilities of Mathematica are fully utilized * Monte--Carlo solutions of scalar and multivariable SDEs are developed and utilized heavily in discussing trading issues such as Black--Scholes hedging * Black--Scholes and Dupire PDEs are solved symbolically and numerically * Fast numerical solutions to free boundary problems with details of their Mathematica realizations are provided * Comprehensive study of optimal portfolio diversification, including an original theory of optimal portfolio hedging under non-Log-Normal asset price dynamics is presented The book is designed for the academic community of instructors and students, and most importantly, will meet the everyday trading needs of quantitatively inclined professional and individual investors.

Life Cycle assessment (LCA) is a tool for environmental decision-support in relation to products from the cradle to the grave. Until now, more emphasis has been put on the inclusion quantitative models and databases and on the design of guidebooks for applying LCA than on the integrative aspect of combining these models and data. This is a remarkable thing, since LCA in practice deals with thousands of quantitative data items that have to be combined in the correct manner. For this, one needs mathematical rules and algorithmic principles for carrying out an LCA. This book presents the first coherent treatment of the mathematical and algorithmic aspects of LCA. These computational aspects are presented in matrix form, so that a concise and elegant formulation is achieved. This form, moreover, provides a platform for further extension of analysis using perturbation theory, structural theory and economic input-output analysis.

Computational Problems, Methods, and Results in Algebraic Number Theory (Lecture Notes in Mathematics) [paperback] Zimmer, H. G. [Jun 20, 1972]

Honorable Mention, 1998, category of Computer Science, Professional/Scholarly Publishing Annual Awards Competition presented by the Association of American Publishers, Inc. "Simulation," writes Gary Flake in his preface, "becomes a form of experimentation in a universe of theories. The primary purpose of this book is to celebrate this fact." In this book, Gary William Flake develops in depth the simple idea that recurrent rules can produce rich and complicated behaviors. Distinguishing "agents" (e.g., molecules, cells, animals, and species) from their interactions (e.g., chemical reactions, immune system responses, sexual reproduction, and evolution), Flake argues that it is the computational properties of interactions that account for much of what we think of as "beautiful" and "interesting." From this basic thesis, Flake explores what he considers to be today's four most interesting computational topics: fractals, chaos, complex systems, and adaptation. Each of the book's parts can be read independently, enabling even the casual reader to understand and work with the basic equations and programs. Yet the parts are bound together by the theme of the computer as a laboratory and a metaphor for understanding the universe. The inspired reader will experiment further with the ideas presented to create fractal landscapes, chaotic systems, artificial life forms, genetic algorithms, and artificial neural networks.

Empower tomorrow’s tech innovators Our students are avid users and consumers of technology. Isn’t it time that they see themselves as the next technological innovators, too?  Computational Thinking and Coding for Every Student is the beginner’s guide for K-12 educators who want to learn to integrate the basics of computer science into their curriculum. Readers will find  Strategies and activities for teaching computational thinking and coding inside and outside of school, at any grade level, across disciplines Instruction-ready lessons for every grade A discussion guide and companion website with videos, activities, and other resources

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Presents some common problems in mathematics and how they can be investigated using the Mathematica computer system. Problems and exercises include the calendar, sequences, the n-Queens problems, digital computing, blackjack and computing pi. This book is for those that would like to see how Mathematica is applied to real-world mathematics.

This extensively revised and expanded third edition of the Artech House bestseller, Computational Electrodynamics: The Finite-Difference Time-Domain Method, offers engineers the most up-to-date and definitive resource on this critical method for solving Maxwell's equations. The method helps practitioners design antennas, wireless communications devices, high-speed digital and microwave circuits, and integrated optical devices with unsurpassed efficiency. There has been considerable advancement in FDTD computational technology over the past few years, and the third edition brings professionals the very latest details with entirely new chapters on important techniques, major updates on key topics, and new discussions on emerging areas such as nanophotonics. What's more, to supplement the third edition, the authors have created a Web site with solutions to problems, downloadable graphics and videos, and updates, making this new edition the ideal textbook on the subject as well.

In spite of the rapid growth of interest in the computer analysis of language, this book provides an integrated introduction to the field. Inevitably, when many different approaches are still being considered, a straightforward work of synthesis would be neither possible nor practicable. Nevertheless, Ralph Grishman provides a valuable survey of various approaches to the problems of syntax analysis, semantic analysis, text analysis and natural language generation, while considering in greater detail those that seem to him most productive. The book is written for readers with some background in computer science and finite mathematics, but advanced knowledge of programming languages or compilers is not necessary and nor is a background in linguistics. The exposition is always clear and students will find the exercises and extensive bibliography supporting the text particularly helpful.

Computational Methods for Electromagnetics is an indispensable resource for making efficient and accurate formulations for electromagnetics applications and their numerical treatment. Employing a unified coherent approach that is unmatched in the field, the authors detail both integral and differential equations using the method of moments and finite-element procedures. In addition, readers will gain a thorough understanding of numerical solution procedures. Topics covered include: Two- and three-dimensional integral equation/method-of-moments formulations Open-region finite-element formulations based on the scalar and vector Helmholtz equations Finite difference time-domain methods Direct and iterative algorithms for the solutions of linear systems Error analysis and the convergence behavior of numerical results Radiation boundary conditions Acceleration methods for periodic Green's functions Vector finite elements Detail is provided to enable the reader to implement concepts in software and, in addition, a collection of related computer programs are available via the Internet. Computational Methods for Electromagnetics is designed for graduate-level classroom use or self-study, and every chapter includes problems. It will also be of particular interest to engineers working in the aerospace, defense, telecommunications, wireless, electromagnetic compatibility, and electronic packaging industries.

Recent advances in computing and algorithms make it easier to do many classical problems in algebra. Suitable for graduate students, this book brings advanced algebra to life with many examples. The first three chapters provide an introduction to commutative algebra and connections to geometry. The remainder of the book focuses on three active areas of contemporary algebra: homological algebra; algebraic combinatorics and algebraic topology; and algebraic geometry.

An excellent introduction to the real world of environmental work, this title helps both college students and working professionals improve their understanding of the data collection process. It covers all phases of data collection planning, field sampling, laboratory analysis, and data quality assessment , and is a single source comprehensive reference for the resolution of the most common problems that environmental professionals face daily in their work. Why This TitleThis title is written in a clear and logical manner that is accessible to environmental professionals of all disciplines. It contains hundreds of practical tips on planning, sampling, and interactions with analytical laboratories. Having this text as a desk reference will greatly improve skills in planning and sampling, and elevate understanding of chemical data to a new level. This topic is of importance to a wide range of environmental professionals from a variety of disciplines see audience . Written by a practicing professional for practicing professionals, this handbook provides everything an environmental professional needs to know to competently collect environmental chemical data.