Comprehensive Mathematics for Computer Scientists, 2 Ed (2 Volumes)

Guerino Mazzola, Gerard Milmeister, Jody Weissmann, "Comprehensive Mathematics for Computer Scientists (2 Volumes)"
Springer | 2006 | ISBN: 3540368736, 3540208615 | 388, 355 pages | PDF | 3,7+3,5 MB

Vol. 1: Sets and Numbers, Graphs and Algebra, Logic and Machines, Linear Geometry
Vol. 2: Calculus and ODEs, Splines, Probability, Fourier and Wavelet Theory, Fractals and Neural Networks, Categories and Lambda Calculus

The two-volume textbook Comprehensive Mathematics for Computer Scientists, of which this is the first volume, is a self-contained comprehensive presentation of mathematics including sets, numbers, graphs, algebra, logic, grammars, machines, linear geometry, calculus, ODEs, and special themes such as neural networks, Fourier theory, wavelets, numerical issues, statistics, categories, and manifolds. The concept framework is streamlined but defining and proving virtually everything. The style implicitly follows the spirit of recent topos-oriented theoretical computer science. Despite the theoretical soundness, the material stresses a large number of core computer science subjects, such as, for example, a discussion of floating point arithmetic, Backus-Naur normal forms, L-systems, Chomsky hierarchies, algorithms for data encoding, e.g., the Reed-Solomon code. The numerous course examples are motivated by computer science and bear a generic scientific meaning. For the second edition the entire text has been carefully reread, and many examples have been added, as well as illustrations and explications to statements and proofs which were exposed in a too shorthand style. This makes the book more comfortable to handle for instructors as well as for students.

Review
From the reviews: "The solution proposed by the authors of this book consists essentially of a course on the foundations of mathematics and computer science. … As one can see … the book covers a lot of material. … One of the good things about the book is that it covers a lot of ground in an extremely systematic way. … the book is written with conviction, and one can see that the authors made a great effort to make it interesting to their readers." (S. C. Coutinho, The Mathematical Gazette, Vol. 90 (517), 2006) "This book meets the needs of a sound mathematical education of computer scientists improving formal competence and flexibility. It very well sets forth (and proves) the essential core theory and theorist or executive on all levels of Computer Science and IT industry will appreciate. … Having passed through all … the student will have a broad and sufficiently deep mathematical knowledge." (H. Mitsch, Monatshefte für Mathematik, Vol. 145 (2), 2005) From the reviews of the second edition: "As the title of this book suggests, it covers a broad range of topics in mathematics; it is intended for use as an introductory textbook for computer science undergraduates. … It may be suitable for people who are already familiar with the subject and need a reference to quickly check definitions and theorems." (I-Lun Tseng, ACM Computing Reviews, Vol. 49 (4), April, 2008)

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Applied Probability+Handbook of Multivalued Analysis

Applied Probability ISBN: 0387004254 + Handbook of Multivalued Analysis ISBN: 0792361644
PDF and DJVU | 10,8 mb

Applied Probability
This textbook on applied probability is intended for graduate students in applied mathematics, biostatistics, computational biology, computer science, physics, and statistics. It presupposes knowledge of multivariate calculus, linear algebra, ordinary differential equations, and elementary probability theory. Given these prerequisites, Applied Probability presents a unique blend of theory and applications, with special emphasis on mathematical modeling, computational techniques, and examples from the biological sciences.
Handbook of Multivalued Analysis
This is the second of a two-volume exposition on the theory and applications of set-valued maps. Multivalued analysis is a remarkable mixture of many different fields of mathematics, such as topology, measure theory, nonlinear functional analysis and applied mathematics. This two-volume work provides a comprehensive survey of the general theory and applications of set-valued analysis.

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Mechanics: Complete Advanced Level Mathematics

Mechanics: Complete Advanced Level Mathematics

Martin Adams, "Mechanics: Complete Advanced Level Mathematics"
Trans-Atlantic Publications | 1999 | ISBN: 0748735593 | 616 pages | PDF | 35,1 MB

In text, 'hints' support key areas, for example, specific calculations in worked examples. Clear, two-colour, labelled illustrations provide extra clarity and a visual aid to understanding. Numerous exercises, worked examples and clear explanations with questions and diagrams provide exceptional learning support. Applications and Activities provide extension material and further opportunities for coursework. Review and Technique exercises and Consolidation 'A' and 'B' exercises provide complete exam practice and course support.

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Elements of Modern Algebra

Elements of Modern Algebra

Elements of Modern Algebra
Publisher: Brooks Cole | ISBN: 0534373518 | edition 1999 | PDF | 416 pages | 14,6 mb

The authors gradually introduce and develop concepts to help make the material more accessible. This text is intended for the introductory course in algebraic structures and covers groups before rings. This course often is used to bridge the gap from manipulative to theoretical mathematics and to help prepare secondary mathematics teachers for their careers. This text includes some optional sections to give instructors flexibility.

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Error Calculus for Finance and Physics: The Language of Dirichlet Forms

Error Calculus for Finance and Physics: The Language of Dirichlet Forms

Nicolas Bouleau, "Error Calculus for Finance and Physics: The Language of Dirichlet Forms"
Walter de Gruyter | 2003 | ISBN: 3110180367 | 234 pages | PDF | 1,1 MB

Many recent advances in modelling within the applied sciences and engineering have focused on the increasing importance of sensitivity analyses. For a given physical, financial or environmental model, increased emphasis is now placed on assessing the consequences of changes in model outputs that result from small changes or errors in both the hypotheses and parameters. The approach proposed in this book is entirely new and features two main characteristics. Even when extremely small, errors possess biases and variances. The methods presented here are able, thanks to a specific differential calculus, to provide information about the correlation between errors in different parameters of the model, as well as information about the biases introduced by non-linearity. The approach makes use of very powerful mathematical tools (Dirichlet forms), which allow one to deal with errors in infinite dimensional spaces, such as spaces of functions or stochastic processes. The method is therefore applicable to non-elementary models along the lines of those encountered in modern physics and finance. This text has been drawn from presentations of research done over the past ten years and that is still ongoing. The work was presented in conjunction with a course taught jointly at the Universities of Paris 1 and Paris 6. The book is intended for students, researchers and engineers with good knowledge in probability theory.

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First Order Mathematical Logic

First Order Mathematical Logic

Angelo Margaris "First Order Mathematical Logic"
Dover Publications | English | 1990-03-01 | ISBN: 0486662691 | 212 pages | DJVU | 1,6 MB

Well-written undergraduate-level introduction begins with symbolic logic and set theory, followed by presentation of statement calculus and predicate calculus. First-order theories are discussed in some detail, with special emphasis on number theory. After a discussion of truth and models, the completeness theorem is proved. "...an excellent text."—Mathematical Reviews. Exercises. Bibliography.

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Pre-Calculus Know-It-ALL

Pre-Calculus Know-It-ALL

Stan Gibilisco "Pre-Calculus Know-It-ALL"
McGraw-Hill/TAB Electronics | English | 2009-10-23 | ISBN: 0071627022 | 608 pages | PDF | 2 MB

Master pre-calculus from the comfort of home!

Want to "know it ALL" when it comes to pre-calculus? This book gives you the expert, one-on-one instruction you need, whether you're new to pre-calculus or you're looking to ramp up your skills. Providing easy-to-understand concepts and thoroughly explained exercises, math whiz Stan Gibilisco serves as your own private tutor--without the expense! His clear, friendly guidance helps you tackle the concepts and problems that confuse you the most and work through them at your own pace.

Train your brain with ease!

Pre-Calculus Know-It-ALL features:
• Checkpoints to help you track your knowledge and skill level
• Problem/solution pairs and chapter-ending quizzes to reinforce learning
• Fully explained answers to all practice exercises
• A multiple-choice exam to prepare you for standardized tests
• "Extra Credit" and "Challenge" problems to stretch your mind
Stan's expert guidance gives you the know-how to:
• Calculate distance in Cartesian two-and three-space
• Perform vector multiplication
• Work with cylindrical and spherical coordinates
• Understand relations and functions
• Learn the properties of conic sections
• Graph exponential, logarithmic, and trigonometric curves
• Define curves with parametric equations
• Work with sequences, series, and limits
• Take college entrance examinations with confidence
• And much more!

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Dennis G. Zill, Michael R. Cullen "Differential Equations With Boundary-Value Problems"

Differential Equations With Boundary-Value Problems

Dennis G. Zill, Michael R. Cullen "Differential Equations With Boundary-Value Problems"
Thomson Brooks/Cole | English | 1996-06-30 | ISBN: 0534955800 | 768 pages | DJVU | 18,7 MB

This Fourth Edition of the expanded version of Zill's best-selling A FIRST COURSE IN DIFFERENTIAL EQUATIONS WITH MODELING APPLICATIONS places an even greater emphasis on modeling and the use of technology in problem solving and now features more everyday applications. Both Zill texts are identical through the first nine chapters, but this version includes six additional chapters that provide in-depth coverage of boundary-value problem-solving and partial differential equations, subjects just introduced in the shorter text. Previous editions of these two texts have enjoyed such great success in part because the authors pique students' interest with special features and in-text aids. Pre-publication reviewers also praise the authors' accessible writing style and the text's organization, which makes it easy to teach from and easy for students to understand and use. Understandable, step-by-step solutions are provided for every example. And this edition makes an even greater effort to show students how the mathematical concepts have relevant, everyday applications.

Among the boundary-value related topics covered in this expanded text are: plane autonomous systems and stability; orthogonal functions; Fourier series; the Laplace transform; and elliptic, parabolic, and hyperparabolic partial differential equations, and their applications.

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Reconceiving Mathematics Instruction: A Focus on Errors

Reconceiving Mathematics Instruction: A Focus on Errors

Raffaella Borasi, "Reconceiving Mathematics Instruction: A Focus on Errors"
Praeger | 1996 | ISBN: 1567501672, 1567501680 | 321 pages | PDF | 36,2 MB

As dissatisfaction with the current status of school mathematics grows worldwide, educators and professionals alike are calling for reforms and instructional changes. Yet, significant changes can only be achieved if each educator of school mathematics personally rethinks various aspects of mathematics instruction, and identifies concrete ways in which their current practice could be modified. Before such visions can be meaningfully implemented in classrooms, it is important that mathematics teachers and educators examine critically both the assumptions and implications of the vision for school mathematics that the reports propose. This book is intended to support educators in such a challenging enterprise by focusing attention on "errors" and their use in mathematics instruction. Throughout the book, an approach to errors as opportunities for learning and inquiry will be developed and employed both as a means to create the kinds of instructional experiences advocated for school mathematics reform, and as a heuristic to invite reflections about school mathematics as well as mathematics as a discipline. REVIEWS: "...Raffaella Borasi's newest book offers important contributions to the current debate on school mathematics reform." - Journal for Research in Mathematics Education "There are some great bits of philosophy in this book..." - Mathematics Teaching

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Lectures in Functional Analysis and Operator Theory

Lectures in Functional Analysis and Operator Theory

S.K. Berberian, "Lectures in Functional Analysis and Operator Theory"
Springer | 1974 | ISBN: 0387900802 | 345 pages | Djvu | 4,1 MB

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John Polking - Ordinary Differential Equations Using MATLAB (3rd Edition)

John Polking - Ordinary Differential Equations Using MATLAB (3rd Edition)

John Polking - Ordinary Differential Equations Using MATLAB (3rd Edition)
Publisher: Prentice Hall | 2003-10-26 | ISBN: 0131456792 | PDF | 264 pages | 1.53 MB

This is a superb supplement, written by one of the leaders of using technology in the ODE course, that can be wrapped with any Prentice Hall Differential Equations text at a reduced price.

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A Matlab Companion for Multivariable Calculus

A Matlab Companion for Multivariable Calculus

A Matlab Companion for Multivariable Calculus By Jeffery Cooper
Publisher: Academic Press 2001 | 294 Pages | ISBN: 012187625X | PDF | 6 MB

"This text does a good job of explaining how MATLAB works at exactly the appropriate level. The use of MATLAB also encourages students toward more numerical thinking than do the packages that are primarily symbolic manipulations."
"The author's writing is very clear. Students should find it pleasant reading, as I did."
"I liked the problems. They presented the main issues and calculations from a variety of angles, so that students have to think and learn on almost all of them."
"I like the serious applications at the end-to fluids, for example: this would also be helpful for nice demonstrations which the instructor could do in class."
"My favorite aspect of this text is that by using MATLAB it naturally incorporates more numerical thinking into Multivariable Calculus. This builds on recent trends in Single-Variable Calculus 'reform'."

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Geometric Description of Images as Topographic Maps

Geometric Description of Images as Topographic Maps

Geometric Description of Images as Topographic Maps (Lecture Notes in Mathematics) By Vicent Caselles, Pascal Monasse
Publisher: Springer 2009-12-10 | 192 Pages | ISBN: 364204610X | PDF | 5 MB

This volume discusses the basic geometric contents of an image and presents a tree data structure to handle those contents efficiently. The nodes of the tree are derived from connected components of level sets of the intensity, while the edges represent inclusion information. Grain filters, morphological operators simplifying these geometric contents, are analyzed and several applications to image comparison and registration, and to edge and corner detection, are presented.
The mathematically inclined reader may be most interested in Chapters 2 to 6, which generalize the topological Morse description to continuous or semicontinuous functions, while mathematical morphologists may more closely consider grain filters in Chapter 3. Computer scientists will find algorithmic considerations in Chapters 6 and 7, the full justification of which may be found in Chapters 2 and 4 respectively. Lastly, all readers can learn more about the motivation for this work in the image processing applications presented in Chapter 8.

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Metric Driven Design Verification: An Engineer's and Executive's Guide to First Pass Success

Metric Driven Design Verification: An Engineer's and Executive's Guide to First Pass Success

Hamilton B. Carter; Shankar G. Hemmady "Metric Driven Design Verification: An Engineer's and Executive's Guide to First Pass Success"
Springer | English | 2007-05-25 | ISBN: 0387381511 | 350 pages | PDF | 3,3 MB

Exponentially increasing design complexity has necessitated the adoption of metric driven planning and project management. Metric Driven Design Verification provides the semiconductor industry s first metric driven based approach to functional verification. A metric based flow is described that focuses on the four steps of:

1. Planning: Defining what needs to be done and the automatically trackable metrics that will be used to measure progress.
2. Execution: Implementing verification environments and then extensively exercising the device under verification utilizing comprehensive, massively parallel regression strategies.
3. Measurement: Automatically capturing the metrics defined in planning to provide objective data with which to manage the verification project. Custom tailoring those metrics through an automated reporting framework to provide all stakeholders a real-time meaningful view of project status.
4. Response: Utilizing the returned metrics to effectively adapt to changing project conditions. Making use of automated response mechanisms to automate engineering processed and management response to streamline project management processes.

The primary audience for this book is professional engineers, managers, and executives. It is written in an easily understandable style and consists of four parts. The first three parts are tailored for executives, engineering managers, and engineers respectively. The fourth part presents case studies and commentaries from industry luminaries and experts on metric driven verification.

Metric Driven Design Verification brings together the best practices and real-life experiences of several leading electronic companies worldwide in planning and managing verification projects, while automating critical processes. It addresses all aspects of verification and summarizes the different options available to engineers, managers and executives.

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Economists' Mathematical Manual, 4th Edition

Economists' Mathematical Manual, 4th Edition

Economists' Mathematical Manual, 4th Edition
Springer | 2005-09-13 | ISBN: 3540260889 | 225 pages | PDF | 1,6 MB

This volume presents mathematical formulas and theorems commonly used in economics. It includes both formulas like Roy`s identity that are peculiar to economics and formulas like Leibniz's rule that are common to many areas of applied mathematics. The volume is meant to be a reference work, to be used by students in conjunction with a textbook and by researchers in need of exact statements of mathematical results. The volume is the first grouping of this material for a specifically economist audience.

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Complex Variables and Applications 7th Edition (Solution Manual)

Complex Variables and Applications 7th Edition (Solution Manual)

Complex Variables and Applications 7th Edition (Solution Manual)
Publisher: McGraw Hill Higher Education | ISBN: 0071233652 | edition 2003 | PDF | 480 pages | 10 mb

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Advanced Engineering Mathematics

Advanced Engineering Mathematics

Advanced Engineering Mathematics
By Erwin Kreyszig
Publisher: John Wiley & Sons; 9th Edition, International Edition edition | 2005 | 1248 Pages | ISBN: 0471728977 | PDF | 74.77 MB

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Mathematics of Classical and Quantum Physics

Mathematics of Classical and Quantum Physics

Mathematics of Classical and Quantum Physics
By Frederick W. Byron, Robert W. Fuller
Publisher: Dover Publications | 1992 | 661 Pages | ISBN: 048667164X | PDF | 13.86 MB

Well-organized text designed to complement graduate-level physics texts in classical mechanics, electricity, magnetism and quantum mechanics. Topics include theory of vector spaces, analytic function theory, Green’s function method of solving differential and partial differential equations, theory of groups, more. Many problems, suggestions for further reading.

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Schaum's Outline of Basic Mathematics with Applications to Science and Technology

Schaum's Outline of Basic Mathematics with Applications to Science and Technology

Schaum's Outline of Basic Mathematics with Applications to Science and Technology
By Haym Kruglak, John Moore, Ramon Mata-Toledo
Publisher:McGraw-Hill; 2 edition | 1998 | 341 Pages | ISBN: 0070371326 | PDF | 15.96 MB

Master basic mathematics with applications to science and technology with this simple-to-use guide. It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams! Students love Schaum's Outlines because they produce results. Each year, hundreds of thousands of students improve their test scores and final grades with these indispensable study guides. Get the edge over your classmates. Use Schaum's! If you don't have a lot of time but want to excel in class, this book helps you: Brush up before tests; Find answers fast; Study quickly and more effectively; Get the big picture without spending hours poring over lengthy texts. Schaum's Outlines give you the information your teachers expect you to know in handy and succinct format, without overwhelming you with unnecessary details. You get a complete overview of the subject. Plus, you get plenty of practice exercises to test your skill. Compatible with any classroom text, Schaum's lets you study at your own pace and reminds you of all the important facts you need to remember, fast! And Schaum's are so complete they're perfect for preparing for graduate or professional exams. Inside, you will find: * Coverage of all course fundamentals, supplementing any class text * 627 fully worked problems, including step-by-step solutions * Ideal format for independent study * New chapter on descriptive statistics * New sections on binary representation of integers * Boolean operations, floating-point representation, and how to read ASCII * An introduction to graphing calculators If you want top grades and a thorough understanding of basic mathematics with applications to science and technology, this powerful study tool is the best tutor you can have! * Chapters include: * Decimal Fractions * Measurement and Scientific Notation * Common Fractions * Percentage; Essentials of Algebra * Ratio and Proportion * Linear Equations * Exponents and Radicals * Logarithms * Quadratic Equations and Square Roots * Essentials of Plane Geometry; Solid Figures * Trigonometric Functions * Solution of Triangles * Vectors * Radian Measure * Conic Sections * The Binary, Octal, and Hexadecimal Numbering Systems

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Music and Mathematics: From Pythagoras to Fractals

Music and Mathematics: From Pythagoras to Fractals

Music and Mathematics: From Pythagoras to Fractals
By John Fauvel, Raymond Flood, Robin Wilson
Publisher: Oxford University Press, USA | 2006 | 200 Pages | ISBN: 0199298939 | PDF | 21.50 MB

From Ancient Greek times, music has been seen as a mathematical art, and the relationship between mathematics and music has fascinated generations. This collection of wide ranging, comprehensive and fully-illustrated papers, authorized by leading scholars, presents the link between these two subjects in a lucid manner that is suitable for students of both subjects, as well as the general reader with an interest in music. Physical, theoretical, physiological, acoustic, compositional and analytical relationships between mathematics and music are unfolded and explored with focus on tuning and temperament, the mathematics of sound, bell-ringing and modern compositional techniques.

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