Visualization in Mathematics Reading and Science Education by Linda M. Phillips (2010)

Linda M. Phillips, Stephen P. Norris, John S. Macnab - Visualization in Mathematics, Reading and Science Education
Published: 2010-09-17 | ISBN: 9048188156 | PDF | 120 pages | 3 MB

Book Description :

Visualizations—either self-created or external visual stimuli used as an aid to learning—are probably as old as learning itself. Yet surprisingly little research has been done either into how precisely they help us learn, or how to produce ones that are effective pedagogical tools. This volume, a comprehensive review of theory and research on the use of visualization in mathematics, science and reading, contrasts the two dominant theoretical paradigms of how people construct and interpret visualizations. However, the authors never lose sight of practical applications, providing frequent, accessible synopses of research findings in addition to succinct summaries of how the research affects practice. Written by a team with decades of experience in research and practice in the three subjects, the chapters show how cognitive psychology can enhance practical pedagogy, place visualizations in their proper historical context, and analyze in detail the effectiveness of paper-, computer- and video-based visualizations, with some surprising results. The book is published at a time when, it seems, there is no limit to the art of creating visualizations, as powerful computers make graphics ever more colorful and realistic and ‘interactivity’ is firmly established as a buzzword in the educational lexicon. The aim of the volume is to explore some central questions in the field, including how to evaluate visualizations and whether or not they can act as an aid to reading development, and to mathematics and science learning.

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Handbook of Nonlinear Partial Differential Equations (Second Edition) by Andrei D. Polyanin - Valentin F. Zaitsev (2012)

Andrei D. Polyanin, Valentin F. Zaitsev, "Handbook of Nonlinear Partial Differential Equations, Second Edition"
2012 | ISBN: 1420087231 | PDF | 1912 pages | 34,5 MB

Book Description :

More than 1,000 pages with over 1,500 new first-, second-, third-, fourth-, and higher-order nonlinear equations with solutions
Parabolic, hyperbolic, elliptic, and other systems of equations with solutions
Some exact methods and transformations
Symbolic and numerical methods for solving nonlinear PDEs with Maple™, Mathematica®, and MATLAB®
Many new illustrative examples and tables
A large list of references consisting of over 1,300 sources

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European Women in Mathematics by Catherine Hobbs- Sylvie Paycha (2010)

Catherine Hobbs, Sylvie Paycha - European Women in Mathematics
Published: 2010-03-31 | ISBN: 9814277673 | PDF | 199 pages | 5 MB

Book Description :

This volume offers a unique collection of outstanding contributions from renowned women mathematicians who met in Cambridge for a conference under the auspices of European Women in Mathematics (EWM). These contributions serve as excellent surveys of their subject areas, including symplectic topology, combinatorics and number theory. The volume moreover sheds light on prominent women mathematicians who worked in Cambridge in the late 19th and early 20th centuries by providing an insightful historical introduction at the beginning of the volume. The volume concludes with short contributions from women mathematicians from across Europe working in various areas of mathematics ranging from group theory to magnetic fields.

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Decision-Making in Committees: Game-Theoretic Analysis by Nicola Friederike Maaser (2010)

Nicola Friederike Maaser - Decision-Making in Committees: Game-Theoretic Analysis
Published: 2010-02-01 | ISBN: 3642041523 | PDF | 148 pages | 3 MB

Book Description :
Political and economic institutions are typically governed by committees that face the challenge to reconcile the preferences of their members. How should decision rules be designed to generate fair and sustainable agreements, for example if committee members represent groups of different sizes? This book uses game-theoretic concepts and models to address the issue of political decision-making processes. In addition to providing a survey on basic game-theoretic tools in the analysis of political decisions, the author looks at specific issues such as two-tiered voting systems or the influence of lobbyists on legislative committees, and shows how the models can be applied to real-world contexts such as the EU decision-making institutions.

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Learning Mathematics for Life: A Perspective from PISA

Learning Mathematics for Life: A Perspective from PISA
Published: 2010-04-01 | ISBN: 9264074996 | PDF | 248 pages | 5 MB

Book Description :

People from many countries have expressed interest in the tests students take for the Programme for International Student Assessment (PISA). Learning Mathematics for Life examines the link between the PISA test requirements and student performance. It focuses specifically on the proportions of students who answer questions correctly across a range of difficulty. The questions are classified by content, competencies, context and format, and the connections between these and student performance are then analysed.

This analysis has been carried out in an effort to link PISA results to curricular programmes and structures in participating countries and economies. Results from the student assessment reflect differences in country performance in terms of the test questions. These findings are important for curriculum planners, policy makers and in particular teachers - especially mathematics teachers of intermediate and lower secondary school classes.

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Arithmetic Optimization Techniques for Hardware and Software Design by Ryan Kastner - Anup Hosangadi (2010)

Ryan Kastner, Anup Hosangadi, Farzan Fallah, "Arithmetic Optimization Techniques for Hardware and Software Design"
Cambridge University Press | 2010 | ISBN: 0521880998 | 200 pages | PDF | 3 MB  

Book Description :

Obtain better system performance, lower energy consumption, and avoid hand-coding arithmetic functions with this concise guide to automated optimization techniques for hardware and software design. High-level compiler optimizations and high-speed architectures for implementing FIR filters are covered, which can improve performance in communications, signal processing, computer graphics, and cryptography. Clearly explained algorithms and illustrative examples throughout make it easy to understand the techniques and write software for their implementation. Background information on the synthesis of arithmetic expressions and computer arithmetic is also included, making the book ideal for newcomers to the subject. This is an invaluable resource for researchers, professionals, and graduate students working in system level design and automation, compilers, and VLSI CAD.

 

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Nonlinear Dynamics in Complex Systems: Theory and Applications for the Life-, Neuro- and Natural Sciences by Armin Fuchs (2013)

Armin Fuchs, "Nonlinear Dynamics in Complex Systems: Theory and Applications for the Life-, Neuro- and Natural Sciences"
English | ISBN: 3642335519 | 2013 | 250 pages | PDF | 10 MB

Book Description :

With many areas of science reaching across their boundaries and becoming more and more interdisciplinary, students and researchers in these fields are confronted with techniques and tools not covered by their particular education. Especially in the life- and neurosciences quantitative models based on nonlinear dynamics and complex systems are becoming as frequently implemented as traditional statistical analysis. Unfamiliarity with the terminology and rigorous mathematics may discourage many scientists to adopt these methods for their own work, even though such reluctance in most cases is not justified. This book bridges this gap by introducing the procedures and methods used for analyzing nonlinear dynamical systems. In Part I, the concepts of fixed points, phase space, stability and transitions, among others, are discussed in great detail and implemented on the basis of example elementary systems. Part II is devoted to specific, non-trivial applications: coordination of human limb movement (Haken-Kelso-Bunz model), self-organization and pattern formation in complex systems (Synergetics), and models of dynamical properties of neurons (Hodgkin-Huxley, Fitzhugh-Nagumo and Hindmarsh-Rose). Part III may serve as a refresher and companion of some mathematical basics that have been forgotten or were not covered in basic math courses. Finally, the appendix contains an explicit derivation and basic numerical methods together with some programming examples as well as solutions to the exercises provided at the end of certain chapters. Throughout this book all derivations are as detailed and explicit as possible, and everybody with some knowledge of calculus should be able to extract meaningful guidance follow and apply the methods of nonlinear dynamics to their own work. “This book is a masterful treatment, one might even say a gift, to the interdisciplinary scientist of the future.” “With the authoritative voice of a genuine practitioner, Fuchs is a master teacher of how to handle complex dynamical systems.” “What I find beautiful in this book is its clarity, the clear definition of terms, every step explained simply and systematically.” (J.A.Scott Kelso, excerpts from the foreword).

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Mathematics of Discrete Structures for Computer Science by Gordon J. Pace (2012)

Gordon J. Pace, "Mathematics of Discrete Structures for Computer Science"
English | ISBN: 3642298397 | 2012 | 309 pages | PDF | 3 MB

Book Description :

Mathematics plays a key role in computer science, some researchers would consider computers as nothing but the physical embodiment of mathematical systems. And whether you are designing a digital circuit, a computer program or a new programming language, you need mathematics to be able to reason about the design -- its correctness, robustness and dependability. This book covers the foundational mathematics necessary for courses in computer science. The common approach to presenting mathematical concepts and operators is to define them in terms of properties they satisfy, and then based on these definitions develop ways of computing the result of applying the operators and prove them correct. This book is mainly written for computer science students, so here the author takes a different approach: he starts by defining ways of calculating the results of applying the operators and then proves that they satisfy various properties. After justifying his underlying approach the author offers detailed chapters covering propositional logic, predicate calculus, sets, relations, discrete structures, structured types, numbers, and reasoning about programs. The book contains chapter and section summaries, detailed proofs and many end-of-section exercises -- key to the learning process. The book is suitable for undergraduate and graduate students, and although the treatment focuses on areas with frequent applications in computer science, the book is also suitable for students of mathematics and engineering.

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Algebra (2nd Edition) by Michael Artin (2010)

Michael Artin, "Algebra, 2nd Edition"
2010 | ISBN-10: 0132413779, 8120343298 | Djvu | 560 pages | 12 MB

Book Description :

Algebra, Second Edition, by Michael Artin, provides comprehensive coverage at the level of an honors-undergraduate or introductory-graduate course. The second edition of this classic text incorporates twenty years of feedback plus the author’s own teaching experience. This book discusses concrete topics of algebra in greater detail than others, preparing readers for the more abstract concepts; linear algebra is tightly integrated throughout.

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Mathematical Analysis: An Introduction to Functions of Several Variables by Mariano Giaquinta - Giuseppe Modica

Mariano Giaquinta, Giuseppe Modica - Mathematical Analysis: An Introduction to Functions of Several Variables
Published: 2009-04-14 | ISBN: 0817645071, 0817645098 | PDF | 348 pages | 3 MB

Book Description :

This self-contained work is an introductory presentation of basic ideas, structures, and results of differential and integral calculus for functions of several variables.
The wide range of topics covered include: differential calculus of several variables, including differential calculus of Banach spaces, the relevant results of Lebesgue integration theory, differential forms on curves, a general introduction to holomorphic functions, including singularities and residues, surfaces and level sets, and systems and stability of ordinary differential equations. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis.
Mathematical Analysis: An Introduction to Functions of Several Variables motivates the study of the analysis of several variables with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering.
Other books recently published by the authors include: Mathematical Analysis: Functions of One Variable, Mathematical Analysis: Approximation and Discrete Processes, and Mathematical Analysis: Linear and Metric Structures and Continuity, all of which provide the reader with a strong foundation in modern-day analysis.

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Leonhard Euler and the Bernoullis: Mathematicians from Basel by Margaret B. W. Tent (2009)

Margaret B. W. Tent - Leonhard Euler and the Bernoullis: Mathematicians from Basel
Published: 2009-10-05 | ISBN: 156881464X | PDF | 200 pages | 3 MB

Book Description :

In the 17th century, the small but culturally and intellectually eminent city of Basel was the home of one of the most prominent mathematical families of all time, the Bernoullis, and their friend, protege, and master Leonhard Euler. The author chronicles their lives and achievements at a time when modern analysis and its applications to physics burst on the scene and created a methodological framework for modern science. Written for young adults, this book conveys the excitement of a scientific culture that impacts our life to this day and will serve as an inspiration to gifted young people to devote their lives to scientific pursuits.

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Measure and Integration: Publications 1997-2011 by Heinz König (2012)

Heinz König - Measure and Integration: Publications 1997-2011
Published: 2012-06-07 | ISBN: 3034803818 | DJVU | 519 pages | 4 MB

Book Description :

This volume presents a collection of twenty-five of Heinz König’s recent and most influential works. Connecting to his book of 1997 “Measure and Integration”, the author has developed a consistent new version of measure theory over the past years. For the first time, his publications are collected here in one single volume. Key features include: - A first-time, original and entirely uniform treatment of abstract and topological measure theory - The introduction of the inner • and outer • premeasures and their extension to unique maximal measures - A simplification of the procedure formerly described in Chapter II of the author’s previous book - The creation of new “envelopes” for the initial set function (to replace the traditional Carathéodory outer measures), which lead to much simpler and more explicit treatment - The formation of products, a unified Daniell-Stone-Riesz representation theorem, and projective limits, which allows to obtain the Kolmogorov type projective limit theorem for even huge domains far beyond the countably determined ones - The incorporation of non-sequential and of inner regular versions, which leads to much more comprehensive results - Significant applications to stochastic processes. “Measure and Integration: Publications 1997–2011” will appeal to both researchers and advanced graduate students in the fields of measure and integration and probabilistic measure theory.

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The Beltrami Equation: A Geometric Approach by Vladimir Gutlyanskii - Vladimir Ryazanov (2012)

Vladimir Gutlyanskii, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov - The Beltrami Equation: A Geometric Approach
Published: 2012-04-20 | ISBN: 1461431905 | PDF | 314 pages | 3 MB

Book Description : 

This book is devoted to the Beltrami equations that play a significant role in Geometry, Analysis and Physics and, in particular, in the study of quasiconformal mappings and their generalizations, Riemann surfaces, Kleinian groups, Teichmuller spaces, Clifford analysis, meromorphic functions, low dimensional topology, holomorphic motions, complex dynamics, potential theory, electrostatics, magnetostatics, hydrodynamics and magneto-hydrodynamics. The purpose of this book is to present the recent developments in the theory of Beltrami equations; especially those concerning degenerate and alternating Beltrami equations. The authors study a wide circle of problems like convergence, existence, uniqueness, representation, removal of singularities, local distortion estimates and boundary behavior of solutions to the Beltrami equations. The monograph contains a number of new types of criteria in the given problems, particularly new integral conditions for the existence of regular solutions to the Beltrami equations that turned out to be not only sufficient but also necessary. The most important feature of this book concerns the unified geometric approach based on the modulus method that is effectively applied to solving the mentioned problems. Moreover, it is characteristic for the book application of many new concepts as strong ring solutions, tangent dilatations, weakly flat and strongly accessible boundaries, functions of finite mean oscillations and new integral conditions that make possible to realize a more deep and refined analysis of problems related to the Beltrami equations. Mastering and using these new tools also gives essential advantages for the reader in the research of modern problems in many other domains. Every mathematics graduate library should have a copy of this book.

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Homogeneous Finsler Spaces by Shaoqiang Deng (2012)

Shaoqiang Deng - Homogeneous Finsler Spaces
Published: 2012-08-01 | ISBN: 1461442435 | PDF | 254 pages | 3 MB

Book Description :

Homogeneous Finsler Spaces is the first book to emphasize the relationship between Lie groups and Finsler geometry, and the first to show the validity in using Lie theory for the study of Finsler geometry problems. This book contains a series of new results obtained by the author and collaborators during the last decade. The topic of Finsler geometry has developed rapidly in recent years. One of the main reasons for its surge in development is its use in many scientific fields, such as general relativity, mathematical biology, and phycology (study of algae). This monograph introduces the most recent developments in the study of Lie groups and homogeneous Finsler spaces, leading the reader to directions for further development. The book contains many interesting results such as a Finslerian version of the Myers-Steenrod Theorem, the existence theorem for invariant non-Riemannian Finsler metrics on coset spaces, the Berwaldian characterization of globally symmetric Finsler spaces, the construction of examples of reversible non-Berwaldian Finsler spaces with vanishing S-curvature, and a classification of homogeneous Randers spaces with isotropic S-curvature and positive flag curvature. Readers with some background in Lie theory or differential geometry can quickly begin studying problems concerning Lie groups and Finsler geometry.

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Applied Complex Variables for Scientists and Engineers by Yue Kuen Kwok

Yue Kuen Kwok, "Applied Complex Variables for Scientists and Engineers"
Cambridge University Press | 0511775008 / 0521701384 | ISBN: 3527314059 | 456 pages | PDF | 4 MB  

Book Description :

This introduction to complex variable methods begins by carefully defining complex numbers and analytic functions, and proceeds to give accounts of complex integration, Taylor series, singularities, residues and mappings. Both algebraic and geometric tools are employed to provide the greatest understanding, with many diagrams illustrating the concepts introduced. The emphasis is laid on understanding the use of methods, rather than on rigorous proofs. Throughout the text, many of the important theoretical results in complex function theory are followed by relevant and vivid examples in physical sciences. This second edition now contains 350 stimulating exercises of high quality, with solutions given to many of them. Material has been updated and additional proofs on some of the important theorems in complex function theory are now included, e.g. the Weierstrass-Casorati theorem. The book is highly suitable for students wishing to learn the elements of complex analysis in an applied context. 

 

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The Local Structure of Algebraic K-Theory by Bjørn Ian Dundas - Thomas G. Goodwillie - Randy McCarthy

Bjørn Ian Dundas, Thomas G. Goodwillie and Randy McCarthy, "The Local Structure of Algebraic K-Theory"
English | ISBN: 1447143922 | 2012 | 450 pages | PDF | 4 MB

 

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Deskripsi Buku :

Algebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic geometry. As is commonly encountered, this powerful mathematical object is very hard to calculate. Apart from Quillen's calculations of finite fields and Suslin's calculation of algebraically closed fields, few complete calculations were available before the discovery of homological invariants offered by motivic cohomology and topological cyclic homology. This book covers the connection between algebraic K-theory and Bökstedt, Hsiang and Madsen's topological cyclic homology and proves that the difference between the theories are ‘locally constant’. The usefulness of this theorem stems from being more accessible for calculations than K-theory, and hence a single calculation of K-theory can be used with homological calculations to obtain a host of ‘nearby’ calculations in K-theory. For instance, Quillen's calculation of the K-theory of finite fields gives rise to Hesselholt and Madsen's calculations for local fields, and Voevodsky's calculations for the integers give insight into the diffeomorphisms of manifolds. In addition to the proof of the full integral version of the local correspondence between K-theory and topological cyclic homology, the book provides an introduction to the necessary background in algebraic K-theory and highly structured homotopy theory; collecting all necessary tools into one common framework. It relies on simplicial techniques, and contains an appendix summarizing the methods widely used in the field. The book is intended for graduate students and scientists interested in algebraic K-theory, and presupposes a basic knowledge of algebraic topology.

 

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Classical Mechanics - Dynamics by J Awrejcewicz

J. Awrejcewicz, "Classical Mechanics: Dynamics"
English | ISBN: 1461437393 | 2012 | 479 pages | PDF | 7 MB

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Deskripsi Buku :
This is the second volume of three books, by the same author, devoted to classical mechanics. In this book, Classical Mechanics: Dynamics, dynamical and advanced mechanics problems are stated, illustrated, and discussed, including a few novel concepts by comparison to standard text books and monographs. Aside from being addressed to a wide spectrum of graduate students, postgraduate students, researchers, and instructors, from the fields of mechanical and civil engineering, this volume, which includes a wealth of worked examples and applications, is also intended to be used as a self-contained reference for researchers in applied mathematics and physical sciences. Chapter 1 covers dynamics of a particle and systems of particles, as well as rigid body motion about a point. Mathematical and physical pendulums are discussed in Chapter 2, and Chapter 3 presents static and dynamic problems of discrete mechanical systems. Classical equations of mechanics are studied in Chapter 4, and Chapter 5 introduces and illustrates classical impact theory. Chapter 6 deals with the vibrations of mechanical systems, and Chapter 7 briefly studies the dynamics of planets. Dynamics of variable mass systems are presented in Chapter 8, and body and multibody dynamics are studied in Chapter 9. A geometric approach to dynamical problems is the focus of Chapter 10, and Chapter 11 ends the text with geometric dynamics.

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Classical Mechanics - Applied Mechanics and Mechatronics by Jan Awrejcewicz and Zbigniew Koruba

Jan Awrejcewicz and Zbigniew Koruba, "Classical Mechanics: Applied Mechanics and Mechatronics"
English | ISBN: 1461439779 | 2012 | 271 pages | PDF | 8 MB

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Deskripsi Buku :
This is the final volume of a triad of works by Jan Awrejcewicz (this third book with Zbigniew Koruba) devoted to classical mechanics. Classical Mechanics: Mechanics and Mechatronics presents a unique approach to studying mechanical and electromagnetic processes occurring in applied mechanics and mechatronics with emphasis on theory, modeling, and analysis and control of gyropscopic devices, including military applications. This volume address a wide spectrum of graduate students, postgraduate students, researchers, and instructors from the field of mechanics, this volume, and has a strong focus on advanced applications that will be of particular use and interest to engineers and designers practicing in the mechanical/mechatronic industry. Chapter 1 deals with dynamics in mechatronic systems. Dynamics of a rigid spherical body is studied in Chapter 2 with emphasis on applications. Chapters 3 and 4 are dedicated to the theory, evolution, and dynamics and control of the gyroscope and Chapter 5 focuses on gyroscopic control in the self-guidance systems of flying objects.

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