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Mathematical Studies
by Mal Coad Sandra Haese Glen Whiffen Michael Haese Mark HumphriesMathematics for the International Student: Mathematical Studies SL has been written to embrace the syllabus for the two-year Mathematical Studies SL Course, to be first examined in 2014.
Mathematical Subjects
by Fiona WallsWe know the process by which children become social, moral, and creative beings, but when--and how--do they become mathematical beings? This thought-provoking volume follows ten children (ages seven through eighteen) in schools in New Zealand, England, Australia, Sweden, and an international school in Switzerland as they come to recognize the mathematical as part of their lives, their academic identities, and their identities as human beings. Through these students' experiences important themes emerge, including mathematics as work, a domain of learning, and an avenue for competition; mathematical ability as a key to how they are perceived by others; and the relationships between mathematics achievement and the larger social and academic picture. This comparative study of educational systems and academic development will inform readers in these and other salient areas: Theoretical bases for understanding children as mathematical subjects. Help in creating the mathematical self: tutoring and related programs. The roles of compulsory study and standardized assessment. Class and ethnic content in children's math narratives. The gendering of mathematical ability and activity. What children's math experience can teach us about teaching the subject. Children Talk about Their Mathematics Lives opens bold windows onto how young people learn and how disparities arise, making it a cutting-edge resource for researchers and libraries, graduates and teachers in mathematics education and early childhood education.
Mathematical Summary for Digital Signal Processing Applications with Matlab
by E. S. GopiMathematical summary for Digital Signal Processing Applications with Matlab consists of Mathematics which is not usually dealt in the DSP core subject, but used in DSP applications. Matlab programs with illustrations are given for the selective topics such as generation of Multivariate Gaussian distributed sample outcomes, Bacterial foraging algorithm, Newton's iteration, Steepest descent algorithm, etc. are given exclusively in the separate chapter. Also Mathematical summary for Digital Signal Processing Applications with Matlab is written in such a way that it is suitable for Non-Mathematical readers and is very much suitable for the beginners who are doing research in Digital Signal Processing.
Mathematical Tablets from Tell Harmal
by Carlos GonçalvesThis work offers a re-edition of twelve mathematical tablets from the site of Tell Harmal, in the borders of present-day Baghdad. In ancient times, Tell Harmal was Saduppûm, a city representative of the region of the Diyala river and of the kingdom of Esnunna, to which it belonged for a time. These twelve tablets were originally published in separate articles in the beginning of the 1950s and mostly contain solved problem texts. Some of the problems deal with abstract matters such as triangles and rectangles with no reference to daily life, while others are stated in explicitly empirical contexts, such as the transportation of a load of bricks, the size of a vessel, the number of men needed to build a wall and the acquisition of oil and lard. This new edition of the texts is the first to group them, and takes into account all the recent developments of the research in the history of Mesopotamian mathematics. Its introductory chapters are directed to readers interested in an overview of the mathematical contents of these tablets and the language issues involved in their interpretation, while a chapter of synthesis discusses the ways history of mathematics has typically dealt with the mathematical evidence and inquires how and to what degree mathematical tablets can be made part of a picture of the larger social context. Furthermore, the volume contributes to a geography of the Old Babylonian mathematical practices, by evidencing that scribes at Saduppûm made use of cultural material that was locally available. The edited texts are accompanied by translations, philological, and mathematical commentaries.
Mathematical Tasks: The Bridge Between Teaching and Learning
by Mark McCourt Chris McGraneIf we want our pupils to develop fluency, understanding and the ability to solve complex problems, then it is vital that teachers develop the ability to select, adapt and design appropriate mathematical tasks. In 'Mathematical Tasks: The Bridge Between Teaching and Learning', Chris McGrane and Mark McCourt a range of practical approaches, strategies and principles behind the design and effective use of tasks in the mathematics classroom that lead to all pupils becoming successful learners. First-hand interviews with world class mathematics education experts and practicing teachers bring to life the ideas behind how tasks can act as a bridge between what the teacher wants the pupil to make sense of and what the pupil actually does makes sense of; tasks are how we enable pupils to enact mathematics - it is only by being mathematical that pupils can truly make connections across mathematical ideas and understand the bigger picture. This is a book for classroom teachers. Chris McGrane offers a range of practical examples for nurturing deep learning in mathematics that can be adapted and embedded in one's own classroom practice. This is also a book for those who are interested in the theory behind tasks. Chris and his interviewees examine the key role tasks play in shaping learning, teaching, curriculum and assessment. Suitable for teachers at all stages in their careers and teachers are encouraged to return to the book from time to time over the years to notice how their use of tasks in the classroom changes as they themselves develop.
Mathematical Tasks: The Bridge Between Teaching and Learning
by Mark McCourt Chris McGraneIf we want our pupils to develop fluency, understanding and the ability to solve complex problems, then it is vital that teachers develop the ability to select, adapt and design appropriate mathematical tasks. In 'Mathematical Tasks: The Bridge Between Teaching and Learning', Chris McGrane and Mark McCourt a range of practical approaches, strategies and principles behind the design and effective use of tasks in the mathematics classroom that lead to all pupils becoming successful learners. First-hand interviews with world class mathematics education experts and practicing teachers bring to life the ideas behind how tasks can act as a bridge between what the teacher wants the pupil to make sense of and what the pupil actually does makes sense of; tasks are how we enable pupils to enact mathematics - it is only by being mathematical that pupils can truly make connections across mathematical ideas and understand the bigger picture. This is a book for classroom teachers. Chris McGrane offers a range of practical examples for nurturing deep learning in mathematics that can be adapted and embedded in one's own classroom practice. This is also a book for those who are interested in the theory behind tasks. Chris and his interviewees examine the key role tasks play in shaping learning, teaching, curriculum and assessment. Suitable for teachers at all stages in their careers and teachers are encouraged to return to the book from time to time over the years to notice how their use of tasks in the classroom changes as they themselves develop.
Mathematical Teaching and Learning: Perspectives on Mathematical Minds in the Elementary and Middle School Years
by Katherine M. Robinson Donna Kotsopoulos Adam K. DubéThis book focusses on teaching and learning in elementary and middle school mathematics and suggests practices for teachers to help children be successful mathematical thinkers. Contributions from diverse theoretical and disciplinary perspectives are explored. Topics include the roles of technology, language, and classroom discussion in mathematics learning, the use of creativity, visuals, and teachers’ physical gestures to enhance problem solving, inclusive educational activities to promote children’s mathematics understanding, how learning in the home can enhance children’s mathematical skills, the application of mathematics learning theories in designing effective teaching tools, and a discussion of how students, teachers, teacher educators, and school boards differentially approach elementary and middle school mathematics. This book and its companion, Mathematical Cognition and Understanding, take an interdisciplinary perspective to mathematical learning and development in the elementary and middle school years. The authors and perspectives in this book draw from education, neuroscience, developmental psychology, and cognitive psychology. The book will be relevant to scholars/educators in the field of mathematics education and also those in childhood development and cognition. Each chapter also includes practical tips and implications for parents as well as for educators and researchers.
Mathematical Techniques for Wave Interaction with Flexible Structures (IIT Kharagpur Research Monograph Series)
by Trilochan SahooMathematical Techniques for Wave Interaction with Flexible Structures is a thoughtful compilation of the various mathematical techniques used to deal with wave structure interaction problems. The book emphasizes unique determination of the solution for a class of physical problems associated with Laplace- or Helmholtz-type equations satisfying high
Mathematical Techniques in Finance: Tools for Incomplete Markets - Second Edition
by Ales CernýOriginally published in 2003, Mathematical Techniques in Finance has become a standard textbook for master's-level finance courses containing a significant quantitative element while also being suitable for finance PhD students. This fully revised second edition continues to offer a carefully crafted blend of numerical applications and theoretical grounding in economics, finance, and mathematics, and provides plenty of opportunities for students to practice applied mathematics and cutting-edge finance. Ales Cerný mixes tools from calculus, linear algebra, probability theory, numerical mathematics, and programming to analyze in an accessible way some of the most intriguing problems in financial economics. The textbook is the perfect hands-on introduction to asset pricing, optimal portfolio selection, risk measurement, and investment evaluation. The new edition includes the most recent research in the area of incomplete markets and unhedgeable risks, adds a chapter on finite difference methods, and thoroughly updates all bibliographic references. Eighty figures, over seventy examples, twenty-five simple ready-to-run computer programs, and several spreadsheets enhance the learning experience. All computer codes have been rewritten using MATLAB and online supplementary materials have been completely updated. A standard textbook for graduate finance courses Introduction to asset pricing, portfolio selection, risk measurement, and investment evaluation Detailed examples and MATLAB codes integrated throughout the text Exercises and summaries of main points conclude each chapter
Mathematical Techniques in GIS
by Peter DaleThe second edition of a bestseller, Mathematical Techniques in GIS demystifies the mathematics used in the manipulation of spatially related data. The author takes a step-by-step approach through the basics of arithmetic, algebra, geometry, trigonometry and calculus that underpin the management of such data. He then explores the use of matrices, de
Mathematical Techniques: An Introduction For The Engineering, Physical, And Mathematical Sciences
by Peter Smith Dominic JordanMathematical concepts and theories underpin engineering and many of the physical sciences. Yet many engineering and science students find math challenging and even intimidating. The fourth edition of Mathematical Techniques provides a complete course in mathematics, covering all the essential topics with which a physical sciences or engineering student should be familiar. By breaking the subject into small, modular chapters, the book introduces and builds on concepts in a progressive, carefully-layered way - always with an emphasis on using math to the best effect, rather than relying on theoretical proofs. With a huge array of end of chapter problems and new self-check questions, the fourth edition of Mathematical Techniques provides extensive opportunities for students to exercise and enhance their mathematical knowledge and skills.
Mathematical Technology of Networks
by Delio MugnoloDynamical models on graphs or random graphs are increasingly used in applied sciences as mathematical tools to study complex systems whose exact structure is too complicated to be known in detail. Besides its importance in applied sciences, the field is increasingly attracting the interest of mathematicians and theoretical physicists also because of the fundamental phenomena (synchronization, phase transitions etc. ) that can be studied in the relatively simple framework of dynamical models of random graphs. This volume was developed from the Mathematical Technology of Networks conference held in Bielefeld, Germany in December 2013. The conference was designed to bring together functional analysts, mathematical physicists, and experts in dynamical systems. The contributors to this volume explore the interplay between theoretical and applied aspects of discrete and continuous graphs. Their work helps to close the gap between different avenues of research on graphs, including metric graphs and ramified structures.
Mathematical Theory and Simulation of Scientific Problems: FIAM-2023, Dubai, UAE, December 21–22 (Springer Proceedings in Mathematics & Statistics #487)
by Rajesh Kumar Sharma Ali Cemal Benim Shailesh Kumar SrivastavaThis book contains select chapters of proceedings presented at the 6th International Conference on Frontiers in Industrial and Applied Mathematics (FIAM-2023), held at the Birla Institute of Technology and Science, Pilani-Dubai Campus, UAE, on 21–22 December 2023. It deals with mathematical theory and its applications to the various disciplines of engineering and sciences. The book illustrates the mathematical simulation of scientific problems and cutting-edge development in multiple branches of mathematics, including various computational and modeling techniques with case studies and concrete examples. The book is useful to graduate students, research scholars and professionals who are interested in the real applications of mathematics in the areas of computational and theoretical fluid dynamics, server queues, Lie group theory, fixed point theory, image processing, biomathematics, nonlinear dynamics and approximation theory.
Mathematical Theory in Periodic Plane Elasticity (Modern Analysis Series)
by Hai-Tao Cai Jian-Ke LuPresenting the mathematical theory of period problems in plane elasticity by methods of complex variables. The most general formulations of such problems are proposed under the assumption that the stresses are periodic and the displacements are quasi-periodic. The general expression of complex displacements are illustrated. Periodic welding problem
Mathematical Theory of Bayesian Statistics
by Sumio WatanabeMathematical Theory of Bayesian Statistics introduces the mathematical foundation of Bayesian inference which is well-known to be more accurate in many real-world problems than the maximum likelihood method. Recent research has uncovered several mathematical laws in Bayesian statistics, by which both the generalization loss and the marginal likelihood are estimated even if the posterior distribution cannot be approximated by any normal distribution. <P><P> Features <li>Explains Bayesian inference not subjectively but objectively. <li>Provides a mathematical framework for conventional Bayesian theorems. <li>Introduces and proves new theorems. <li>Cross validation and information criteria of Bayesian statistics are studied from the mathematical point of view. <li>Illustrates applications to several statistical problems, for example, model selection, hyperparameter optimization, and hypothesis tests. <li>This book provides basic introductions for students, researchers, and users of Bayesian statistics, as well as applied mathematicians. <P><P>Author <P><P>Sumio Watanabe is a professor of Department of Mathematical and Computing Science at Tokyo Institute of Technology. He studies the relationship between algebraic geometry and mathematical statistics.
Mathematical Theory of Black Holes in Higher Dimensions (Lecture Notes in Physics #1031)
by Petya Nedkova Stoytcho YazadjievThis book portraits the mathematical theory which lies behind black hole solutions in spacetimes with an extra dimension. Step by step the authors build a comprehensive picture of the main concepts and tools necessary to understand these geometries. In this way the book addresses questions like: How do we describe black holes in higher dimensions? How can we construct such geometries explicitly as exact solutions to the field equations? How many independent solutions can exist and how are they classified?The book concentrates on five-dimensional stationary and axisymmetric spacetimes in electro-vacuum and systematically introduces the most important black geometries which can arise in these settings. The authors follow the natural progress of the research area by initially describing the first results that were obtained intuitively and sparkled interest in the community. Then the elaborate mathematical techniques are introduced which allow to systematically construct exact black hole solutions. Topics like the integrability of the theory, the hidden symmetries of the field equations, the available Bäcklund transformations and solution generation techniques based on the inverse scattering method are covered. The last part of the book is devoted to uniqueness theorems showing how to classify the black hole spacetimes and distinguish the non-equivalent ones.The book is not just a mere collection of facts but a methodological description of the most important mathematical techniques and constructions in an active research area. The discussion is pedagogical and all the methods are demonstrated on a variety of examples. Most of the book is adapted to the level of a graduate student possessing a basic knowledge of general relativity and differential equations, and can serve as a practical guide for quickly acquiring the specific concepts and calculation techniques. Both authors have contributed to the research area by their original results, and share their own experience and perspective.
Mathematical Theory of Compressible Fluid Flow
by Richard Von MisesA pioneer in the fields of statistics and probability theory, Richard von Mises (1883-1953) made notable advances in boundary-layer-flow theory and airfoil design. This text on compressible flow, unfinished upon his sudden death, was subsequently completed in accordance with his plans, and von Mises' first three chapters were augmented with a survey of the theory of steady plane flow. Suitable as a text for advanced undergraduate and graduate students -- as well as a reference for professionals -- Mathematical Theory of Compressible Fluid Flow examines the fundamentals of high-speed flows, with detailed considerations of general theorems, conservation equations, waves, shocks, and nonisentropic flows.In this, the final work of his distinguished career, von Mises summarizes his extensive knowledge of a central branch of fluid mechanics. Characteristically, he pays particular attention to the basics, both conceptual and mathematical. The novel concept of a specifying equation clarifies the role of thermodynamics in the mechanics of compressible fluids. The general theory of characteristics receives a remarkably complete and simple treatment, with detailed applications, and the theory of shocks as asymptotic phenomena appears within the context of rational mechanics.
Mathematical Theory of Compressible Fluids on Moving Domains (Advances in Mathematical Fluid Mechanics)
by Šárka Nečasová Aneta Wróblewska-Kamińska Ondřej Kreml Václav Mácha Tomasz PiaseckiThis monograph presents the existence and properties of both weak and strong solutions to the problems of the flow of a compressible fluid in a domain whose motion is prescribed. Chapters build upon the research of Lions and Feireisl with regards to weak solutions to the compressible version of the Navier-Stokes system, and extend it to problems on moving domains. The authors also show the existence of strong solutions to the compressible Navier-Stokes system for either a small time interval or small data. The opening chapters introduce the notation, tools, and problems covered in the rest of the book, emphasizing pedagogy and accessibility throughout. Mathematical Theory of Compressible Fluids on Moving Domains will be suitable for graduate students and researchers interested in mathematical fluid mechanics.
Mathematical Theory of Fuzzy Sets
by Hsien-Chung WuMathematical Theory of Fuzzy Sets presents the mathematical theory of non-normal fuzzy sets such that it can be rigorously used as a basic tool to study engineering and economic problems under a fuzzy environment. It may also be used as a textbook at the graduate level, or as a reference for researchers.The book explores the current state of affairs in set operations of fuzzy sets, arithmetic operations of fuzzy interval, and fuzzification of crisp functions, which are frequently adopted to model engineering and economic problems with fuzzy uncertainty. In particular, the concepts of gradual sets and gradual elements are presented in order to cope with the difficulty of considering elements of fuzzy sets like considering elements of crisp sets.Features Many extensions and equivalences for the essence of non-normal fuzzy sets Generalization of extension principle Presentation of the concepts of gradual sets and gradual elements
Mathematical Theory of Hemivariational Inequalities and Applications (Chapman And Hall/crc Pure And Applied Mathematics Ser.)
by P. D. Panagiotopoulos Zdzistaw NaniewiczGives a complete and rigorous presentation of the mathematical study of the expressions - hemivariational inequalities - arising in problems that involve nonconvex, nonsmooth energy functions. A theory of the existence of solutions for inequality problems involving monconvexity and nonsmoothness is established.
Mathematical Theory of Optimal Processes: Selected Works (Classics Of Soviet Mathematics Ser.)
by L.S. PontryaginThe fourth and final volume in this comprehensive set presents the maximum principle as a wide ranging solution to nonclassical, variational problems. This one mathematical method can be applied in a variety of situations, including linear equations with variable coefficients, optimal processes with delay, and the jump condition. As with the three preceding volumes, all the material contained with the 42 sections of this volume is made easily accessible by way of numerous examples, both concrete and abstract in nature.
Mathematical Theory of Subdivision: Finite Element and Wavelet Methods
by Sandeep Kumar Ashish Pathak Debashis KhanThis book provides good coverage of the powerful numerical techniques namely, finite element and wavelets, for the solution of partial differential equation to the scientists and engineers with a modest mathematical background. The objective of the book is to provide the necessary mathematical foundation for the advanced level applications of these numerical techniques. The book begins with the description of the steps involved in finite element and wavelets-Galerkin methods. The knowledge of Hilbert and Sobolev spaces is needed to understand the theory of finite element and wavelet-based methods. Therefore, an overview of essential content such as vector spaces, norm, inner product, linear operators, spectral theory, dual space, and distribution theory, etc. with relevant theorems are presented in a coherent and accessible manner. For the graduate students and researchers with diverse educational background, the authors have focused on the applications of numerical techniques which are developed in the last few decades. This includes the wavelet-Galerkin method, lifting scheme, and error estimation technique, etc. Features: • Computer programs in Mathematica/Matlab are incorporated for easy understanding of wavelets. • Presents a range of workout examples for better comprehension of spaces and operators. • Algorithms are presented to facilitate computer programming. • Contains the error estimation techniques necessary for adaptive finite element method. This book is structured to transform in step by step manner the students without any knowledge of finite element, wavelet and functional analysis to the students of strong theoretical understanding who will be ready to take many challenging research problems in this area.
Mathematical Theory of Uniformity and its Applications in Ecology and Chaos (SpringerBriefs in Applied Sciences and Technology)
by Chuanwen Luo Chuncheng WangThis book puts forward a new mathematical theory to study chaotic phenomenon. The uniform theory is established on the basis of two elementary concept of circle and externally tangent square in mathematics. The author studies the uniformity of a finite set of points distributed in space by uniform theory. This book also illustrates that uniform theory performs better than other indices such as entropy and Lyapunov exponent in chaos measurement by numerous examples. This book develops a new mathematical tool for studying chaos so it will be appealing to students and researchers interested in theory of chaos. It also has potential applications in various fields such as Engineering, Forestry and Ecology.
Mathematical Thermodynamics of Complex Fluids: Cetraro, Italy 2015 (Lecture Notes in Mathematics #2200)
by Eduard Feireisl Elisabetta Rocca John M. Ball Felix OttoEduard FeireislThe main goal of this book is to provide an overview of the state of the art in the mathematical modeling of complex fluids, with particular emphasis on its thermodynamical aspects. The central topics of the text, the modeling, analysis and numerical simulation of complex fluids, are of great interest and importance both for the understanding of various aspects of fluid dynamics and for its applications to special real-world problems. New emerging trends in the subject are highlighted with the intent to inspire and motivate young researchers and PhD students.
