Author: Eugenio Filloy Publisher: Springer Science & Business Media ISBN: 0387712542 Category : Education Languages : en Pages : 302
Book Description
This book takes a theoretical perspective on the study of school algebra, in which both semiotics and history occur. The Methodological design allows for the interpretation of specific phenomena and the inclusion of evidence not addressed in more general treatments. The book gives priority to "meaning in use" over "formal meaning". These approaches and others of similar nature lead to a focus on competence rather than a user’s activity with mathematical language.
Author: Sudipto Banerjee Publisher: CRC Press ISBN: 1420095382 Category : Mathematics Languages : en Pages : 586
Book Description
Linear Algebra and Matrix Analysis for Statistics offers a gradual exposition to linear algebra without sacrificing the rigor of the subject. It presents both the vector space approach and the canonical forms in matrix theory. The book is as self-contained as possible, assuming no prior knowledge of linear algebra. The authors first address the rudimentary mechanics of linear systems using Gaussian elimination and the resulting decompositions. They introduce Euclidean vector spaces using less abstract concepts and make connections to systems of linear equations wherever possible. After illustrating the importance of the rank of a matrix, they discuss complementary subspaces, oblique projectors, orthogonality, orthogonal projections and projectors, and orthogonal reduction. The text then shows how the theoretical concepts developed are handy in analyzing solutions for linear systems. The authors also explain how determinants are useful for characterizing and deriving properties concerning matrices and linear systems. They then cover eigenvalues, eigenvectors, singular value decomposition, Jordan decomposition (including a proof), quadratic forms, and Kronecker and Hadamard products. The book concludes with accessible treatments of advanced topics, such as linear iterative systems, convergence of matrices, more general vector spaces, linear transformations, and Hilbert spaces.
Author: Jay P. Abramson Publisher: ISBN: 9781938168376 Category : Algebra Languages : en Pages : 1564
Book Description
"The text is suitable for a typical introductory algebra course, and was developed to be used flexibly. While the breadth of topics may go beyond what an instructor would cover, the modular approach and the richness of content ensures that the book meets the needs of a variety of programs."--Page 1.
Author: Jerome E. Kaufmann Publisher: Thomson Brooks/Cole ISBN: 9780534953591 Category : Algebra Languages : en Pages : 0
Book Description
From the author of several highly successful mathematics texts comes this easy-to-understand and effective book. This early functions version of Kaufmann's highly successful text helps students to visualize the relationship between algebraic equations and functions and their geometric representations by introducing graphing early on. The author weaves a common thread into each chapter - learn a skill, use the skill to solve equations, and use equations to solve problems - thereby providing students with as easy-to-follow plan for tackling the problems and concepts presented.
Author: Peter J. Olver Publisher: Springer ISBN: 3319910418 Category : Mathematics Languages : en Pages : 702
Book Description
This textbook develops the essential tools of linear algebra, with the goal of imparting technique alongside contextual understanding. Applications go hand-in-hand with theory, each reinforcing and explaining the other. This approach encourages students to develop not only the technical proficiency needed to go on to further study, but an appreciation for when, why, and how the tools of linear algebra can be used across modern applied mathematics. Providing an extensive treatment of essential topics such as Gaussian elimination, inner products and norms, and eigenvalues and singular values, this text can be used for an in-depth first course, or an application-driven second course in linear algebra. In this second edition, applications have been updated and expanded to include numerical methods, dynamical systems, data analysis, and signal processing, while the pedagogical flow of the core material has been improved. Throughout, the text emphasizes the conceptual connections between each application and the underlying linear algebraic techniques, thereby enabling students not only to learn how to apply the mathematical tools in routine contexts, but also to understand what is required to adapt to unusual or emerging problems. No previous knowledge of linear algebra is needed to approach this text, with single-variable calculus as the only formal prerequisite. However, the reader will need to draw upon some mathematical maturity to engage in the increasing abstraction inherent to the subject. Once equipped with the main tools and concepts from this book, students will be prepared for further study in differential equations, numerical analysis, data science and statistics, and a broad range of applications. The first author’s text, Introduction to Partial Differential Equations, is an ideal companion volume, forming a natural extension of the linear mathematical methods developed here.
Author: Lynn Harold Loomis Publisher: World Scientific Publishing Company ISBN: 9814583952 Category : Mathematics Languages : en Pages : 595
Book Description
An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
Author: Eugenio Filloy
Author: Sudipto Banerjee
Author: Jay P. Abramson
Author: W. Michael Kelley
Author: Marvin Bittinger
Author: Jerome E. Kaufmann
Author: Peter J. Olver
Author: Lynn Harold Loomis
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