Download or read book Linear Algebra for the 21st Century written by Anthony Roberts and published by Oxford University Press, USA. This book was released on 2020-06-29 with total page 681 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Algebra for 21st Century Applications adapts linear algebra to best suit modern teaching and application, and it places SVD as central to the text early on to empower the students in these disciplines to learn and use the best techniques.
Download or read book Linear Algebra for the 21st Century written by Anthony Roberts and published by Oxford University Press. This book was released on 2020-10-09 with total page 750 pages. Available in PDF, EPUB and Kindle. Book excerpt: Customarily, much of traditional mathematics curricula was predicated on 'by hand' calculation. However, ubiquitous computing requires us to refresh what we teach and how it is taught. This is especially true in the rapidly broadening fields of Data Mining and Artificial Intelligence, and also in fields such as Bioinformatics, which all require the use of Singular Value Decomposition (SVD). Indeed, SVD is sometimes called the jewel in the crown of linear algebra. Linear Algebra for 21st Century Applications adapts linear algebra to best suit modern teaching and application, and it places the SVD as central to the text early on to empower science and engineering students to learn and use potent practical and theoretical techniques. No rigour is lost in this new route as the text demonstrates that most theory is better proved with an SVD. In addition to this, there is earlier introduction, development, and emphasis on orthogonality that is vital in so many applied disciplines throughout science, engineering, computing and increasingly within the social sciences. To assimilate the so-called third arm of science, namely computing, Matlab/Octave computation is explicitly integrated into developing the mathematical concepts and applications. A strong graphical emphasis takes advantage of the power of visualisation in the human brain and examples are included to exhibit modern applications of linear algebra, such as GPS, text mining, and image processing. Active learning is encouraged with exercises throughout that are aimed to enhance ectures, quizzes, or 'flipped' teaching.
Download or read book Linear Algebra written by Harold M. Edwards and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Proposes a radically new and thoroughly algorithmic approach to linear algebra * Each proof is an algorithm described in English that can be translated into the computer language the class is using and put to work solving problems and generating new examples * Designed for a one-semester course, this text gives the student many examples to work through and copious exercises to test their skills and extend their knowledge of the subject
Download or read book Linear Algebra written by Jeff Suzuki and published by CRC Press. This book was released on 2021-05-04 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Algebra: An Inquiry-based Approach is written to give instructors a tool to teach students to develop a mathematical concept from first principles. The Inquiry-based Approach is central to this development. The text is organized around and offers the standard topics expected in a first undergraduate course in linear algebra. In our approach, students begin with a problem and develop the mathematics necessary to describe, solve, and generalize it. Thus students learn a vital skill for the 21st century: the ability to create a solution to a problem. This text is offered to foster an environment that supports the creative process. The twin goals of this textbook are: Providing opportunities to be creative, Teaching "ways of thinking" that will make it easier for to be creative. To motivate the development of the concepts and techniques of linear algebra, we include more than two hundred Activities on a wide range of problems, from purely mathematical questions, through applications in biology, computer science, cryptography, and more. Table of Contents Introduction and Features For the Student . . . and Teacher Prerequisites Suggested Sequences 1. Tuples and Vectors 2. Systems of Linear Equations 3. Transformations 4. Matrix Algebra 5. Vector Spaces 6. Determinants 7. Eigenvalues and Eigenvectors 8. Decomposition 9. Extras Bibliography Index Bibliography Jeff Suzuki is Associate Professor of Mathematics at Brooklyn College and holds a Ph.D. from Boston University. His research interests include mathematics education, history of mathematics, and the application of mathematics to society and technology. He is a two-time winner of the prestigious Carl B. Allendoerfer Award for expository writing. His publications have appeared in The College Mathematics Journals; Mathematics Magazine; Mathematics Teacher; and the American Mathematical Society's blog on teaching and learning mathematics. His YouTube channel (http://youtube.com/jeffsuzuki1) includes videos on mathematical subjects ranging from elementary arithmetic to linear algebra, cryptography, and differential equations.
Download or read book Linear Algebra written by Jörg Liesen and published by Springer. This book was released on 2015-11-20 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exercises.
Download or read book Linear Models and the Relevant Distributions and Matrix Algebra written by David A. Harville and published by CRC Press. This book was released on 2023-10-23 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: • Exercises and solutions are included throughout, from both the first and second volume • Includes coverage of additional topics not covered in the first volume • Highly valuable as a reference book for graduate students or researchers
Download or read book Linear Algebra with Applications written by Hugh G. Campbell and published by . This book was released on 1971 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied Linear Algebra written by Peter J. Olver and published by Springer. This book was released on 2018-05-30 with total page 679 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Abstract and Linear Algebra written by Zhexian Wan and published by . This book was released on 1992 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is known that linear algebra is a useful tool in engineering but, since the middle of this century, abstract linear algebra has also found more and more applications. For instance, finite fields play a prominent role in coding theory and ring theory is the foundation of linear systems over rings. Both linear and abstract algebra should now be in the curriculum of undergraduate engineering students. This introductory book on algebra aims to provide the basic material for such a course. It also constitutes a solid algebraic basis for the non-specialists who wish to become specialists in, for example, coding theory, cryptography and linear systems theory.
Download or read book Landscape of 21st Century Mathematics written by Bogdan Grechuk and published by Springer Nature. This book was released on 2021-09-21 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: Landscape of 21st Century Mathematics offers a detailed cross section of contemporary mathematics. Important results of the 21st century are motivated and formulated, providing an overview of recent progress in the discipline. The theorems presented in this book have been selected among recent achievements whose statements can be fully appreciated without extensive background. Grouped by subject, the selected theorems represent all major areas of mathematics: number theory, combinatorics, analysis, algebra, geometry and topology, probability and statistics, algorithms and complexity, and logic and set theory. The presentation is self-contained with context, background and necessary definitions provided for each theorem, all without sacrificing mathematical rigour. Where feasible, brief indications of the main ideas of a proof are given. Rigorous yet accessible, this book presents an array of breathtaking recent advances in mathematics. It is written for everyone with a background in mathematics, from inquisitive university students to mathematicians curious about recent achievements in areas beyond their own.
Download or read book Linear Algebra II written by Frederick P. Greenleaf and published by American Mathematical Soc.. This book was released on 2020-05-06 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the second of two volumes on linear algebra for graduate students in mathematics, the sciences, and economics, who have: a prior undergraduate course in the subject; a basic understanding of matrix algebra; and some proficiency with mathematical proofs. Both volumes have been used for several years in a one-year course sequence, Linear Algebra I and II, offered at New York University's Courant Institute. The first three chapters of this second volume round out the coverage of traditional linear algebra topics: generalized eigenspaces, further applications of Jordan form, as well as bilinear, quadratic, and multilinear forms. The final two chapters are different, being more or less self-contained accounts of special topics that explore more advanced aspects of modern algebra: tensor fields, manifolds, and vector calculus in Chapter 4 and matrix Lie groups in Chapter 5. The reader can choose to pursue either chapter. Both deal with vast topics in contemporary mathematics. They include historical commentary on how modern views evolved, as well as examples from geometry and the physical sciences in which these topics are important. The book provides a nice and varied selection of exercises; examples are well-crafted and provide a clear understanding of the methods involved.
Download or read book An Invitation to Abstract Algebra written by Steven J. Rosenberg and published by CRC Press. This book was released on 2021-12-22 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studying abstract algebra can be an adventure of awe-inspiring discovery. The subject need not be watered down nor should it be presented as if all students will become mathematics instructors. This is a beautiful, profound, and useful field which is part of the shared language of many areas both within and outside of mathematics. To begin this journey of discovery, some experience with mathematical reasoning is beneficial. This text takes a fairly rigorous approach to its subject, and expects the reader to understand and create proofs as well as examples throughout. The book follows a single arc, starting from humble beginnings with arithmetic and high-school algebra, gradually introducing abstract structures and concepts, and culminating with Niels Henrik Abel and Evariste Galois’ achievement in understanding how we can—and cannot—represent the roots of polynomials. The mathematically experienced reader may recognize a bias toward commutative algebra and fondness for number theory. The presentation includes the following features: Exercises are designed to support and extend the material in the chapter, as well as prepare for the succeeding chapters. The text can be used for a one, two, or three-term course. Each new topic is motivated with a question. A collection of projects appears in Chapter 23. Abstract algebra is indeed a deep subject; it can transform not only the way one thinks about mathematics, but the way that one thinks—period. This book is offered as a manual to a new way of thinking. The author’s aim is to instill the desire to understand the material, to encourage more discovery, and to develop an appreciation of the subject for its own sake.
Download or read book Applied Linear Algebra and Matrix Methods written by Timothy G. Feeman and published by Springer Nature. This book was released on 2023-11-24 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is designed for a first course in linear algebra for undergraduate students from a wide range of quantitative and data driven fields. By focusing on applications and implementation, students will be prepared to go on to apply the power of linear algebra in their own discipline. With an ever-increasing need to understand and solve real problems, this text aims to provide a growing and diverse group of students with an applied linear algebra toolkit they can use to successfully grapple with the complex world and the challenging problems that lie ahead. Applications such as least squares problems, information retrieval, linear regression, Markov processes, finding connections in networks, and more, are introduced on a small scale as early as possible and then explored in more generality as projects. Additionally, the book draws on the geometry of vectors and matrices as the basis for the mathematics, with the concept of orthogonality taking center stage. Important matrix factorizations as well as the concepts of eigenvalues and eigenvectors emerge organically from the interplay between matrix computations and geometry. The R files are extra and freely available. They include basic code and templates for many of the in-text examples, most of the projects, and solutions to selected exercises. As much as possible, data sets and matrix entries are included in the files, thus reducing the amount of manual data entry required.
Download or read book Linear Algebra written by Kuldeep Singh and published by Oxford University Press. This book was released on 2013-10 with total page 617 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is intended for first- and second-year undergraduates arriving with average mathematics grades ... The strength of the text is in the large number of examples and the step-by-step explanation of each topic as it is introduced. It is compiled in a way that allows distance learning, with explicit solutions to all of the set problems freely available online http://www.oup.co.uk/companion/singh" -- From preface.
Download or read book Transforming Education for the 21st Century Innovative Teaching Approaches written by S G Mohanraj and published by OrangeBooks Publication. This book was released on 2024-06-04 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Transforming Education for the 21st Century - Innovative Teaching Approaches" explores cutting-edge methods and strategies to revolutionize teaching in today's dynamic educational landscape. This comprehensive guide offers educators insights into incorporating innovative techniques, such as project-based learning, flipped classrooms, and personalized instruction, to engage and empower students for success in the digital age. With practical tips, case studies, and actionable advice, this book equips teachers with the tools they need to create enriching learning experiences that prepare students to thrive in an ever-evolving world. It's a must-read for educators seeking to reimagine education and inspire lifelong learning.
Download or read book The Universe of Conics written by Georg Glaeser and published by Springer. This book was released on 2016-03-22 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents the classical theory of conics in a modern form. It includes many novel results that are not easily accessible elsewhere. The approach combines synthetic and analytic methods to derive projective, affine and metrical properties, covering both Euclidean and non-Euclidean geometries. With more than two thousand years of history, conic sections play a fundamental role in numerous fields of mathematics and physics, with applications to mechanical engineering, architecture, astronomy, design and computer graphics. This text will be invaluable to undergraduate mathematics students, those in adjacent fields of study, and anyone with an interest in classical geometry. Augmented with more than three hundred fifty figures and photographs, this innovative text will enhance your understanding of projective geometry, linear algebra, mechanics, and differential geometry, with careful exposition and many illustrative exercises.
Download or read book Applied Linear Algebra written by Lorenzo Sadun and published by American Mathematical Society. This book was released on 2022-06-07 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear algebra permeates mathematics, as well as physics and engineering. In this text for junior and senior undergraduates, Sadun treats diagonalization as a central tool in solving complicated problems in these subjects by reducing coupled linear evolution problems to a sequence of simpler decoupled problems. This is the Decoupling Principle. Traditionally, difference equations, Markov chains, coupled oscillators, Fourier series, the wave equation, the Schrödinger equation, and Fourier transforms are treated separately, often in different courses. Here, they are treated as particular instances of the decoupling principle, and their solutions are remarkably similar. By understanding this general principle and the many applications given in the book, students will be able to recognize it and to apply it in many other settings. Sadun includes some topics relating to infinite-dimensional spaces. He does not present a general theory, but enough so as to apply the decoupling principle to the wave equation, leading to Fourier series and the Fourier transform. The second edition contains a series of Explorations. Most are numerical labs in which the reader is asked to use standard computer software to look deeper into the subject. Some explorations are theoretical, for instance, relating linear algebra to quantum mechanics. There is also an appendix reviewing basic matrix operations and another with solutions to a third of the exercises.
