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Linear Algebra As An Introduction To Abstract Mathematics
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Book Synopsis Linear Algebra as an Introduction to Abstract Mathematics by : Isaiah Lankham
Download or read book Linear Algebra as an Introduction to Abstract Mathematics written by Isaiah Lankham and published by World Scientific Publishing Company. This book was released on 2015-11-30 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory textbook designed for undergraduate mathematics majors with an emphasis on abstraction and in particular, the concept of proofs in the setting of linear algebra. Typically such a student would have taken calculus, though the only prerequisite is suitable mathematical grounding. The purpose of this book is to bridge the gap between the more conceptual and computational oriented undergraduate classes to the more abstract oriented classes. The book begins with systems of linear equations and complex numbers, then relates these to the abstract notion of linear maps on finite-dimensional vector spaces, and covers diagonalization, eigenspaces, determinants, and the Spectral Theorem. Each chapter concludes with both proof-writing and computational exercises.
Book Synopsis Linear Algebra by : Robert J. Valenza
Download or read book Linear Algebra written by Robert J. Valenza and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on lectures given at Claremont McKenna College, this text constitutes a substantial, abstract introduction to linear algebra. The presentation emphasizes the structural elements over the computational - for example by connecting matrices to linear transformations from the outset - and prepares the student for further study of abstract mathematics. Uniquely among algebra texts at this level, it introduces group theory early in the discussion, as an example of the rigorous development of informal axiomatic systems.
Book Synopsis Linear Algebra As An Introduction To Abstract Mathematics by : Bruno Nachtergaele
Download or read book Linear Algebra As An Introduction To Abstract Mathematics written by Bruno Nachtergaele and published by . This book was released on 2015 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Linear Algebra by : Robert J. Valenza
Download or read book Linear Algebra written by Robert J. Valenza and published by Springer. This book was released on 1999-02-01 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on lectures given at Claremont McKenna College, this text constitutes a substantial, abstract introduction to linear algebra. The presentation emphasizes the structural elements over the computational - for example by connecting matrices to linear transformations from the outset - and prepares the student for further study of abstract mathematics. Uniquely among algebra texts at this level, it introduces group theory early in the discussion, as an example of the rigorous development of informal axiomatic systems.
Book Synopsis Abstract Algebra by : Gary L. Mullen
Download or read book Abstract Algebra written by Gary L. Mullen and published by CRC Press. This book was released on 2016-12-19 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract Algebra: A Gentle Introduction advantages a trend in mathematics textbook publishing towards smaller, less expensive and brief introductions to primary courses. The authors move away from the ‘everything for everyone’ approach so common in textbooks. Instead, they provide the reader with coverage of numerous algebraic topics to cover the most important areas of abstract algebra. Through a careful selection of topics, supported by interesting applications, the authors Intend the book to be used for a one-semester course in abstract algebra. It is suitable for an introductory course in for mathematics majors. The text is also very suitable for education majors who need to have an introduction to the topic. As textbooks go through various editions and authors employ the suggestions of numerous well-intentioned reviewers, these book become larger and larger and subsequently more expensive. This book is meant to counter that process. Here students are given a "gentle introduction," meant to provide enough for a course, yet also enough to encourage them toward future study of the topic. Features Groups before rings approach Interesting modern applications Appendix includes mathematical induction, the well-ordering principle, sets, functions, permutations, matrices, and complex nubers. Numerous exercises at the end of each section Chapter "Hint and Partial Solutions" offers built in solutions manual
Book Synopsis Introduction to Abstract Mathematics by : Theodore A. Bick
Download or read book Introduction to Abstract Mathematics written by Theodore A. Bick and published by . This book was released on 1971 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Vectors, Pure and Applied by : T. W. Körner
Download or read book Vectors, Pure and Applied written by T. W. Körner and published by Cambridge University Press. This book was released on 2013 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explains both the how and the why of linear algebra to get students thinking like mathematicians.
Book Synopsis An Introduction to Linear Algebra by : Leonid Mirsky
Download or read book An Introduction to Linear Algebra written by Leonid Mirsky and published by Courier Corporation. This book was released on 1990-01-01 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The straight-forward clarity of the writing is admirable." — American Mathematical Monthly. This work provides an elementary and easily readable account of linear algebra, in which the exposition is sufficiently simple to make it equally useful to readers whose principal interests lie in the fields of physics or technology. The account is self-contained, and the reader is not assumed to have any previous knowledge of linear algebra. Although its accessibility makes it suitable for non-mathematicians, Professor Mirsky's book is nevertheless a systematic and rigorous development of the subject. Part I deals with determinants, vector spaces, matrices, linear equations, and the representation of linear operators by matrices. Part II begins with the introduction of the characteristic equation and goes on to discuss unitary matrices, linear groups, functions of matrices, and diagonal and triangular canonical forms. Part II is concerned with quadratic forms and related concepts. Applications to geometry are stressed throughout; and such topics as rotation, reduction of quadrics to principal axes, and classification of quadrics are treated in some detail. An account of most of the elementary inequalities arising in the theory of matrices is also included. Among the most valuable features of the book are the numerous examples and problems at the end of each chapter, carefully selected to clarify points made in the text.
Book Synopsis Abstract Algebra by : John W. Lawrence
Download or read book Abstract Algebra written by John W. Lawrence and published by Cambridge University Press. This book was released on 2021-04-15 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Through this book, upper undergraduate mathematics majors will master a challenging yet rewarding subject, and approach advanced studies in algebra, number theory and geometry with confidence. Groups, rings and fields are covered in depth with a strong emphasis on irreducible polynomials, a fresh approach to modules and linear algebra, a fresh take on Gröbner theory, and a group theoretic treatment of Rejewski's deciphering of the Enigma machine. It includes a detailed treatment of the basics on finite groups, including Sylow theory and the structure of finite abelian groups. Galois theory and its applications to polynomial equations and geometric constructions are treated in depth. Those interested in computations will appreciate the novel treatment of division algorithms. This rigorous text 'gets to the point', focusing on concisely demonstrating the concept at hand, taking a 'definitions first, examples next' approach. Exercises reinforce the main ideas of the text and encourage students' creativity.
Book Synopsis Sets, Groups, and Mappings: An Introduction to Abstract Mathematics by : Andrew D. Hwang
Download or read book Sets, Groups, and Mappings: An Introduction to Abstract Mathematics written by Andrew D. Hwang and published by American Mathematical Soc.. This book was released on 2019-09-26 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces students to the world of advanced mathematics using algebraic structures as a unifying theme. Having no prerequisites beyond precalculus and an interest in abstract reasoning, the book is suitable for students of math education, computer science or physics who are looking for an easy-going entry into discrete mathematics, induction and recursion, groups and symmetry, and plane geometry. In its presentation, the book takes special care to forge linguistic and conceptual links between formal precision and underlying intuition, tending toward the concrete, but continually aiming to extend students' comfort with abstraction, experimentation, and non-trivial computation. The main part of the book can be used as the basis for a transition-to-proofs course that balances theory with examples, logical care with intuitive plausibility, and has sufficient informality to be accessible to students with disparate backgrounds. For students and instructors who wish to go further, the book also explores the Sylow theorems, classification of finitely-generated Abelian groups, and discrete groups of Euclidean plane transformations.
Book Synopsis Linear Algebra by : James R. Kirkwood
Download or read book Linear Algebra written by James R. Kirkwood and published by CRC Press. This book was released on 2020-11-03 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Algebra, James R. Kirkwood and Bessie H. Kirkwood, 978-1-4987-7685-1, K29751 Shelving Guide: Mathematics This text has a major focus on demonstrating facts and techniques of linear systems that will be invaluable in higher mathematics and related fields. A linear algebra course has two major audiences that it must satisfy. It provides an important theoretical and computational tool for nearly every discipline that uses mathematics. It also provides an introduction to abstract mathematics. This book has two parts. Chapters 1–7 are written as an introduction. Two primary goals of these chapters are to enable students to become adept at computations and to develop an understanding of the theory of basic topics including linear transformations. Important applications are presented. Part two, which consists of Chapters 8–14, is at a higher level. It includes topics not usually taught in a first course, such as a detailed justification of the Jordan canonical form, properties of the determinant derived from axioms, the Perron–Frobenius theorem and bilinear and quadratic forms. Though users will want to make use of technology for many of the computations, topics are explained in the text in a way that will enable students to do these computations by hand if that is desired. Key features include: Chapters 1–7 may be used for a first course relying on applications Chapters 8–14 offer a more advanced, theoretical course Definitions are highlighted throughout MATLAB® and R Project tutorials in the appendices Exercises span a range from simple computations to fairly direct abstract exercises Historical notes motivate the presentation About the Authors James R. Kirkwood holds a PhD from the University of Virginia. He has had over a dozen mathematics textbooks published on various topics including calculus, real analysis, mathematical biology, and mathematical physics. His original research was in mathematical physics, and he co-authored the seminal paper in a topic now called Kirkwood–Thomas Theory in mathematical physics. He has been awarded several National Science Foundation grants. Bessie H. Kirkwood holds PhDs in both mathematics and statistics. She co-authored papers in publications such as the Journal of Algebra and the Journal of Multivariate Analysis. Until retirement, she was a professor of mathematics at Sweet Briar College.
Download or read book Linear Algebra written by G. Viglino and published by . This book was released on 2017-04-15 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is no mathematical ramp that will enable you to continuously inch your way higher and higher in mathematics. The climb calls for a ladder consisting of discrete steps designed to take you from one mathematical level to another. You are about to take an important step on that ladder, one that will take you to a plateau where mathematical abstraction abounds. Linear algebra rests on a small number of axioms (accepted rules, or "laws"), upon which a beautiful and practical theory emerges.
Book Synopsis A (Terse) Introduction to Linear Algebra by : Yitzhak Katznelson
Download or read book A (Terse) Introduction to Linear Algebra written by Yitzhak Katznelson and published by American Mathematical Soc.. This book was released on 2008 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear algebra is the study of vector spaces and the linear maps between them. It underlies much of modern mathematics and is widely used in applications.
Download or read book Linear Algebra written by L. Smith and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is written for a course in linear algebra at the (U.S.) sophomore undergraduate level, preferably directly following a one-variable calculus course, so that linear algebra can be used in a course on multidimensional calculus. Realizing that students at this level have had little contact with complex numbers or abstract mathematics the book deals almost exclusively with real finite-dimensional vector spaces in a setting and formulation that permits easy generalization to abstract vector spaces. The parallel complex theory is developed in the exercises. The book has as a goal the principal axis theorem for real symmetric transformations, and a more or less direct path is followed. As a consequence there are many subjects that are not developed, and this is intentional. However a wide selection of examples of vector spaces and linear trans formations is developed, in the hope that they will serve as a testing ground for the theory. The book is meant as an introduction to linear algebra and the theory developed contains the essentials for this goal. Students with a need to learn more linear algebra can do so in a course in abstract algebra, which is the appropriate setting. Through this book they will be taken on an excursion to the algebraic/analytic zoo, and introduced to some of the animals for the first time. Further excursions can teach them more about the curious habits of some of these remarkable creatures.
Book Synopsis A Concise Introduction to Linear Algebra by : Géza Schay
Download or read book A Concise Introduction to Linear Algebra written by Géza Schay and published by Springer Science & Business Media. This book was released on 2012-03-30 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on the author's previous edition on the subject (Introduction to Linear Algebra, Jones & Bartlett, 1996), this book offers a refreshingly concise text suitable for a standard course in linear algebra, presenting a carefully selected array of essential topics that can be thoroughly covered in a single semester. Although the exposition generally falls in line with the material recommended by the Linear Algebra Curriculum Study Group, it notably deviates in providing an early emphasis on the geometric foundations of linear algebra. This gives students a more intuitive understanding of the subject and enables an easier grasp of more abstract concepts covered later in the course. The focus throughout is rooted in the mathematical fundamentals, but the text also investigates a number of interesting applications, including a section on computer graphics, a chapter on numerical methods, and many exercises and examples using MATLAB. Meanwhile, many visuals and problems (a complete solutions manual is available to instructors) are included to enhance and reinforce understanding throughout the book. Brief yet precise and rigorous, this work is an ideal choice for a one-semester course in linear algebra targeted primarily at math or physics majors. It is a valuable tool for any professor who teaches the subject.
Book Synopsis An Introduction to Abstract Mathematics by : Robert J. Bond
Download or read book An Introduction to Abstract Mathematics written by Robert J. Bond and published by Waveland Press. This book was released on 2007-08-24 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bond and Keane explicate the elements of logical, mathematical argument to elucidate the meaning and importance of mathematical rigor. With definitions of concepts at their disposal, students learn the rules of logical inference, read and understand proofs of theorems, and write their own proofs all while becoming familiar with the grammar of mathematics and its style. In addition, they will develop an appreciation of the different methods of proof (contradiction, induction), the value of a proof, and the beauty of an elegant argument. The authors emphasize that mathematics is an ongoing, vibrant disciplineits long, fascinating history continually intersects with territory still uncharted and questions still in need of answers. The authors extensive background in teaching mathematics shines through in this balanced, explicit, and engaging text, designed as a primer for higher- level mathematics courses. They elegantly demonstrate process and application and recognize the byproducts of both the achievements and the missteps of past thinkers. Chapters 1-5 introduce the fundamentals of abstract mathematics and chapters 6-8 apply the ideas and techniques, placing the earlier material in a real context. Readers interest is continually piqued by the use of clear explanations, practical examples, discussion and discovery exercises, and historical comments.
Book Synopsis Abstract Linear Algebra by : Morton L. Curtis
Download or read book Abstract Linear Algebra written by Morton L. Curtis and published by Springer. This book was released on 1990-07-12 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended for a first course on the subject, this text begins from scratch and develops the standard topics of Linear Algebra. Its progresses simply towards its ultimate goal, the Theorem of Hurwitz, which argues that the only normed algebras over the real numbers are the real numbers, the complex numbers, the quaternions, and the octonions. The book stresses the complete logical development of the subject.
