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Linear Algebra for the Young Mathematician by Steven H. Weintraub Pdf
Linear Algebra for the Young Mathematician is a careful, thorough, and rigorous introduction to linear algebra. It adopts a conceptual point of view, focusing on the notions of vector spaces and linear transformations, and it takes pains to provide proofs that bring out the essential ideas of the subject. It begins at the beginning, assuming no prior knowledge of the subject, but goes quite far, and it includes many topics not usually treated in introductory linear algebra texts, such as Jordan canonical form and the spectral theorem. While it concentrates on the finite-dimensional case, it treats the infinite-dimensional case as well. The book illustrates the centrality of linear algebra by providing numerous examples of its application within mathematics. It contains a wide variety of both conceptual and computational exercises at all levels, from the relatively straightforward to the quite challenging. Readers of this book will not only come away with the knowledge that the results of linear algebra are true, but also with a deep understanding of why they are true.
Fundamentals of Linear Algebra is like no other book on the subject. By following a natural and unified approach to the subject it has, in less than 250 pages, achieved a more complete coverage of the subject than books with more than twice as many pages. For example, the textbooks in use in the United States prove the existence of a basis only for finite dimensional vector spaces. This book proves it for any given vector space. With his experience in algebraic geometry and commutative algebra, the author defines the dimension of a vector space as its Krull dimension. By doing so, most of the facts about bases when the dimension is finite, are trivial consequences of this definition. To name one, the replacement theorem is no longer needed. It becomes obvious that any two bases of a finite dimensional vector space contain the same number of vectors. Moreover, this definition of the dimension works equally well when the geometric objects are nonlinear. Features: Presents theories and applications in an attempt to raise expectations and outcomes The subject of linear algebra is presented over arbitrary fields Includes many non-trivial examples which address real-world problems About the Author: Dr. J.S. Chahal is a professor of mathematics at Brigham Young University. He received his Ph.D. from Johns Hopkins University and after spending a couple of years at the University of Wisconsin as a post doc, he joined Brigham Young University as an assistant professor and has been there ever since. He specializes and has published a number of papers about number theory. For hobbies, he likes to travel and hike, the reason he accepted the position at Brigham Young University
A First Course in Linear Algebra by Kenneth Kuttler,Ilijas Farah Pdf
"A First Course in Linear Algebra, originally by K. Kuttler, has been redesigned by the Lyryx editorial team as a first course for the general students who have an understanding of basic high school algebra and intend to be users of linear algebra methods in their profession, from business & economics to science students. All major topics of linear algebra are available in detail, as well as justifications of important results. In addition, connections to topics covered in advanced courses are introduced. The textbook is designed in a modular fashion to maximize flexibility and facilitate adaptation to a given course outline and student profile. Each chapter begins with a list of student learning outcomes, and examples and diagrams are given throughout the text to reinforce ideas and provide guidance on how to approach various problems. Suggested exercises are included at the end of each section, with selected answers at the end of the textbook."--BCcampus website.
An Introduction to Linear Algebra by L. Mirsky Pdf
Rigorous, self-contained coverage of determinants, vectors, matrices and linear equations, quadratic forms, more. Elementary, easily readable account with numerous examples and problems at the end of each chapter.
A First Course in Linear Algebra by Hal G. Moore,Adil Yaqub Pdf
This text intends to transform students from passive observers of mathematics to participants in it. The book employs a spiral development of ideas to blend the requirements of problem solving, analytical thinking, computational technique, and applications, and emphasizes the interplay of algebraic and geometric concepts. It includes an extensive number of exercises, ranging from routine to challenging. The Third Edition offers 40 percent new material, including manynew applications. It incorporates MATLAB to demonstrate how computational software tools can be used in this field. * Offers a proven, successful approach to Linear Algebra * Contains a practical presentation, illuminating examples, and exceptional exercises, thus enabling instructors to emphasize computational techniques, theoretical material, and applications * Includes a wide variety of effective applications * Provides a student friendly writing style * Begins with the familiar and proceeds to the new in a well-motivated manner * Acknowledges current reforms and proceeds from there * Explains how to solve some examples in MATLAB, demonstrating how such software tools can be used in this field * Includes student projects at close of chapter exercise sets
Introduction to Linear Algebra by Rita Fioresi,Marta Morigi Pdf
Linear algebra provides the essential mathematical tools to tackle all the problems in Science. Introduction to Linear Algebra is primarily aimed at students in applied fields (e.g. Computer Science and Engineering), providing them with a concrete, rigorous approach to face and solve various types of problems for the applications of their interest. This book offers a straightforward introduction to linear algebra that requires a minimal mathematical background to read and engage with. Features Presented in a brief, informative and engaging style Suitable for a wide broad range of undergraduates Contains many worked examples and exercises
Linear Algebra II by Frederick P. Greenleaf,Sophie Marques Pdf
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.
Linear Algebra by R. B. J. T. Allenby,Reg Allenby Pdf
Linear algebra is the most widely taught sub-division of pure mathematics, the basis of equation (and therefore problem) solving. This book includes historical information about the founders of the subject, together with a basic introduction to linear alge
Basic Linear Algebra by Thomas S. Blyth,Edmund F. Robertson Pdf
Basic Linear Algebra is a text for first year students, working from concrete examples towards abstract theorems, via tutorial-type exercises. The book explains the algebra of matrices with applications to analytic geometry, systems of linear equations, difference equations, and complex numbers. Linear equations are treated via Hermite normal forms, which provides a successful and concrete explanation of the notion of linear independence. Another highlight is the connection between linear mappings and matrices, leading to the change of basis theorem which opens the door to the notion of similarity. The authors are well known algebraists with considerable experience of teaching introductory courses on linear algebra to students at St Andrews. This book is based on one previously published by Chapman and Hall, but it has been extensively updated to include further explanatory text and fully worked solutions to the exercises that all 1st year students should be able to answer.
A (Terse) Introduction to Linear Algebra by Yitzhak Katznelson,Yonatan R. Katznelson Pdf
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.
Many books in linear algebra focus purely on getting students through exams, but this text explains both the how and the why of linear algebra and enables students to begin thinking like mathematicians. The author demonstrates how different topics (geometry, abstract algebra, numerical analysis, physics) make use of vectors in different ways and how these ways are connected, preparing students for further work in these areas. The book is packed with hundreds of exercises ranging from the routine to the challenging. Sketch solutions of the easier exercises are available online.
Linear Algebra: A First Course with Applications explores the fundamental ideas of linear algebra, including vector spaces, subspaces, basis, span, linear independence, linear transformation, eigenvalues, and eigenvectors, as well as a variety of applications, from inventories to graphics to Google's PageRank. Unlike other texts on the subject, thi
Elementary Linear Algebra by James R. Kirkwood,Bessie H. Kirkwood Pdf
Elementary Linear Algebra is written for the first undergraduate course. The book focuses on the importance of linear algebra in many disciplines such as engineering, economics, statistics, and computer science. The text reinforces critical ideas and lessons of traditional topics. More importantly, the book is written in a manner that deeply ingrains computational methods.
Elementary Linear Algebra 11th edition gives an elementary treatment of linear algebra that is suitable for a first course for undergraduate students. The aim is to present the fundamentals of linear algebra in the clearest possible way; pedagogy is the main consideration. Calculus is not a prerequisite, but there are clearly labeled exercises and examples (which can be omitted without loss of continuity) for students who have studied calculus.
Welcome to the beginning of this book -- an algebra book that shows and explains further topics than those that are covered in a primary course on linear algebra. Such course usually leaves the student with the question "Why in the world do I have to go through linear algebra?" which is absolutely understandable. Algebra, and other sciences in general, are not entities that one just needs to pass as a course. Sciences are masters that stay with you and are always there whenever you need them, that in some occasions we do not understand that those masters are something else.Before talking about the importance of algebra, let us first clear some details about this text. This book does not only contain a set of complicated equations with heavy definitions about abstract entities and problems that arise in several fields of mathematics, which in many other texts, makes you feel like you're reading Mandarin. This book also contains clear and deductive explanations from different perspectives about those set of complicated equations, with the hope of making them accessible and easy to assimilate for the reader. Algebra is the science of representing life through equations while keeping it simple. The reason for writing this book was, at first, the decision to spread knowledge of such a great science that is usually feared by many young students and ignored by others, when in reality Algebra is a body of knowledge so beautiful within itself, as well as necessary dealing with or approaching many mathematical situations. As this book is being developed, another reason to continue to write it arose - there is a lack of easy-to-understand texts, which are supposed to be the high end books that today's generation are obligated to read, in order to understand the subjects they should know to continue their formation in their respective careers.This book is dedicated to those who really want to learn linear algebra. But be warned, the journey is not promised to be easy as it will require dedication, honesty and time from the reader; but the journey will also be nurturing and revealing in the sense that at the end of each chapter, the reader will be able to say "I've got it " in much the same way when Archimedes said "Eureka " which means "I've found it " In addition, this book also contains techniques and algorithms, along with their derivations and examples, which are used in the real world, thus helping the reader become a well prepared professional.Many texts, articles and lessons were used as resources for this book, however, the most used resource in the development of this text was common sense. You see, mathematics is a free science, a body of knowledge that anyone can derive on its own. This book is just a compendium of the works of many mathematicians through the centuries, making it possible for humankind to get to where it is today. And as life goes on, it is probable that further developments, researches and advances will continue. That was one of the main ideas in the background while writing this text -- to make the reader able to fully understand as much knowledge in linear algebra as possible, especially those concerning methods and algorithms that arose in the twentieth century.Just as a brief comment, the first chapter of this book is dedicated to making certain topics clear to avoid confusion, and answering questions that usually arise during the first course in linear algebra. The rest of the chapters are more advanced and developed.
