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The Linear Algebra A Beginning Graduate Student Ought To Know

Author: Jonathan S. Golan
Publisher: Springer Science & Business Media
ISBN: 9400726368
Size: 51.13 MB
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Linear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics, both pure and applied, as well as to computer science, to the physical, biological, and social sciences, and to engineering. It encompasses an extensive corpus of theoretical results as well as a large and rapidly-growing body of computational techniques. Unfortunately, in the past decade, the content of linear algebra courses required to complete an undergraduate degree in mathematics has been depleted to the extent that they fail to provide a sufficient theoretical or computational background. Students are not only less able to formulate or even follow mathematical proofs, they are also less able to understand the mathematics of the numerical algorithms they need for applications. Certainly, the material presented in the average undergraduate course is insufficient for graduate study. This book is intended to fill the gap which has developed by providing enough theoretical and computational material to allow the advanced undergraduate or beginning graduate student to overcome this deficiency and be able to work independently or in advanced courses. The book is intended to be used either as a self-study guide, a textbook for a course in advanced linear algebra, or as a reference book. It is also designed to prepare a student for the linear algebra portion of prelim exams or PhD qualifying exams. The volume is self-contained to the extent that it does not assume any previous formal knowledge of linear algebra, though the reader is assumed to have been exposed, at least informally, to some of the basic ideas and techniques, such as manipulation of small matrices and the solution of small systems of linear equations over the real numbers. More importantly, it assumes a seriousness of purpose, considerable motivation, and a modicum of mathematical sophistication on the part of the reader. In the latest edition, new major theorems have been added, as well as many new examples. There are over 130 additional exercises and many of the previous exercises have been revised or rewritten. In addition, a large number of additional biographical notes and thumbnail portraits of mathematicians have been included.

Linear Algebra

Author: Fuzhen Zhang
Publisher: JHU Press
ISBN: 9780801854590
Size: 36.64 MB
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"Linear algebra is an increasingly important part of any curriculum in mathematics in our days... A well-organized problem book, like this, will surely be welcomed by students as well as by instructors." -- Zentralblatt fuer Mathematik

Basic Linear Algebra

Author: Thomas S. Blyth
Publisher: Springer Science & Business Media
ISBN: 1447134966
Size: 53.91 MB
Format: PDF, ePub, Docs
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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.

Numerical Analysis

Author: David Ronald Kincaid
Publisher: American Mathematical Soc.
ISBN: 0821847880
Size: 32.93 MB
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This book introduces students with diverse backgrounds to various types of mathematical analysis that are commonly needed in scientific computing. The subject of numerical analysis is treated from a mathematical point of view, offering a complete analysis of methods for scientific computing with appropriate motivations and careful proofs. In an engaging and informal style, the authors demonstrate that many computational procedures and intriguing questions of computer science arise from theorems and proofs. Algorithms are presented in pseudocode, so that students can immediately write computer programs in standard languages or use interactive mathematical software packages. This book occasionally touches upon more advanced topics that are not usually contained in standard textbooks at this level.

The Linear Algebra A Beginning Graduate Student Ought To Know

Author: CTI Reviews
Publisher: Cram101 Textbook Reviews
ISBN: 146725388X
Size: 71.69 MB
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Facts101 is your complete guide to The Linear Algebra A Beginning Graduate Student Ought To Know. In this book, you will learn topics such as as those in your book plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.

Linear Algebra For Dummies

Author: Mary Jane Sterling
Publisher: John Wiley & Sons
ISBN: 0470538163
Size: 77.62 MB
Format: PDF, Docs
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Learn to: Solve linear algebra equations in several ways Put data in order with matrices Determine values with determinants Work with eigenvalues and eigenvectors Your hands-on guide to real-world applications of linear algebra Does linear algebra leave you feeling lost? No worries —this easy-to-follow guide explains the how and the why of solving linear algebra problems in plain English. From matrices to vector spaces to linear transformations, you'll understand the key concepts and see how they relate to everything from genetics to nutrition to spotted owl extinction. Line up the basics — discover several different approaches to organizing numbers and equations, and solve systems of equations algebraically or with matrices Relate vectors and linear transformations — link vectors and matrices with linear combinations and seek solutions of homogeneous systems Evaluate determinants — see how to perform the determinant function on different sizes of matrices and take advantage of Cramer's rule Hone your skills with vector spaces — determine the properties of vector spaces and their subspaces and see linear transformation in action Tackle eigenvalues and eigenvectors — define and solve for eigenvalues and eigenvectors and understand how they interact with specific matrices Open the book and find: Theoretical and practical ways of solving linear algebra problems Definitions of terms throughout and in the glossary New ways of looking at operations How linear algebra ties together vectors, matrices, determinants, and linear transformations Ten common mathematical representations of Greek letters Real-world applications of matrices and determinants

Quantum Calculus

Author: Victor Kac
Publisher: Springer Science & Business Media
ISBN: 1461300711
Size: 32.16 MB
Format: PDF
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Simply put, quantum calculus is ordinary calculus without taking limits. This undergraduate text develops two types of quantum calculi, the q-calculus and the h-calculus. As this book develops quantum calculus along the lines of traditional calculus, the reader discovers, with a remarkable inevitability, many important notions and results of classical mathematics. This book is written at the level of a first course in calculus and linear algebra and is aimed at undergraduate and beginning graduate students in mathematics, computer science, and physics. It is based on lectures and seminars given by MIT Professor Kac over the last few years at MIT.

A Course In Algebra

Author: Ėrnest Borisovich Vinberg
Publisher: American Mathematical Soc.
ISBN: 0821833189
Size: 37.64 MB
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This is a comprehensive textbook on modern algebra written by an internationally renowned specialist. It covers material traditionally found in advanced undergraduate and basic graduate courses and presents it in a lucid style. The author includes almost no technically difficult proofs, and reflecting his point of view on mathematics, he tries wherever possible to replace calculations and difficult deductions with conceptual proofs and to associate geometric images to algebraic objects.The effort spent on the part of students in absorbing these ideas will pay off when they turn to solving problems outside of this textbook. Another important feature is the presentation of most topics on several levels, allowing students to move smoothly from initial acquaintance with the subject to thorough study and a deeper understanding. Basic topics are included, such as algebraic structures, linear algebra, polynomials, and groups, as well as more advanced topics, such as affine and projective spaces, tensor algebra, Galois theory, Lie groups, and associative algebras and their representations. Some applications of linear algebra and group theory to physics are discussed. The book is written with extreme care and contains over 200 exercises and 70 figures. It is ideal as a textbook and also suitable for independent study for advanced undergraduates and graduate students.

Lie Groups Lie Algebras And Representations

Author: Brian Hall
Publisher: Springer
ISBN: 3319134671
Size: 37.90 MB
Format: PDF
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This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject. In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a self-contained construction of the representations of compact groups, independent of Lie-algebraic arguments The second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincaré–Birkhoff–Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula. Review of the first edition: This is an excellent book. It deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group theory ... an important addition to the textbook literature ... it is highly recommended. — The Mathematical Gazette