Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. Stöbere im größten eBookstore der Welt und lies noch heute im Web, auf deinem Tablet, Telefon oder E-Reader. The last part of the volume is devoted to various "topics" such as Hilbert spaces, tensor products (including a treatment of the determinant as an antisymmetric n-linear form), affine geometry, QR and singular value decompositions, and the umbral calculus ("the first time that this subject has appeared in a true textbook").The development of the subject is elegant, positively Bourbakian. (My personal pick for reference) This is a formidable volume, a compendium of linear algebra theory, classical and modern, intended for "the graduate or advanced undergraduate student." "Lang's Algebra changed the way graduate algebra is taught, retaining classical topics but introducing language and ways of thinking from category theory and homological algebra. It successfully addresses the basic concepts of algebra. How? The book ends with a few applications to analysis (Halmos’s true interest in the subject) and a brief summary of what is needed to extend this theory to Hilbert spaces.This seems to be the standard choice for honors undergraduate courses in the US these days. Abstract Algebra by Dummit and Foote.
Algebra by T.Hungerford (Springer). (2 Volumes.) Download our free books and answer all your questions. Betst linear algebra books. Do not just copy these solutions. The applications cover many areas of science, business, and engineering, with a lot of dynamical systems examples. Blyth, T. S., & Robertson, E. F. (1984). Algebra through practice: A collection of problems in algebra, with solutions. If you want something more applied and less theoretical than the above three books, this is the best linear algebra textbook for you.Great for self-study. Instead it focuses on linear operators, primarily in finite-dimensional spaces but in many cases for general vector spaces. But it is quite affordable. But the book also does a good job of moving up and down between various levels of abstraction, according to which level makes the problem at hand easier to comprehend, and geometrical examples and rotations play an important role in the exposition.This book is the text for Massachusetts Institute of Technology’s Linear Algebra course 18.06, whose goals are “using matrices and also understanding them.” There’s enough material in the book for a year-long course, and the MIT course covers primarily the first seven chapters. It is primarily about linear transformations, and despite the title most of the theorems and proofs work for arbitrary vector spaces.The book does start from the beginning and assumes no prior knowledge of the subject. I would suggest starting with a basic level textbook and then put more effort on one or two intermediate level textbooks. He also has taken the time to point you to useful videos on YouTube that are relevant to the section's material, which is a huge time saver. After a concise (30-page) treatment of set theory and basic algebraic structures, the author embarks on a two-chapter whirlwind tour of introductory linear algebra, including an optional discussion of topological vector spaces. First, the title is the truth. Our authors have contributed textbooks for all levels. None of this goes into enough depth to make you an expert (that would be impossible in a one-semester introductory course), or even able to tackle such applications on your own, but it does give you a good understanding of how linear algebra is used and why it is important.This is the only book I've found that can take you from absolute beginner to confident intermediate in just a few weeks. But it is an unsurpassed text for highly gifted kids who intend to do graduate school right and then go on to do real mathematics.This is a classic but still useful introduction to modern linear algebra. Algebra by Michael Artin. But it has no pictures, no worked examples, no discussion of algorithms or numerical methods, and very little motivation. Basic. It has affected all subsequent graduate-level algebra books."
The proofs are neat, whereas the examples are sparse and would have to be supplemented by the instructor.
This book can make you feel smarter than you are, because there are no ugly surprises in the exercise sections and each new section builds from its predecessors.Problems which provide results used later in the textbook are (usually) marked.
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