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High Quality Content by WIKIPEDIA articles! Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures. For instance, rather than take particular groups as the object of study, in universal algebra one takes "the theory of groups" as an object of study. From the point of view of universal algebra, an algebra (or algebraic structure) is a set A together with a collection of operations on A. An n-ary operation on A is a function that takes n elements of A and returns a single element of A. Thus, a 0-ary operation (or nullary operation) can be represented simply as an element of A, or a constant, often denoted by a letter like a. A 1-ary operation (or unary operation) is simply a function from A to A, often denoted by a symbol placed in front of its argument, like ~x. A 2-ary operation (or binary operation) is often denoted by a symbol placed between its arguments, like x * y. ... Read more

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High Quality Content by WIKIPEDIA articles! In logic, especially mathematical logic, a signature lists and describes the non-logical symbols of a formal language. In universal algebra, a signature lists the operations that characterize an algebraic structure. In model theory, signatures are used for both purposes. Signatures play the same role in mathematics as type signatures in computer programming. They are rarely made explicit in more philosophical treatments of logic. Formally, a signature can be defined as a triple ? = (Sfunc, Srel, ar), where Sfunc and Srel are disjoint sets not containing any other basic logical symbols. ... Read more

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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. "The straight-forward clarity of the writing is admirable."—American Mathematical Monthly. Bibliography.
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Customer Reviews (2)

Rigorous Linear Algebra
This book provides a rigorous formulation of linear algebra aimed at Mathematics majors. However, the presentation though completely rigorous is essentially elementary, so that is should be accessibe to just about everyone who wants to get more than a superficial algorithmic view of the subject. (E,g. most people know how to calculate determinants but not knowing the abstract definitioon, are not in a position to understand or derive simple properties of determinats that make their manipulation so simple and painless)

Some great strengths of the book: 1st: We have exercises distributed all through the exposition, and these serve to reinforce simple consequences of results and definitions. 2nd: Problems, numerous at the end of each chapter, ranging from simple to really challenging.

Topics covered that many such texts ignore include: Matrix Analysis, Quadratic, Bilinear and Hermitian forms, Matrix Groups, inequalities arising from matrcies. All these in addition to the standard presentations.

A great book, not too abstract, and not too concrete.

The best intermediate linear algebra book
This is the best intermediate linear algebra book that I've in my personal library. I recomend this book to anybody who want to take this subjet seriously. This book is the start point for more advanced studies about linear algebra, but the book, by selft, is no a advanced text.

This is a classic text. Mirsky, was born on December 19 of 1918,are referred in the files of McTutor like a mathematician centered in three investigation areas:

(i) The theory of numbers, where has studied r-free numbers, i.e. numbers not divisible by the r th power of any integer. There is obtained analogues of Vinogradov's result on the representation of an odd integer ace the sum of three you prevail, the Goldbach conjecture on the representation of an even integer ace the sum of two prevails, and the twin prevails conjecture.(ii) to Linear algebra, where has wrote his famous text An introduction to line algebra (this one) (1955) and went on to publish 35 papers on the topic. In matter there is proved results on the existence of main with given eigenvalues and given diagonal elements.(iii) Combinatorics, where has developed you devise coming from Hall's theorem: -

Any person whose tendency is this beautiful and potent branch of the mathematics should have this text in its personal library, at least in what concerns to the classic theory.

Other more modern texts (and also very good as that of Shilov for example) they try to focus the Lineal Algebra in a form more abstract that Mirsky, but for the classic content, this it is my favorite one. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

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High Quality Content by WIKIPEDIA articles! In mathematics and theoretical physics, the term quantum group denotes various kinds of noncommutative algebra with additional structure. In general, a quantum group is some kind of Hopf algebra. There is no single, all-encompassing definition, but instead a family of broadly similar objects.The term "quantum group" often denotes a kind of noncommutative algebra with additional structure that first appeared in the theory of quantum integrable systems, and which was then formalized by Vladimir Drinfel'd and Michio Jimbo as a particular class of Hopf algebra. The same term is also used for other Hopf algebras that deform or are close to classical Lie groups or Lie algebras, such as a `bicrossproduct' class of quantum groups introduced by Shahn Majid a little after the work of Drinfeld and Jimbo. ... Read more