A prominent and influential mathematician who has received numerous awards wrote this text to remedy a common failing in teaching algebra: the neglect of related instruction in geometry. Based on his many years of experience as an instructor the University of Chicago, author Irving Kaplansky presents a coherent overview of the correlation between these two branches of mathematics, illustrating his topics with an abundance of examples, exercises, ...

These world-renowned authors integrate linear algebra and ordinary differential equations in this unique book, interweaving instructions on how to use MATLAB? with examples and theory. They use computers in two ways: in linear algebra, computers reduce the drudgery of calculations to help students focus on concepts and methods; in differential equations, computers display phase portraits graphically for students to focus on the qualitative ...

<I>Linear Algebra: An Introduction With Mathematica</I> uses a matrix-based presentation and covers the standard topics any mathematician will need to understand linear algebra while using Mathematica. Development of analytical and computational skills is emphasized, and worked examples provide step-by-step methods for solving basic problems using Mathematica. The subject's rich pertinence to problem solving across ...

This second of two volumes gives an up-to-date exposition of the theory of Banach algebras. ...

Basic Linear Algebra is a text for first year students leading from concrete examples to abstract theorems, via tutorial-type exercises. More exercises (of the kind a student may expect in examination papers) are grouped at the end of each section. The book covers the most important basics of any first course on linear algebra, explaining the algebra of matrices with applications to analytic geometry, systems of linear equations, difference ...

A Polynomial Approach to Linear Algebra is a text which is heavily biased towards functional methods. In using the shift operator as a central object, it makes linear algebra a perfect introduction to other areas of mathematics, operator theory in particular. This technique is very powerful as becomes clear from the analysis of canonical forms (Frobenius, Jordan). It should be emphasized that these functional methods are not only of great ...

From April 1999 Notices of the AMS, announcing that the author was awarded the Leroy P. Steele Prize for Mathematical Exposition for his many mathematics books: "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 has affected all subsequent graduate-level algebra books."From MathSciNet's review of the first ...

This text for a second course in linear algebra is aimed at math majors and graduate students. The approach is novel, banishing determinants to the end of the book and focusing on the central goal of linear algebra: understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof ...

Symmetry methods have long been recognized to be of great importance for the study of the differential equations. This book provides a solid introduction to those applications of Lie groups to differential equations which have proved to be useful in practice. The computational methods are presented so that graduate students and researchers can readily learn to use them. Following an exposition of the applications, the book develops the underlying ...

Quaternionische Methoden finden Anwendung bei der Lösung einer breiten Vielfalt physikalischer Probleme, die in 3, 4 oder mehr Dimensionen modelliert werden. Die Autoren füllen mit diesem Buch eine Lücke zwischen rein theoretischer Darstellung und den Wünschen des Anwenders - sie konzentrieren sich auf die Clifford-Algebra und bieten fortgeschrittenen Interessenten eine gut nachvollziehbare Einführung in dieses Gebiet. ...