This is a short text in linear algebra, intended for a one-term course. In the first chapter, Lang discusses the relation between the geometry and the algebra underlying the subject, and gives concrete examples of the notions which appear later in the book. He then starts with a discussion of linear equations, matrices and Gaussian elimination, and proceeds to discuss vector spaces, linear maps, scalar products, determinants, and eigenvalues. The book contains a large number of exercises, some of the routine computational type, while others are conceptual.
This is a short text in linear algebra, intended for a one-term course. In the first chapter, Lang discusses the relation between the geometry and the...
Vielleicht waren Sie iiberrascht, wenn jemand behauptete, daB Ma thematik etwas ausgesprochen SchOnes sei. Doch sollten Sie wissen, daB es Leute gibt, die sich ihr ganzes Leben lang mit Mathematik befassen und dort genauso schopferisch tatig sind wie ein Komponist in der Mu sik. Gewohnlich ist der Mathematiker damit beschiiftigt, ein Problem zu lOsen, und aus diesem ergeben sich dann wieder neue, ebenso schone Probleme wie das gerade geloste. N atiirlich sind mathematische Pro bleme oft recht schwierig und - wie in anderen Wissenschaften auc- nur zu verstehen, wenn man das Gebiet griindlich...
Vielleicht waren Sie iiberrascht, wenn jemand behauptete, daB Ma thematik etwas ausgesprochen SchOnes sei. Doch sollten Sie wissen, daB es Leute gibt,...
2014 Reprint of 1959 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. In mathematics, particularly in algebraic geometry, complex analysis and number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular functions. Abelian varieties are at the same time among the most studied objects in algebraic geometry and indispensable tools for much research on other topics in algebraic geometry and number theory. Serge Lang was a French-born American...
2014 Reprint of 1959 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. In mathematics, particularly i...
The aim of this book is to illustrate by significant special examples three aspects of the theory of Diophantine approximations: the formal relationships that exist between counting processes and the functions entering the theory; the determination of these functions for numbers given as classical numbers; and certain asymptotic estimates holding almost everywhere. Each chapter works out a special case of a much broader general theory, as yet unknown. Indications for this are given throughout the book, together with reference to current publications. The book may be used in a course in...
The aim of this book is to illustrate by significant special examples three aspects of the theory of Diophantine approximations: the formal relationsh...