Serge Lang Bücher

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 number theory, whose students will thus be put in contact with interesting but accessible problems on the ground floor of mathematics.

InhaltsverzeichnisWer ist Serge Lang?.Lieber Christopher, liebe Rachel, Sylvain, Yaelle und alle anderen!.Was ist pi?.Das Volumen in höheren Dimensionen.Das Volumen der Kugel.Der Umfang des Kreises.Die Oberfläche der Kugel.Pythagoreische Tripel.Unendlich.Postscriptum.

InhaltsverzeichnisWomit beschäftigt sich ein reiner Mathematiker und warum? Primzahlen.Ein lebendiges Tun: Mathematik betreiben Diophantische Gleichungen.Große Probleme der Geometrie und des Raumes.

This calculus textbook aims to introduce students to the fundamental concepts of derivatives and integrals, balancing accessibility with necessary technical exercises. It is designed for beginners rather than advanced mathematicians, providing a pleasant learning experience while maintaining essential rigor in the subject matter.

Based on the work in algebraic geometry by Norwegian mathematician Niels Henrik Abel (1802–29), this monograph was originally published in 1959 and reprinted later in author Serge Lang's career without revision. The treatment remains a basic advanced text in its field, suitable for advanced undergraduates and graduate students in mathematics. Prerequisites include some background in elementary qualitative algebraic geometry and the elementary theory of algebraic groups. The book focuses exclusively on Abelian varieties rather than the broader field of algebraic groups; therefore, the first chapter presents all the general results on algebraic groups relevant to this treatment. Each chapter begins with a brief introduction and concludes with a historical and bibliographical note. Topics include general theorems on Abelian varieties, the theorem of the square, divisor classes on an Abelian variety, functorial formulas, the Picard variety of an arbitrary variety, the I-adic representations, and algebraic systems of Abelian varieties. The text concludes with a helpful Appendix covering the composition of correspondences.

Focusing on the infinite dimensional representation theory of semisimple Lie groups, this book specifically examines SL2(R). It highlights the importance of this area in relation to fields like number theory, particularly through Langlands' work. The text aims to simplify the complexities of representation theory, which has evolved rapidly, making it challenging for newcomers. With only basic prerequisites in real analysis and differential equations, it is designed to be accessible to a broad audience, facilitating entry into this advanced subject.

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.