Algebra (Translation of Cours d' Algebre)

Science & Math

Godement, Roger

Mathematics

Houghton/Mifflin

On chercherait en vain un exposé complet de la Théorie des faisceaux, donnant toutes les démonstrations de tous les théorèmes et les donnant en entier. Alors que la technique des faisceaux envahit les branches les plus diverses des mathématiques, pareille situation ne pouvait être tolérée plus longtemps. C'est pourquoi un spécialiste de l'analyse fonctionnelle présente aujourd'hui un exposé complet de la Théorie des faisceaux.

Topologie algébrique et théorie des faisceaux (HR.ACT.SC.INDUS) (French Edition)

Hermann Glassin

Volume III sets out classical Cauchy theory. It is much more geared towards its innumerable applications than towards a more or less complete theory of analytic functions. Cauchy-type curvilinear integrals are then shown to generalize to any number of real variables (differential forms, Stokes-type formulas). The fundamentals of the theory of manifolds are then presented, mainly to provide the reader with a "canonical'' language and with some important theorems (change of variables in integration, differential equations). A final chapter shows how these theorems can be used to construct the compact Riemann surface of an algebraic function, a subject that is rarely addressed in the general literature though it only requires elementary techniques.
Besides the Lebesgue integral, Volume IV will set out a piece of specialized mathematics towards which the entire content of the previous volumes will converge: Jacobi, Riemann, Dedekind series and infinite products, elliptic functions, classical theory of modular functions and its modern version using the structure of the Lie algebra of SL(2,R).

Analysis III: Analytic and Differential Functions, Manifolds and Riemann Surfaces (Universitext)

Springer

Analysis Volume IV introduces the reader to functional analysis (integration, Hilbert spaces, harmonic analysis in group theory) and to the methods of the theory of modular functions (theta and L series, elliptic functions, use of the Lie algebra of SL2). As in volumes I to III, the inimitable style of the author is recognizable here too, not only because of his refusal to write in the compact style used nowadays in many textbooks. The first part (Integration), a wise combination of mathematics said to be `modern' and `classical', is universally useful whereas the second part leads the reader towards a very active and specialized field of research, with possibly broad generalizations.

Analysis IV: Integration and Spectral Theory, Harmonic Analysis, the Garden of Modular Delights (Universitext)

This textbook covers the general theory of Lie groups. By first considering the case of linear groups (following von Neumann's method) before proceeding to the general case, the reader is naturally introduced to Lie theory. Written by a master of the subject and influential member of the Bourbaki group, the French edition of this textbook has been used by several generations of students. This translation preserves the distinctive style and lively exposition of the original. Requiring only basics of topology and algebra, this book offers an engaging introduction to Lie groups for graduate students and a valuable resource for researchers.

Introduction to the Theory of Lie Groups (Universitext)

Les deux premiers volumes sont consacrés aux fonctions dans R ou C, y compris la théorie élémentaire des séries et intégrales de Fourier et une partie de celle des fonctions holomorphes. L'exposé non strictement linéaire, combine indications historiques et raisonnements rigoureux. Il montre la diversité des voies d'accès aux principaux résultats afin de familiariser le lecteur avec les méthodes de raisonnement et idées fondamentales plutôt qu'avec les techniques de calcul, point de vue utile aussi aux personnes travaillant seules.Les volumes 3 et 4 traitent principalement des fonctions analytiques (théorie de Cauchy, théorie analytique des nombres et fonctions modulaires), ainsi que du calcul différentiel sur les variétés, avec un exposé de l'intégrale de Lebesgue, en suivant d'assez près le célèbre cours donné longtemps par l'auteur à l'Université Paris 7.On reconnaîtra dans ce nouvel ouvrage le style inimitable de l'auteur, et pas seulement par son refus de l'écriture condensée en usage dans ce nombreux manuels.

Analyse mathématique II: Calcul différentiel et intégral, séries de Fourier, fonctions holomorphes (French Edition)

Reference

Foreign Language Study & Reference

Zeta Functions of Simple Algebras (Lecture Notes in Mathematics, 260)

Functions in R and C, including the theory of Fourier series, Fourier integrals and part of that of holomorphic functions, form the focal topic of these two volumes. Based on a course given by the author to large audiences at Paris VII University for many years, the exposition proceeds somewhat nonlinearly, blending rigorous mathematics skilfully with didactical and historical considerations. It sets out to illustrate the variety of possible approaches to the main results, in order to initiate the reader to methods, the underlying reasoning, and fundamental ideas. It is suitable for both teaching and self-study. In his familiar, personal style, the author emphasizes ideas over calculations and, avoiding the condensed style frequently found in textbooks, explains these ideas without parsimony of words. The French edition in four volumes, published from 1998, has met with resounding success: the first two volumes are now available in English.

Analysis I: Convergence, Elementary functions (Universitext)

Ces notes de cours donnés il y a une trentaine d'années à Paris mais restées d'actualité couvrent la théorie générale des groupes de Lie, ainsi que quelques points de la théorie des groupes topologiques, groupes discontinus notamment. Ce livre pourra aussi compléter les volumes III et IV de l'Analyse Mathématique du même auteur.

Introduction à la théorie des groupes de Lie (French Edition)

Analysis II: Differential and Integral Calculus, Fourier Series, Holomorphic Functions (Universitext)

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