الصفحة 1
الصفحة 1
Metodi Matematici della Fisica = Mathematical Methods of Physics
This text draws its origin from my old notes, prepared for the course of Mathematical Methods of Physics and gradually arranged, refined and updated over the course of many years of teaching. The aim has always been to provide as simple and direct a presentation as possible of the mathematical methods relevant to Physics: Fourier series, Hilbert spaces, linear operators, functions of complex variables, Fourier and Laplace transforms, distributions. In addition to these basic topics, a brief introduction to the first notions of group theory, Lie algebras and symmetries in view of their applications to Physics is presented in the Appendix.
Intégration : Chapitres 7 et 8 = Integration : Chapters 7 and 8
Nicolas BOURBAKI's Elements of Mathematics aim to provide a rigorous, systematic presentation without prerequisites of mathematics from their foundations. applications. The concepts introduced, such as Haar measures and the convolution product, are the basis of harmonic analysis. It includes the chapters: Haar measure; Convolution and representations.
Gruppi : Una introduzione a idee e metodi della Teoria dei Gruppi = Groups : An introduction to the ideas and methods of Group Theory
Born from the university courses of Group Theory held by the author for several years, this book deals with the fundamental arguments of the theory: abelian, nilpotent and solvable groups, free groups, permutations, representations and cohomology. After the first notions, Hölder's program for the classification of finite groups is exposed. A long chapter is dedicated to the action of a group on a set and to the permutations, both under the algebraic and combinatorial aspects, with references to the theory of equations. Some questions of a logical nature are also considered, such as the decidability of the word problem for certain classes of groups. An essential aspect of the book is the presence of a great variety of exercises, about 400, mostly solved.
Group theory : Application to the physics of condensed matter
Every process in physics is governed by selection rules that are the consequence of symmetry requirements. The beauty and strength of group theory resides in the transformation of many complex symmetry operations into a very simple linear algebra. This concise and class-tested book has been pedagogically tailored over 30 years MIT and 2 years at the University Federal of Minas Gerais (UFMG) in Brazil. The approach centers on the conviction that teaching group theory in close connection with applications helps students to learn, understand and use it for their own needs. For this reason, the theoretical background is confined to the first 4 introductory chapters (6-8 classroom hours). From there, each chapter develops new theory while introducing applications so that the students can best retain new concepts, build on concepts learned the previous week, and see interrelations between topics as presented.
Lie Groups : An Approach through Invariants and Representations
Lie groups has been an increasing area of focus and rich research since the middle of the 20th century. Procesi's masterful approach to Lie groups through invariants and representations gives the reader a comprehensive treatment of the classical groups along with an extensive introduction to a wide range of topics associated with Lie groups: symmetric functions, theory of algebraic forms, Lie algebras, tensor algebra and symmetry, semisimple Lie algebras, algebraic groups, group representations, invariants, Hilbert theory, and binary forms with fields ranging from pure algebra to functional analysis.
Classification des Groupes Algébriques Semi-simples = The Classification of Semi-Simple Algebraic Groups
The third volume of the Collected Works of Claude Chevalley assembles his work on semi-simple algebraic groups contained, for the most part, in the notes of the famous "Sminaire Chevalley" held at the Ecole Normale Suprieure in Paris between 1956 and 1958 and written up by participants of the seminar namely, P. Cartier, A. Grothendieck, R. Lazard and J.L. Verdier. These texts have been entirely reset in TeX for this edition, and edited and annotated by Pierre Cartier. Almost 50 years after the original writing, these texts still constitute a choice reference from which to enter
Algèbre, Chapitre 9 = Algebra, Chapter 9
Sesquilinear and quadratic forms : The Mathematics Elements of Nicolas BOURBAKI aim to provide a rigorous, systematic presentation without prerequisites of mathematics from their foundations. This ninth chapter of the Book of Algebra, the second Book of the treatise, is devoted to quadratic, symplectic or Hermitian forms and to associated groups.
AiREAS : Sustainocracy for a healthy city : Phase 3 : Civilian participation – Including the global health deal proposition
This volume describes phase 3 of the AiREAS multidisciplinary cocreation effort to produce a Healthy City. Phase 1 referred to making visible the invisible from an air quality and human exposure perspective. Phase 2 studies air quality related to health and Phase 3 looks at air quality, health and lifestyle from the perspective of persuasion to innovative change. The three books together describe the coming about and first results of the AiREAS "healthy city" cooperative in the city of Eindhoven and Province of North Brabant in the Netherlands. AiREAS is an initiative focused on the multidisciplinary co-creation of healthy cities using the core human value of human health and air quality as guiding principle for profound regional innovation.
