Optima and Equilibria
An Introduction to Nonlinear Analysis
Buch in deiner Nähe kaufen
Beschreibung
By Way of Warning As in ordinary language, metaphors may be used in mathematics to explain a given phenomenon by associating it with another which is ( or is considered to be) more familiar. It is this sense of familiarity, whether individual or collective, innate or acquired by education, which enables one to convince oneself that one has understood the phenomenon in question. Contrary to popular opinion, mathematics is not simply a richer or more precise language. Mathematical reasoning is a separate faculty possessed by all human brains, just like the ability to compose or listen to music, to paint or look at paintings, to believe in and follow cultural or moral codes, etc. But it is impossible (and dangerous) to compare these various faculties within a hierarchical framework; in particular, one cannot speak of the superiority of the language of mathematics. Naturally, the construction of mathematical metaphors requires the autonomous development of the discipline to provide theories which may be substituted for or associated with the phenomena to be explained. This is the domain of pure mathematics. The construction of the mathematical corpus obeys its own logic, like that of literature, music or art. In all these domains, an aesthetic satisfaction is at once the objective of the creative activity and a signal which enables one to recognise successful works. (Likewise, in all these domains, fashionable phenomena - reflecting social consensus - are used to develop aesthetic criteria).
Progress in the theory of economic equilibria and in game theory has proceeded hand in hand with that of the mathematical tools used in the field, namely nonlinear analysis and, in particular convex analysis. Jean-Pierre Aubin, one of the leading specialists in nonlinear analysis and its application to economics, has written a rigorous and concise - yet still elementary and self-contained - textbook providing the mathematical tools needed to study optima and equilibria, as solutions to problems arising in economics, management sciences, operations research, cooperative and non-cooperative games, fuzzy games etc. The book contains numerous exercises and problems: the latter allow the reader to venture into areas of nonlinear analysis that lie beyond the scope of the book and most courses.
Autor*in
S. Wilson
Stimmen zu »Optima and Equilibria«
From the reviews:
MATHEMATICAL REVIEWS
"…provides a concise and self-contained exposition of the fundamental results both in the theory and its applications…Overall, the book presents a fundamental introduction to nonlinear analysis and its economic and game-theoretic applications. It can serve as a basic textbook for students and researchers interested in these areas."
()