Fomenko (mathematics, Moscow State U., USSR) uses the current methods of analytical topology to explain some of the solved and unsolved variational problems of topology arising in such fields as mechanics, physics, and mathematics. For graduates and undergraduates in physics and mathematics, he introduces homology, cahomology, and vibration, important topological concepts in physics and mechanics; explores the role of Morse theory in the typology of smooth manifolds, especially of three or four dimensions; discusses minimal surfaces and harmonic mapping; and reviews the classical experiments that underlie modern multidimensional variational calculus. First published in Russian in 1984. Annotation copyright Book News, Inc. Portland, Or.
Many of the modern variational problems in topology arise in different but overlapping fields of scientific study: mechanics, physics and mathematics. In this work, Professor Fomenko offers a concise and clean explanation of some of these problems (both solved and unsolved), using current methods and analytical topology. The author's skillful exposition gives an unusual motivation to the theory expounded, and his work is recommended reading for specialists and nonspecialists alike, involved in the fields of physics and mathematics at both undergraduate and graduate levels.
Arvustused
A superior exposition of topology...If a student (foolishly) wanted to own just one book in topology, I might (sensibly) recommend this one. -H. Cohn of Mathematics Program, Graduate Center, CUNY
Preface,
Chapter I. PRELIMINARIES,
Chapter II. FUNCTIONS ON MANIFOLDS,
Chapter III. MANIFOLDS OF SMALL DIMENSIONS,
Chapter IV. MINIMAL SURFACES, References, Index
Professor Anatolii Fomenko was educated at Moscow State University. He earned his DSc in 1972, and in 1974 he won the Moscow Mathematical Society Award for his doctoral thesis. Professor Fomenko has obtained fundamental results in the fields of geometry, topology and multidimensional variational calculus, and is also a successful teacher and specialist in scientific methodology.
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