Geometric quantizations in action: N. E. Hurt, Reidel, 1983, 336 pp.

✍ Scribed by Gian-Carlo Rota

• Book ID: 102624427
• Publisher: Elsevier Science
• Year: 1983
• Tongue: English
• Weight: 46 KB
• Volume: 50
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1016/0001-8708(83)90041-5

✦ Synopsis

Book Reviews D. J. NEWMAN, A Problem Seminar, Springer, 1983, 113 pp. The master has written his masterpiece at last. The book is short, but every single problem is a jewel. We thought Polya and Szegii could not be beaten, but we were wrong. S. IITAKA, Algebraic Geometry, Springer, 1982, 327 pp. Algebraic geometry is coming of age, and the introductions to the subject are getting better. To be sure, they are never easy to read. The subject is difficult to motivate, but it is so venerable that one feels inclined to engage in the non-trivial effort of reading, especially when the presentation is self-contained, as it is here.

N. E. HURT, Geometric Quantizations in Action, Reidel, 1983, 336 pp. An attempt to bring over to the physicist the language of contemporary geometry, not an easy task. Symplectic manifolds, Borel-Weil theory, geometric quantization, automorphic forms, the Selberg trace formula. C. C. ELGOT, Selected Papers, Springer, 1982, 460 pp. Elgot was one of the first to realize the potential applications of combinatorics and universal algebra to computer science. His influence was at first slow, but now that such applications are in full swing, this selection of his papers comes at the right time to be read and appreciated.

H. BERGSTROM, Weak Convergence of Measures, Academic Press, 1982, 245 pp. Weak convergence of distribution functions is the heart of probability, and one of its permanent contributions to mathematics. No mere functional analyst could ever have thought of the invariance principle. Here we find the latest developments of a sequence that is still a long way from the end.