Some Vistas of Modern Mathematics: Dynamic Programming, Invariant Imbedding, and the Mathematical Biosciences by Richard Bellman (PDF)

Description

Rapid advances in the physical and biological sciences and in related technologies have brought about equally farreaching changes in mathematical research. Focusing on control theory, invariant imbedding, dynamic programming, and quasilinearization, Mr. Bellman explores with ease and clarity the mathematical research problems arising from scientific questions in engineering, physics, biology, and medicine. Special attention is paid in these essays to the use of the digital computer in obtaining the numerical solution of numerical problems, its influence in the formulation of new and old scientific problems in new terms, and to some of the effects of the computer revolution on educational and social systems. The new opportunities for mathematical research presage, Bellman concludes, a renaissance of mathematics in human affairs by involving it closely in the problems of society.

User’s Reviews

Editorial Reviews: About the Author Richard Bellman is a professor of mathematics, electrical engineering, and medicine at the University of Southern California.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Richard Bellman (1920 – 1984) was one of the most prolificmathematicians. His early interest in pure mathematics was sooneclipsed by a consuming passion for applications. He had great talent,lots of energy, and the good fortune to be part of the most fertilecentres of mathematics and its applications: Los Alamos during theSecond World War, Princeton University and the RAND Corporation shortlyafter. Bellman is credited, among other things, with the invention ofDynamic Programming.This book is based on the lectures Bellman delivered to a generalaudience at the University of Kentucky. The book is unusual in that itcontains a little bit of substantial mathematics as well as muchexposition of the context of mathematics and the philosophy ofBellman’s approach to mathematics. The mathematics can be followed byanyone who has taken a course in calculus. Yet it brings across theessence of the ideas that were a breakthrough when Bellman developedthem in the 1950s. His contribution of invariant imbedding, forexample, is illustrated by alternative treatments of the problem ofdetermining how high a stone will go if you throw it upwards with agiven velocity. This is example is simple enough for a first calculuscourse.Even if you skip the few formulas, then you’ll still be rewarded byBellman’s masterly discourse on context and background. You will findit a joy to read and think: “I didn’t know a scientist could writelike this.”

⭐The subject-matter seems that of a physicist or a controls professor, not at all of a mathematician. Also there is a lot of unnecessary, pro-gradualism (institutional, communistic ) statements made throughout the text. In fact, the whole text, should be considered as verging on the edge of disaster. I feel only someone with some very modern, hard-core controls training and scholarship would really benefit much from reading this book. Even though it is obviously aimed at anyone with a first-year or even high-school calculus background.My only real hope that the writing style of my reviews aren’t this narcisisstic. I hope that in the performance control problem of life that my riding of its uni-cycle while I toss a ball doesn’t annoy my core audience as much as this core fan was annoyed by this book.

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