Some Vistas of Modern Mathematics

Some Vistas of Modern Mathematics: Dynamic Programming, Invariant Imbedding, and the Mathematical Biosciences

Richard Bellman
Copyright Date: 1968
Pages: 152
https://www.jstor.org/stable/j.ctt130hpsp
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  • Book Info
    Some Vistas of Modern Mathematics
    Book 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.

    eISBN: 978-0-8131-6207-2
    Subjects: Mathematics, Biological Sciences

Table of Contents

  1. Front Matter
    (pp. i-iv)
  2. PREFACE
    (pp. v-viii)
    Richard Bellman
  3. Table of Contents
    (pp. ix-x)
  4. one DYNAMIC PROGRAMMING AND MODERN CONTROL THEORY
    (pp. 1-49)

    Let me state at the outset that this chapter will be resolutely kept on an expository level. As any academic mathematician knows, it is easy to take refuge in complicated equations that present every appearance of profundity. Unfortunately, in addition to boring the reader, this approach would bore me, and my minimum requirement for a lecture is that I be entertained.

    Therefore, instead of the usual “Satz-Beweis” display of erudition, it will be more interesting to roam about in the fields of dynamic programming and control theory, pointing out where some of the problems and ways of solving them arise....

  5. two INVARIANT IMBEDDING AND MATHEMATICAL PHYSICS
    (pp. 50-96)

    Inasmuch as we ended the last chapter on a philosophical note, it is only appropriate to start this one in the same vein.¹ We begin with the hypothesis that a mathematician is basically an irresponsible person. You may smile at this hypothesis; but if you think about it for a moment, comparing the occupation of the mathematician with that of most other inhabitants of other parts of the university or members of other professions, even of the oldest profession, you see that, generally, they perform definite obligations and tasks. The faculty of the medical or engineering school or people in...

  6. three THE CHALLENGE OF THE MATHEMATICAL BIOSCIENCES
    (pp. 97-137)

    Perhaps what a mathematician does in the area of the biosciences requires some explanation. After all, many of you will recall that even as recently as ten years ago, a mathematician was something of a novelty in a department of engineering. Nowadays it is taken for granted that there are advantages to engineering in having the services of these practitioners of the black arts. Furthermore, it is gradually becoming apparent that there is a great deal to be gained for mathematics itself in the investigation of problems arising in the engineering domain. The same situation holds in the biosciences, as...