New Directions in Applied Mathematics

1. Front Matter

   Pages i-ix

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2. Combinatorics: Trends and Examples

   • Kenneth Baclawski

   Pages 1-10

3. Control Theory and Singular Riemannian Geometry

   • R. W. Brockett

   Pages 11-27

4. On Certain Topological Invariants Arising in System Theory

   • Christopher I. Byrnes, Tyrone E. Duncan

   Pages 29-71

5. Operations Research and Discrete Applied Mathematics

   • D. Kleitman

   Pages 73-79

6. Symplectic Projective Orbits

   • Bertram Kostant, Shlomo Sternberg

   Pages 81-84

7. Four Applications of Nonlinear Analysis to Physics and Engineering

   • Jerrold E. Marsden

   Pages 85-107

8. Bifurcation, Catastrophe, and Turbulence

   • E. C. Zeeman

   Pages 109-153

9. The Emphasis on Applied Mathematics Today and Its Implications for the Mathematics Curriculum

   • Peter J. Hilton

   Pages 155-163

It is close enough to the end of the century to make a guess as to what the Encyclopedia Britannica article on the history of mathematics will report in 2582: "We have said that the dominating theme of the Nineteenth Century was the development and application of the theory of functions of one variable. At the beginning of the Twentieth Century, mathematicians turned optimistically to the study off unctions of several variables. But wholly unexpected difficulties were met, new phenomena were discovered, and new fields of mathematics sprung up to study and master them. As a result, except where development of methods from earlier centuries continued, there was a recoil from applications. Most of the best mathematicians of the first two-thirds of the century devoted their efforts entirely to pure mathe­ matics. In the last third, however, the powerful methods devised by then for higher-dimensional problems were turned onto applications, and the tools of applied mathematics were drastically changed. By the end of the century, the temporary overemphasis on pure mathematics was completely gone and the traditional interconnections between pure mathematics and applications restored. "This century also saw the first primitive beginnings of the electronic calculator, whose development in the next century led to our modern methods of handling mathematics.

• Applied Mathematics
• Invariant
• Mathematik
• calculus
• function
• geometry
• mathematics
• variable

• Department of Mathematics, Case Western Reserve University, Cleveland, USA

  Peter J. Hilton

• Department of Mathematics, University of Wyoming, Laramie, USA

  Gail S. Young

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