J. N. Kapur

The golden ellipse

The concepts of golden section, golden ratio, golden rectangle and golden spirals have fascinated mathematicians for centuries. It is hoped that the concept of a golden ellipse introduced below for the first time will be found to be equally fascinating.

Some problems in biomathematics

Biomathematics is an emerging and dynamic field of mathematics, providing a large number of problems which can enrich mathematics education in science and technology. Some of the problems with such educational and pedagogical value are considered here. These include problems from medicine, genetics, ecology, epidemiology, internal and external biofluid‐dynamics, and neurophysiology. More than a dozen other problems are briefly mentioned.

The golden rectangle revisited

The asymptotic approach of a certain sequence of rectangles (rectangular parallelepipeds/hyperparallelepipeds) to a golden rectangle (rectangular paral‐lelepiped/hyperparallelepiped) is considered.

Optimization in Mathematics, Statistics, Economics, Operations Research, Science and Technology.

The present paper examines the role of optimization in mathematical, physical, biological, social and management sciences and makes a strong plea for this concept being given a central place in the mathematics education of scientists and technologists.

Culture, Excitement and Relevance of Mathematics.

The author discusses some relationships between mathematical, scientific and humanistic cultures. Consideration is given to the acquisition of mathematical concepts, what we mean by mathematical culture and what material could be included in a course on culture, excitement and relevance of mathematics for undergraduate mathematics students.

Difference equation models in ecology and epidemiology

In this paper a plea is made for introducing difference equation models in ecology and epidemics at the high school stage to enliven the teaching of mathematics at this stage and to convince future scientists and engineers that even simple algebra can give deep insight into natural phenomena. These models also provide simple but meaningful examples for the use of hand‐held calculators and computer programming.

Proposal for a course on the nature of mathematical thinking

The introduction into the Indian secondary school curriculum of a course on the nature of mathematical thinking is discussed in this paper.

Mathematical models in medical sciences

† Invited Lecture given at the Third International Congress of Mathematics Modelling held at University of Southern California on 29‐31 August 1981. This paper gives a brief survey of some of the mathematical models for the following problems: (i) pulsatile blood flows in rigid and elastic tubes; (ii) blood flows in arteries with stenosis; (iii) peristaltic flows in tubes and channels; (iv) gas flows in lung airways; (v) oxygen diffusion through the living tissues; (vi) diffusion in dialysers; (vii) fluid flow in renal tubules; (viii) lubrication in human joints; and (ix) deterministic and stochastic compartment analysis.

Optimal portfolio selection

Optimal Portfolio Theory, as developed during the last twenty‐seven years, represents an important application of mathematics to a very useful field and as such should find its proper place in the education of mathematicians, economists, actuaries, business managers, scientists and engineers. The present article gives a tutorial introduction to Markowitzs basic idea of mean‐variance efficient portfolios and his critical‐line method for obtaining them. A new and simpler approach to implementation of critical line method is given. Some ideas from Pareto optimization are used to get a better insight into the theory. Implication of Maximum Expected Utility and other possible criteria are discussed. The last section gives a list of open problems in the field.