Popularizing Mathematical Methods in the People’s Republic of China: Some Personal Experiences(2 Mathematical Modeling)

Professor Hua Loo-Keng is the first person to have undertaken the task of popularizing mathematical methods in China. As early as 1958, he proposed that the application of operations research methods be initiated in industrial production. With his students, Yu Ming-I, Wan Zhe Xian and Wang Yuan, Professor Hua visited various transportation departments to promote mathematical methods for dealing with transportation problems, and a mass campaign was organized by them and other mathematicians to advance and apply linear programming methods to industrial production in Beijing and in Shandong province. However, due to the fact that these methods have limited applications and their computation is rather complex, their popularization and utilization in China have so far been restricted to a small number of sectors such as the above mentioned transportation departments. In 1958 Hua Loo--Keng proposed the use of Input-Output methods in the formulation of national economic plans. Apart from publicizing this method, he carried out in-depth research on the subject. He also gave lectures on related non-negative matrix theory, pointing out the economic significance of various theoretical results.

Table of Contents:
0 Introduction.- § 0.1 Three principles.- § 0.2 Looking for problems in the literature.- § 0.3 Looking for problems in the workshop.- § 0.4 Optimum seeking methods (O.S.M).- § 0.5 The Fibonacci search.- § 0.6 The golden number and numerical integration.- § 0.7 Overall planning methods.- § 0.8 On the use of statistics.- § 0.9 Concluding remarks.- 1 On the Calculation of Mineral Reserves and Hillside Areas on Contour Maps.- § 1.1 Introduction.- § 1.2 Calculation of mineral reserves.- § 1.3 Calculation of hillside areas.- References.- 2 The Meshing Gear-Pair Problem.- § 2.1 Introduction.- § 2.2 Simple continued fractions.- § 2.3 Farey series.- § 2.4 An algorithm for the problem.- § 2.5 The solution to the meshing gear-pair problem.- References.- 3 Optimum Seeking Methods (single variable).- § 3.1 Introduction.- § 3.2 Unimodal functions.- § 3.3 Method of trials by shifting to and fro.- § 3.4 The golden section method.- § 3.5 The proof of Theorem 3.1.- § 3.6 The Fibonacci search.- § 3.7 The proof of Theorem 3.2.- § 3.8 The bisection method.- § 3.9 The parabola method.- References.- 4 Optimum Seeking Methods (several variables).- § 4.1 Introduction.- § 4.2 Unimodal functions (several variables).- § 4.3 The bisection method.- § 4.4 The successive approximation method.- § 4.5 The parallel line method.- § 4.6 The discrete case with two factors.- § 4.7 The equilateral triangle method.- § 4.8 The gradient method.- § 4.9 The paraboloid method.- § 4.10 Convex bodies.- § 4.11 Qie Kuai Fa.- §4.12 The 0–1 variable method.- References.- 5 The Golden Number and Numerical Integration.- § 5.1 Introduction.- § 5.2 Lemmas.- § 5.3 Error estimation for the quadrature formula.- § 5.4 A result for 0 and a lower bound for the quadrature formula.- § 5.5Remarks.- References.- 6 Overall Planning Methods.- § 6.1 Introduction.- § 6.2 Critical Path Method.- § 6.3 Float.- § 6.4 Parallel operations and overlapping operations.- § 6.5 Manpower scheduling.- References.- 7 Program Evaluation and Review Technique (Pert).- § 7.1 Introduction.- § 7.2 Estimation of the probability.- § 7.3 Computation process.- § 7.4 An elementary approach.- § 7.5 Remarks.- References.- 8 Machine Scheduling.- § 8.1 Introduction.- § 8.2 Two-machine problem.- § 8.3 A lemma.- § 8.4 Proof of Theorem 8.1.- References.- 9 The Transportation Problem (Graphical Method).- § 9.1 Introduction.- § 9.2 One cycle.- § 9.3 Proof of Theorem 9.1.- References.- 10 The Transportation Problem (Simplex Method).- § 10.1 Introduction.- § 10.2 Eliminated unknowns and feasible solutions.- § 10.3 Criterion numbers.- § 10.4 A criterion for optimality.- § 10.5 Characteristic numbers.- § 10.6 Substitution.- § 10.7 Linear programming.- References.- 11 The Postman Problem.- § 11.1 Introduction.- § 11.2 Euler paths.- § 11.3 A necessary and sufficient criterion for an optimum solution.- References.