Israel M. Gel'fand

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The theory of optimal design of experiments as we know it today is built on asolid foundation developed by Jack Kiefer, who formulated and resolved some of the major problems of data collection via experimentation. A principal ingredient in his formulation was statistical efficiency of a design. Kiefer's theoretical contributions to optimal designs can be broadly classified into several categories: He rigorously defined, developed, and interrelated statistical notions of optimality. He developed powerful tools for verifying and searching for optimal designs; this includes the "averaging technique"... for approximate or exact theory, and "patchwork"... for exact theory... Kiefer and Wolfowitz provided a theorem now known as the Equivalence Theorem. This result has become a classical theorem in the field. One important feature of this theorem is that it provides a measure of how far a given design is from the optimal design. He characterized and constructed families of optimal designs. Some of the celebrated ones are balanced block designs, generalized Youden designs, and weighing designs. He also developed combinatorial structures of these designs.

#3

Trigonometry, a work in the collection of the Gelfand School Program, is the result of a collaboration between two experienced pre-college teachers, one of whom, I.M. Gelfand, is considered to be among our most distinguished living mathematicians. His impact on generations of young people, some now mathematicians of renown, continues to be remarkable. Trigonometry covers all the basics of the subject through beautiful illustrations and examples. The definitions of the trigonometric functions are geometrically motivated. Geometric relationships are rewritten in trigonometric form and extended. The text then makes a transition to the study of algebraic and analytic properties of trigonometric functions, in a way that provides a solid foundation for more advanced mathematical discussions. Throughout, the treatment stimulates the reader to think of mathematics as a unified subject. Like other I.M. Gelfand treasures in the program—Algebra, Functions and Graphs, and The Method of Coordinates—Trigonometry is written in an engaging style, and approaches the material in a unique fashion that will motivate students and teachers alike. From a review of Algebra, I.M. Gelfand and A. Shen, ISBN 0-8176-3677-3: "The idea behind teaching is to expect students to learn why things are true, rather than have them memorize ways of solving a few problems, as most of our books have done. [This] same philosophy lies behind the current text by Gel'fand and Shen. There are specific 'practical' problems but there is much more development of the ideas.... [The authors] have shown how to write a serious yet lively book on algebra." —R. Askey, The American Mathematics Monthly