Abstract
AMONG the many ways in which the American Mathematical Society has endeavoured to popularise and develop the study of higher mathematics, not the least remarkable and useful is the practice of holding “colloquia” in connection with the summer meetings at intervals of two or three years. It had been felt that the mere reading of a long string of disconnected papers does not produce much lasting impression on the minds of the audience. On the other hand, even a short course of university lectures will often adequately cover a wide range of mathematical study. The society therefore decided in 1896 to arrange for courses of three to six two-hour lectures, each dealing with a substantial part of mathematics. Four such colloquia have been held, at Buffalo in 1896, at Cambridge in 1898, at Ithaca in 1901, and at Boston in 1903. At each of the first three two courses of lectures were given, and Prof. Oskar Bolza's course on “The Simplest Type of Problems in the Calculus of Variations,” given at the Ithaca colloquium of 1901, forms the basis of one of the two volumes before us. The chapters nearly follow the historic order lstid down in the introduction, which is also in close conformity with a logical sequence of treatment. The study of the first and second variations of an integral naturally leads to Weierstrass's examination of the conditions for a minimum and the distinction between a “strong ” and a “weak ” minimum, a terminology introduced by Kneser. The next steps are represented by Weierstrass's theory of parameter representation, Kneser's general theory based on the properties of geodesics, and Hilbert's existence-theorem. For Weierstrass's work (much of which is contained in unpublished courses of lectures) the author has had recourse to his own notes of a course (by Weierstrass) which he attended in 1879, as well as to several other sets of lecture notes, including one on Prof. Schwarz's lectures at Berlin on the same subject.
The Boston Colloquium.
Lectures on Mathematics. By Edward Burr Van Vleck, Henry Seely White, and Frederick Shenstone Woods. Pp. xii + 188. (New York: The Macmillan Company, 1905.) Price 2 dollars net.
Lectures on the Calculus of Variations.
By Dr. Oskar Bolza. Pp. xvi + 272. (Chicago: The University Press, 1904.) Price 4 dollars net.
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The Boston Colloquium Lectures on the Calculus of Variations . Nature 73, 122 (1905). https://doi.org/10.1038/073122a0
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DOI: https://doi.org/10.1038/073122a0