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In this early textbook by mathematician Augustus De Morgan and first published in 1836, serious students of math will find useful lessons, explanations, and diagrams. Math and math textbooks of his time were found to be generally inaccessible to the public at large, so De Morgan, who believed that everyone should be educated in mathematics because it was so essential to science and modern life, relies on simple, straightforward, and easy-to-understand language, despite the depth of his topic. Among the areas covered here are: infinitely small quantities, infinite series, ratios of continuously increasing or decreasing quantities, and algebraical geometry.British mathematician Augustus De Morgan (1806-1871) invented the term mathematical induction. Among his many published works is Trigonometry and Double Algebra and A Budget of Paradoxes.
Practical, concise text covers the existence and uniqueness theorem, characteristics of first-order equations, boundary problems for second-order linear equations, asymptotic methods, and differential equations in the complex field. 1961 edition.
Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure and applied mathematics, as well as physics and engineering should find this textbook useful. Only basic results of one-variable calculus and linear algebra are used, and simple yet pertinent examples and exercises illustrate the usefulness of most theorems. Many of these examples are new or difficult to locate in the literature, and so the original sources of most notions and results are given to help readers understand the development of the field.
For more than two thousand years some familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today the traditional place of mathematics in education is in grave danger. Unfortunately, professional representatives of mathematics share in the reponsibiIity. The teaching of mathematics has sometimes degen erated into empty drill in problem solving, which may develop formal ability but does not lead to real understanding or to greater intellectual indepen dence. Mathematical research has shown a tendency toward overspecialization and over-emphasis on abstraction. Applications and connections with other fields have been neglected . . . But . . . understanding of mathematics cannot be transmitted by painless entertainment any more than education in music can be brought by the most brilliant journalism to those who never have lis tened intensively. Actual contact with the content of living mathematics is necessary. Nevertheless technicalities and detours should be avoided, and the presentation of mathematics should be just as free from emphasis on routine as from forbidding dogmatism which refuses to disclose motive or goal and which is an unfair obstacle to honest effort. (From the preface to the first edition of What is Mathematics? by Richard Courant and Herbert Robbins, 1941.
Includes section "Recent publications."
Founded in 1884, Annals of Mathematics publishes research papers in pure mathematics.