Interpolation and approximation offer important applications in computer science and elsewhere. This intermediate-level survey abounds in useful examples of related subjects, starting with remainder theory, convergence theorems, and uniform and best approximation. Other topics include least square approximation, Hilbert space, orthogonal...
This book has developed from a one-term course in differential geometry given for juniors, seniors, and graduate students at the Massachusetts Institute of Technology. It presents the fundamental conceptions of the theory of curves and surfaces and applies them to a number of examples. Some care is given to historical, biographical, and...
After the appearance in 1952 of my "Introduction to Metamathematics",
written for students at the first-year graduate level, I had no expectation of
writing another text. But various occasions arose which required me to
think about how to present parts of the same material more briefly, to a
more...
Problems that beset Archimedes, Newton, Euler, Cauchy, Gauss, Monge and other greats, ready to challenge today’s would-be problem solvers. Among them: How is a sundial constructed? How can you calculate the logarithm of a given number without the use of logarithm table? No advanced math is required. 100 problems with proofs.
Stimulating collection of over 300 unusual problems involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms and more. Problems range from easy to difficult. Detailed solutions, as well as brief answers, for all problems are provided.
This text for upper-level undergraduates and graduate students examines the events that led to a 19th-century intellectual revolution: the reinterpretation of the calculus undertaken by Augustin-Louis Cauchy and his peers. These intellectuals transformed the uses of calculus from problem-solving methods into a collection of well-defined...
Experiment with cryptography — the science of secret writing. Cipher and decipher codes: transposition and polyalphabetical ciphers, famous codes, typewriter and telephone codes, codes that use playing cards, knots, and swizzle sticks...even invisible writing and sending messages through outer space. Hours of intrigue and challenge. 45...
This text features Leibniz's own accounts of his work and comprises critical and historical notes and essays. An informative Introduction leads to the "postscript" to Leibniz's 1703 letter to James Bernoulli, his "Historia et Origio Calculi Differentialis," and manuscripts of the period 1673-77. Essays by C. I....
IN recent years there has been a strong revival of interest in the foundations of statistical mechanics, and a great deal of important work has been done both in this country and abroad.
"The Conceptual Foundations of Statistical Mechanics" is the title of a celebrated article which the late Paul Ehrenfest prepared in...
Tms book deals with the geometry of the triangle and the circle, as developed extensively in the nineteenth century by British and Continental writers. This geometry, based entirely on the elementary plane geometry of Euclid or its modern equivalent, is rapidly coming to its due recognition as excellent material for college courses. Perhaps in no...
This text illustrates the fundamental simplicity of the properties of orthogonal functions and their developments in related series. Begins with a definition and explanation of the elements of Fourier series, and examines Legendre polynomials and Bessel functions. Also includes Pearson frequency functions and chapters on orthogonal,...
Since 1934 the analytic theory of numbers has been largely transformed by the \vork of Vinogradov. This \vork, which has led to remarkable ne\v results, is characterized by its supreme ingenuity and great power.
Vinogradov has expounded his method and its applications in a series of papers and in two monographs 1), which appeared in 1937...