Covers textual and linguistic matters; mathematical analyses of Euclid's ideas; commentators; refutations, supports, extrapolations, reinterpretations and historical notes. Vol. 1 includes Introduction, Books 1-2: Triangles, rectangles.

    It comprises non-technical essays on every aspect of the vast subject, including articles by scores of eminent mathematicians and other thinkers.

    Written by one of the foremost experts on mathematical magic, it employs considerable historical data to summarize all previous work in this field. It is also a creative examination of laws and their exemplification, with scores of new tricks, insights, and demonstrations. Dozens of topological tricks are explained, and dozens of manipulation tricks are aligned with mathematical law.Nontechnical, detailed, and clear, this volume contains 115 sections discussing tricks with cards, dice, coins, etc.; topological tricks with handkerchiefs, cards, etc.; geometrical vanishing effects; demonstrations with pure numbers; and dozens of other topics. You will learn how a Moebius strip works and how a Curry square can "prove" that the whole is not equal to the sum of its parts.No skill at sleight of hand is needed to perform the more than 500 tricks described because mathematics guarantees their success. Detailed examination of laws and their application permits you to create your own problems and effects.

    It was his feeling that a proper analysis of the use of language would clarify concepts and lead to the solution of (what seem to be) philosophical problems.Sometimes, Wittgenstein's expository method is pre-Socratic: a flow of disconnected statements, not unlike Heraclitean fragments, that range from clear aphorisms to cryptic oracles. Elsewhere, there are brief Socratic dialogues with imaginary persons, opponents of equally severe seriousness, representatives of the other half of Wittgenstein strove for total clarity of language as a means of solving philosophical problems, but some of his most meaningful statements here are expressed suggestively, subjectively, poetically.

    The topics covered include, in particular, recurrence, the ergodic theorems, and a general discussion of ergodicity and mixing properties. There is also a general discussion of the relation between conjugacy and equivalence. With minimal prerequisites of some analysis and measure theory, this work can be used for a one-semester course in ergodic theory or for self-study.

    Topics include methods for solving integral equations, finding Green’s function for ordinary or partial differential equations, and for finding the spectral representation of ordinary differential operators. Problems. Appendices. Bibliography.

    Alonzo Church was a pioneer in the field of mathematical logic, whose contributions to number theory and the theories of algorithms and computability laid the theoretical foundations of computer science. His first Princeton book, The Calculi of Lambda-Conversion (1941), established an invaluable tool that computer scientists still use today.Even beyond the accomplishment of that book, however, his second Princeton book, Introduction to Mathematical Logic, defined its subject for a generation. Originally published in Princeton's Annals of Mathematics Studies series, this book was revised in 1956 and reprinted a third time, in 1996, in the Princeton Landmarks in Mathematics series. Although new results in mathematical logic have been developed and other textbooks have been published, it remains, sixty years later, a basic source for understanding formal logic.Church was one of the principal founders of the Association for Symbolic Logic; he founded the Journal of Symbolic Logic in 1936 and remained an editor until 1979 At his death in 1995, Church was still regarded as the greatest mathematical logician in the world.

    Formerly published as "Elements Of Physical Biology", this classic work is the first major attempt to apply modern mathematics to the problems of phylogeny, ontology, ecology, physiology, endocrinology, psychology, and other branches of biology.