Mathematics is one of the most basic -- and most ancient -- types of knowledge. Yet the details of its historical development remain obscure to all but a few specialists. The two-volume Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences recovers this mathematical heritage, bringing together many of the world's leading historians of mathematics to examine the history and philosophy of the mathematical sciences in a cultural context, tracing their evolution from ancient times to the twentieth century. In 176 concise articles divided into twelve parts, contributors describe and analyze the variety of problems, theories, proofs, and techniques in all areas of pure and applied mathematics, including probability and statistics. This indispensable reference work demonstrates the continuing importance of mathematics and its use in physics, astronomy, engineering, computer science, philosophy, and the social sciences. Also addressed is the history of higher education in mathematics. Carefully illustrated, with annotated bibliographies of sources for each article, The Companion Encyclopedia is a valuable research tool for students and teachers in all branches of mathematics. Contents of Volume 1: -Ancient and Non-Western Traditions -The Western Middle Ages and the Renaissance -Calculus and Mathematical Analysis -Functions, Series, and Methods in Analysis -Logic, Set Theories, and the Foundations of Mathematics -Algebras and Number Theory Contents of Volume 2: -Geometries and Topology -Mechanics and Mechanical Engineering -Physics, Mathematical Physics, and Electrical Engineering -Probability, Statistics, and the Social Sciences -Higher Education andInstitutions -Mathematics and Culture -Select Bibliography, Chronology, Biographical Notes, and Index