Mathematics is often seen only as a tool for science, engineering, and other quantitative disciplines. Lost in the focus on the tools are the intricate interconnecting patterns of logic and ingenious methods of representation discovered over millennia which form the broader themes of the subject. This book, building from the basics of numbers, algebra, and geometry provides sufficient background to make these themes accessible to those not specializing in mathematics. The various topics are also covered within the historical context of their development and include such great innovators as Euclid, Descartes, Newton, Cauchy, Gauss, Lobachevsky, Riemann, Cantor, and Gdel, whose contributions would shape the directions that mathematics would take. The detailed explanations of all subject matter along with extensive references are provided with the goal of allowing readers an entre to a lifetime of the unique pleasures of mathematics.
Topics include the axiomatic development of number systems and their algebraic rules, the role of infinity in the real and transfinite numbers, logic, and the axiomatic path from traditional to non Euclidean geometries. The themes of algebra and geometry are then brought together through the concepts of analytic geometry and functions. With this background, more advanced topics are introduced: sequences, vectors, tensors, matrices, calculus, set theory, and topology. Drawing the common themes of this book together, the final chapter discusses the struggle over the meaning of mathematics in the twentieth century and provides a meditation on its success.
Sobre o autor
Robert G. Bill, Jr. was a researcher in fire and fire protection for twenty–five years at FM Global, a major industrial property insurer which operates the world’s largest full–scale fire research facility. There, he was Assistant Vice President and Director of Research for Fire Hazards and Protection, overseeing research in areas of flammability, fire spread, material reactivity, and fire protection systems. Previous to joining FM Global, he was an Assistant Professor in the Department of Mechanical Engineering at Columbia University conducting research in turbulent combustion. He had received BS, MS and Ph D degrees in Mechanical Engineering from Cornell University. His publications include research in the areas of fluid mechanics, micro–meteorology, combustion, and fire protection. In 1994 and 2003, he received the National Fire Protection Association’s Bigglestone Award for communication of scientific concepts in fire protection. From 2002 to 2008 he served on the executive committee of the International Association for Fire Safety Science and in 2009 was elected as a lifetime honorary member equivalent to the grade of Fellow of the Society of Fire Protection Engineering. Currently retired, Dr. Bill enjoys time with family, community volunteering, playing the violin, and walking his fox terrier while continuing to be fascinated by the universe of mathematics.
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