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The Role of Mathematics in Science aims to illustrate the many ways in which mathematical methods have helped discovery in science. It is aimed at a group of readers who are interested in mathematics beyond the level of high school. The authors occasionally use some calculus and more intricate arguments. The book should appeal to college students and general readers with some background in mathematics. The authors state that, 'If we succeed in giving an impression of the beauty and power of mathematical reasoning in science, the purpose of our work will have been achieved.' This book includes the laws of levers and inclined planes, the laws of exponential versus limited population growth, ray optics, and relativity.

Mathematical physics. --- Mathematics. --- Science.

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The first of its kind, this book presents a widely accessible exposition of topos theory, aimed at the philosopher-logician as well as the mathematician. It is suitable for individual study or use in class at the graduate level (it includes 500 exercises). It begins with a fully motivated introduction to category theory itself, moving always from the particular example to the abstract concept. It then introduces the notion of elementary topos, with a wide range of examples and goes on to develop its theory in depth, and to elicit in detail its relationship to Kripke's intuitionistic semantics,

Mathematical logic --- Toposes. --- Topoi (Mathematics) --- Categories (Mathematics) --- Toposes

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Mathematical statistics --- Probabilities --- Inequalities (Mathematics) --- Mathematical statistics --- Probabilities --- Inequalities (Mathematics) --- Congresses --- Congresses --- Congresses

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Stochastic analysis, a branch of probability theory stemming from the theory of stochastic differential equations, is becoming increasingly important in connection with partial differential equations, non-linear functional analysis, control theory and statistical mechanics.

Stochastic processes --- Shape theory (Topology) --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Homotopy theory --- Mappings (Mathematics) --- Topological manifolds --- Topological spaces --- Stochastic analysis. --- Analysis, Stochastic --- Mathematical analysis

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Singularity theory is not a field in itself, but rather an application of algebraic geometry, analytic geometry and differential analysis. The adjective 'singular' in the title refers here to singular points of complex-analytic or algebraic varieties or mappings. A tractable (and very natural) class of singularities to study are the isolated complete intersection singularities, and much progress has been made over the past decade in understanding these and their deformations.

Geometry, Algebraic. --- Singularities (Mathematics) --- Geometry, Algebraic --- Algebraic geometry --- Geometry