A classic introduction to mathematical logic from the perspective of category theory, this text is suitable for advanced undergraduates and graduate students and accessible to both philosophically and mathematically oriented readers. Its approach moves always from the particular to the general, following through the steps of the abstraction process until the abstract concept emerges naturally.
Beginning with a survey of set theory and its role in mathematics, the text proceeds to definitions and examples of categories and explains the use of arrows in place of set-membership. The...

Appropriate for advanced undergraduates and graduate students, this text introduces terminology, approaches, and goals in modelling. Topics include population dynamics, group interaction, political transitions, evolutionary economics, and urbanization. 2002 edition.

Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory.
Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing...

This concise text for advanced undergraduates and graduate students covers eigenvalue problems in classical physics, orthogonal functions and expansions, the Sturm-Liouville theory and linear operators on functions, and linear vector spaces. It emphasizes the unity of a variety of techniques and is enduringly relevant to many physical systems. 1962 edition.

Set theory permeates much of contemporary mathematical thought. This text for undergraduates offers a natural introduction, developing the subject through observations of the physical world. Its progressive development leads from concrete finite sets to cardinal numbers, infinite cardinals, and ordinals.
Although set theory begins in the intuitive and the concrete, it ascends to a very high degree of abstraction. All that is necessary to its grasp, declares author Joseph Breuer, is patience. Breuer illustrates the grounding of finite sets in arithmetic, permutations, and combinations,...

Highlighted by numerous examples, this book explores methods of the projective geometry of the plane. It derives the projective properties of the conic and discusses representation by the general equation of the 2nd degree, concluding with a study of the relationship between Euclidean and projective geometry. 1960 edition.

Compact treatment highlights logic and simplicity of the mathematical structure of quantum mechanics. Suitable for advanced undergraduates and graduate students, it treats the language of quantum mechanics as expressed in mathematics of linear operators. Topics include linear spaces, functionals, and operators; diagonalizing operators; operator algebras; and equations of motion. 1969 edition.

Focusing on the archetypes of linear partial differential equations, this text for upper-level undergraduates and graduate students employs nontraditional methods to explain classical material. Topics include the Cauchy problem, boundary value problems, and mixed problems and evolution equations. Nearly 400 exercises enable students to reconstruct proofs. 1975 edition.

More than a history of mathematics, this lively book traces mathematical ideas and processes to their sources, stressing the methods used by the masters of the ancient world. Author Tobias Dantzig portrays the human story behind mathematics, showing how flashes of insight in the minds of certain gifted individuals helped mathematics take enormous forward strides. Dantzig demonstrates how the Greeks organized their precursors' melange of geometric maxims into an elegantly abstract deductive system. He also explains the ways in which some of the famous mathematical brainteasers of antiquity led...

This text develops the theory of systems of stochastic differential equations, and it presents applications in probability, partial differential equations, and stochastic control problems. Originally published in two volumes, it combines a book of basic theory and selected topics with a book of applications.
The first part explores Markov processes and Brownian motion; the stochastic integral and stochastic differential equations; elliptic and parabolic partial differential equations and their relations to stochastic differential equations; the Cameron-Martin-Girsanov theorem; and...