Beginning with ordinary language models or realistic mathematical models of physical or biological phenomena, the author derives tractable mathematical models that are amenable to further mathematical analysis or to elucidating computer simulations. For the most part, derivations are based on perturbation methods. Because of this, the majority of the text is devoted to careful derivations of implicit function theorems, methods of averaging, and quasi-static state approximation methods. The duality between stability and perturbation is developed and used, relying heavily on the concept of stability under persistent disturbances.
Challenging and stimulating collection of diverting brain-teasers helps high school students integrate simple techniques and complex problem-solving strategies in an enjoyable way. Problems involving squares and cubes, polyhedra, prime numbers, chess pieces, and other subjects are grouped into 29 sections, with easier problems appearing at the beginning of each. A valuable tool for teachers, this absorbing book will also appeal to individuals working alone who want to develop problem-solving techniques.
A Mathematical Introduction to Conformal Field Theory
Part I gives a detailed, self-contained and mathematically rigorous exposition of classical conformal symmetry in n dimensions and its quantization in two dimensions. Part II surveys more advanced topics of conformal field theory such as the representation theory of the Virasoro algebra, conformal symmetry within string theory, an axiomatic approach to Euclidean conformally covariant quantum field theory and a mathematical interpretation of the Verlinde formula in the context of moduli spaces of holomorphic vector bundles on a Riemann surface.
Problem-Solving and Selected Topics in Number Theory: In the Spirit of the Mathematical Olympiads
The book provides a self-contained introduction to classical Number Theory. All the proofs of the individual theorems and the solutions of the exercises are being presented step by step. Some historical remarks are also presented. The book will be directed to advanced undergraduate, beginning graduate students as well as to students who prepare for mathematical competitions (ex. Mathematical Olympiads and Putnam Mathematical competition).
Mathematical Subjects: Children Talk About Their Mathematics Lives
We know the process by which children become social, moral, and creative beings, but when—and how—do they become mathematical beings? This thought-provoking volume follows ten children (ages seven through eighteen) in schools in New Zealand, England, Australia, Sweden, and an international school in Switzerland as they come to recognize the mathematical as part of their lives, their academic identities, and their identities as human beings.
