Bøker i AIMS Library of Mathematical Sciences-serien

How do mathematicians approach a problem and explore the possibilities? Beardon explains that a mathematical problem is just one of many related ones that should be simultaneously investigated and discussed at various levels, and that understanding this is a crucial step in becoming a creative mathematician.

From Measures to Ito Integrals gives a clear account of measure theory, leading via L2-theory to Brownian motion, Ito integrals and a brief look at martingale calculus. Modern probability theory and the applications of stochastic processes rely heavily on an understanding of basic measure theory. This text is ideal preparation for graduate-level courses in mathematical finance and perfect for any reader seeking a basic understanding of the mathematics underpinning the various applications of Ito calculus.

This practical guide is ideal for students and beginning researchers working in one of the many scientific disciplines in which ordinary differential equations play a fundamental role. It introduces the key concepts and techniques, assuming only minimal mathematical prerequisites, so the reader can understand the subject in a short time.

This graduate-level introduction shows how mathematical modelling helps us to understand atmospheric phenomena. Written for students with backgrounds in mathematics, physics and engineering, this book will be a valuable resource as they begin studying atmospheric science.

Understanding Fluid Flow takes a fresh approach to introducing fluid dynamics, with physical reasoning and mathematical developments inextricably intertwined. It gives a flavour of theoretical, experimental and numerical approaches to analysing fluid flow, and implicitly develops skills in applied mathematical modelling. It is supplemented by movies that are freely downloadable.

This quick guide is designed for young students with some background in algebra who wish to perform their first experiments in computational geometry. It provides a compact presentation of the basic theory, with particular emphasis on explicit computational examples using the computer algebra system Singular.

Mathematical Modelling in One Dimension demonstrates the universality of mathematical techniques through a wide variety of applications. Learn how the same mathematical idea governs loan repayments, drug accumulation in tissues or growth of a population, or how the same argument can be used to find the trajectory of a dog pursuing a hare, the trajectory of a self-guided missile or the shape of a satellite dish. The author places equal importance on difference and differential equations, showing how they complement and intertwine in describing natural phenomena.

Mathematical Explorations follows on from the author's previous book, Creative Mathematics, in the same series, and gives the reader experience in working on problems requiring a little more mathematical maturity. The author's main aim is to show that problems are often solved by using mathematics that is not obviously connected to the problem, and readers are encouraged to consider as wide a variety of mathematical ideas as possible. In each case, the emphasis is placed on the important underlying ideas rather than on the solutions for their own sake. To enhance understanding of how mathematical research is conducted, each problem has been chosen not for its mathematical importance, but because it provides a good illustration of how arguments can be developed. While the reader does not require a deep mathematical background to tackle these problems, they will find their mathematical understanding is enriched by attempting to solve them.