Author: Grae Worster
Publication Date: January 2010

Understanding Fluid Flow takes a fresh approach to introducing fluid dynamics, with physical reasoning and mathematical developments inextricably intertwined. The ‘dry’ fluid dynamics described by potential theory is set within the context of real viscous flows to give fundamental insight into how fluids behave.  The book gives a flavour of theoretical, experimental and numerical approaches to analysing fluid flow, and implicitly develops skills in applied mathematical modelling of physical systems. It is supplemented by movies that are freely downloadable.

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Author: Alan F. Beardon
Publication Date: March 2010

Explores mathematical situations, and problem solving, in the sense of doing research. The problems discussed here are open-ended, and are capable of being generalised far beyond the original question.

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.

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Author: Ekkehard Kopp
Publication Date: April 2011

From Measures to Itô Integrals gives a clear account of measure theory, leading via L2-theory to Brownian motion, Itô integrals and a brief look at martingale calculus.

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 Itô calculus.

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Author: Bernd J. Schroers
Publication Date: September 2011

Ordinary Differential Equations introduces key concepts and techniques in the field and shows how they are used in current mathematical research and modelling. It deals specifically with initial value problems, which play a fundamental role in a wide range of scientific disciplines, including mathematics, physics, computer science, statistics and biology.

This practical book is ideal for students and beginning researchers working in any of these fields who need to understand the area of ordinary differential equations in a short time.

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Authors: Wolfram Decker and Gerhard Pfister
Publication Date: December 2012 

A First Course in Computational Algebraic Geometry is designed for young students with some background in algebra who wish to perform their first experiments in computational geometry. Originating from a course taught at the African Institute for Mathematical Sciences, the book gives a compact presentation of the basic theory, with particular emphasis on explicit computational examples using the freely available computer algebra system, Singular. Readers will quickly gain the confidence to begin performing their own experiments.

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Author: Jacek Banasiak
Publication date: February 2013

Mathematical Modelling in One Dimension demonstrates the universality of mathematical techniques through a wide variety of application. 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 of 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.

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Author: Douw G Steyn
Publication date: April 2015

Introduction to Atmospheric Modelling explores the power of mathematics to help us understand complex atmospheric phenomena through mathematical modelling. The author has thoughtfully chosen a path into and through the subject that gives the reader a glimpse of the dynamics underlying phenomena ranging from sea breeze through mid-latitude cyclonic disturbances to Rossby waves, mainly through the lens of scaling analysis. Written for students with backgrounds in mathematics, physics and engineering, this book will be a valuable resource as they begin studying atmospheric science.

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Author: Alan F. Beardon
Publication Date: September 2016

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.

• Helps the reader learn how to conduct mathematical research
• Provides theorems which encourage the reader to ask more questions and discover the real nature of research
• No deep mathematical background is required to understand the problems in this book

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