[Lecture review] 4. 'Three great mathematicians: Euler', 6 March 2002

Tony Mann provides a review of the lecture: 'Three great mathematicians: Euler' held on 6 March 2002 as the fourth and last lecture of the Gresham College History of Mathematics season.

Generalized Markov branching processes

A generalized Markov Brnching Process (GMBP) is a Markov branching model where the infinitesimal branching rates are modified with an interaction index. It is proved that there always exists only one GMBP. An associated differential-integral equation is derived. The extinction probalility and the mean and conditional mean extinction times are obtained. Ergodicity and stability of GMBP with resurrection are also considered. Easy checking criteria are established for ordinary and strong ergodicty. The equilibrium distribution is given in an elegant closed form. The probability meaning of our results is clear and thus explained.

[Book review] Piero della Francesca: A Mathematician's art by J.V. Field, Yale University Press.

Review of the book 'Piero della Francesca: A Mathematician’s Art' by J.V. Field, Yale University Press, 420 pp, £35 ISBN 0300103425.

[Review] M. Feistauer, J. Felcman, I. Straskbraba, Mathematical and Computational Methods for Compressible Flow, Oxford Science Publication, Oxford, ISBN 0198505884, 2004 (535pp.)

The growth of computer power allows the solution of complex problems related to compressible flow, which is an important class of problems in modern day CFD. Over the last 15 years or so, many review works on CFD have been published. This book concerns both mathematical and numerical methods for compressible flow. In particular, it provides a clear cut introduction as well as in depth treatment of modern numerical methods in CFD. This book is organised in two parts. The first part consists of Chapters 1 and 2, and is mainly devoted to theoretical discussions and results. Chapter 1 concerns fundamental physical concepts and theoretical results in gas dynamics. Chapter 2 describes the basic mathematical theory of compressible flow using the inviscid Euler equations and the viscous Navier–Stokes equations. Existence and uniqueness results are also included. The second part consists of modern numerical methods for the Euler and Navier–Stokes equations. Chapter 3 is devoted entirely to the finite volume method for the numerical solution of the Euler equations and covers fundamental concepts such as order of numerical schemes, stability and high-order schemes. The finite volume method is illustrated for 1-D as well as multidimensional Euler equations. Chapter 4 covers the theory of the finite element method and its application to compressible flow. A section is devoted to the combined finite volume–finite element method, and its background theory is also included. Throughout the book numerous examples have been included to demonstrate the numerical methods. The book provides a good insight into the numerical schemes, theoretical analysis, and validation of test problems. It is a very useful reference for applied mathematicians, numerical analysts, and practice engineers. It is also an important reference for postgraduate researchers in the field of scientific computing and CFD.

[Reviews] Finding moonshine: a mathematician's journey through symmetry

Review of 'Finding Moonshine: A Mathematician’s Journey Through Symmetry' by Marcus du Sautoy, published by Fourth Estate, 2008 (ISBN 0-007-214618).