This volume will be edited by Dr. Michael Grinfeld, Department of Mathematics and Statistics at the University of Strathclyde in Glasgow, UK. His areas of interest are topological methods in differential equations and continuum models in material science.Michael Grinfeld serves on the Editorial Boards of Proceedings EMS and Mathematical methods in the Applied Sciences.

The new edition is significantly updated and expanded.
This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized.
While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.

Part I
Probability
1 Stochastic processes
Andrew R. Wade, James R. Cruise, Ostap Hryniv
2 Monte-Carlo Methods
Kurt Binder
3 Stochastic Differential Equations
Gabriel Lord
Part II
Discrete Mathematics, Geometry, Topology
4 Graph and Network Theory
Ernesto Estrada
5 Group Theory
Robert Gilmore
6 Algebraic Topology
Vanessa Robins
7 Special Functions
Christopher Athorne
8 Computer Algebra
James Davenport
9 Differentiable Manifolds
Marcelo Epstein
10 Topics in Differential Geometry
Marcelo Epstein
Part III
Analysis
11 Dynamical Systems
David A. W. Barton
12 Perturbation Methods
James Murdock
13 Functional Analysis
Pavel Exner
14 Numerical Analysis
Lyonell Boulton
15 Mathematical Transformations
Rainer Picard, Des McGhee, Sascha Trostorff, Marcus Waurick
16 Partial Differential Equations
Des McGhee, Rainer Picard, Sascha Trostorff, Marcus Waurick
17 Calculus of Variations
Tomas Roubicek