# LTCC Advanced Mathematical Series

The LTCC Advanced Mathematics Series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. The concise books introduce research students to new areas of mathematical sciences research — some of obvious relevance to their research, but most where the potential relevance is less transparent. They therefore support readers in broadening their mathematical knowledge outside of their immediate research area.

The volumes can be used as a Masters or advanced level teaching support or as a reference handbook for PhD students outside the classroom. The series is published by World Scientific and can be purchased from their website here.

**Volume 1 - Advanced Techniques in Applied Mathematics**

Edited By: Shaun Bullett (Queen Mary University of London, UK), Tom Fearn (University College London, UK) and Frank Smith (University College London, UK)

**Contents:**

- Practical Analytical Methods for Partial Differential Equations
*(Helen J Wilson)* - Resonances in Wave Scattering
*(Dmitry V Savin)* - Modelling — What is it Good For?
*(Oliver S Kerr)* - Finite Elements
*(Matthias Maischak)* - Introduction to Random Matrix Theory
*(Igor E Smolyarenko)* - Symmetry Methods for Differential Equations
*(Peter A Clarkson)*

This book is a guide to advanced techniques used widely in applied mathematical sciences research. Chapter by chapter, readers will be led from a foundation level understanding to advanced level understanding. This is the perfect text for graduate or PhD mathematical-science students looking for support in techniques such as practical analytical methods, finite elements and symmetry methods for differential equations.

Available to purchase here (link to external website).

**Volume 2 - Fluid and Solid Mechanics**

Edited By: Shaun Bullett (Queen Mary University of London, UK), Tom Fearn (University College London, UK) and Frank Smith (University College London, UK)

**Contents:**

- Introductory Geophysical Fluid Dynamics
*(Michael Davey)* - Multiple Deck Theory
*(S N Timoshin)* - Time-Mean Turbulent Shear Flows: Classical Modelling — Asymptotic Analysis — New Perspectives
*(Bernhard Scheichl)* - Nonlinear Free Surface Flows with Gravity and Surface Tension
*(J-M Vanden-Broeck)* - Internal Fluid Dynamics
*(Frank T Smith)* - Fundamentals of Physiological Solid Mechanics
*(N C Ovenden and C L Walsh)*

This book leads readers from a basic foundation to an advanced-level understanding of fluid and solid mechanics. Perfect for graduate or PhD mathematical-science students looking for help in understanding the fundamentals of the topic, it also explores more specific areas such as multi-deck theory, time-mean turbulent shear flows, non-linear free surface flows, and internal fluid dynamics.

Available to purchase here (link to external website).

**Volume 3 - Algebra, Logic and Combinatorics**

Edited By: Shaun Bullett (Queen Mary University of London, UK), Tom Fearn (University College London, UK) and Frank Smith (University College London, UK)

**Contents:**

- Enumerative Combinatorics
*(Peter J Cameron)* - Introduction to the Finite Simple Groups
*(Robert A Wilson)* - Introduction to Representations of Algebras and Quivers
*(Anton Cox)* - The Invariant Theory of Finite Groups
*(Peter Fleischmann and James Shank)* - Model Theory
*(Ivan Tomašić)*

This book leads readers from a basic foundation to an advanced level understanding of algebra, logic and combinatorics. Perfect for graduate or PhD mathematical-science students looking for help in understanding the fundamentals of the topic, it also explores more specific areas such as invariant theory of finite groups, model theory, and enumerative combinatorics.

Available to purchase here (link to external website).

**Volume 4 - Geometry in Advanced Pure Mathematics**

**Contents:**

- Algebraic Geometry
*(Ivan Tomašić)* - Introduction to the Modular Group and Modular Forms
*(W J Harvey)* - Geometric Group Theory
*(Ian Chiswell)* - Holomorphic Dynamics and Hyperbolic Geometry
*(Shaun Bullett)* - Minimal Surfaces and the Bernstein Theorem
*(T Bourni and G Tinaglia)* - Syzygies and Minimal Resolutions
*(F E A Johnson)*

This book leads readers from a basic foundation to an advanced level understanding of geometry in advanced pure mathematics. Chapter by chapter, readers will be led from a foundation level understanding to advanced level understanding. This is the perfect text for graduate or PhD mathematical-science students looking for support in algebraic geometry, geometric group theory, modular group, holomorphic dynamics and hyperbolic geometry, syzygies and minimal resolutions, and minimal surfaces.

Available to purchase here (link to external website).

**Volume 5 - Dynamical and Complex Systems**

**Contents:**

- Chaos in Statistical Physics
*(Rainer Klages)* - Aperiodic Order
*(Uwe Grimm)* - Complex Systems Dynamics
*(Hannah M Fry)* - Dynamical Systems in Cosmology
*(Christian G Böhmer and Nyein Chan)* - Lotka–Volterra Dynamical Systems
*(Stephen Baigent)* - Applied Dynamical Systems
*(David Arrowsmith)*

This book leads readers from a basic foundation to an advanced level understanding of dynamical and complex systems. It is the perfect text for graduate or PhD mathematical-science students looking for support in topics such as applied dynamical systems, Lotka–Volterra dynamical systems, applied dynamical systems theory, dynamical systems in cosmology, aperiodic order, and complex systems dynamics.

Available to purchase here (link to external website).

**Volume 6 - Analysis and Mathematical Physics**

**Contents:**

- Differential Geometry and Mathematical Physics
*(Andrew Hone and Steffen Krusch)* - Distributions, Fourier Transforms and Microlocal Analysis
*(Yuri Safarov)* - C* Algebras
*(Cho-Ho Chu)* - Special Functions
*(Rod Halburd)* - Non-commutative Differential Geometry
*(Shahn Majid)* - Mathematical Problems of General Relativity
*(Juan A Valiente Kroon)* - Value Distribution of Meromorphic Functions
*(Rod Halburd)*

This is a concise reference book on analysis and mathematical physics, leading readers from a foundation to advanced level understanding of the topic. This is the perfect text for graduate or PhD mathematical-science students looking for support in topics such as distributions, Fourier transforms and microlocal analysis, C* Algebras, value distribution of meromorphic functions, noncommutative differential geometry, differential geometry and mathematical physics, mathematical problems of general relativity, and special functions of mathematical physics.

Available to purchase here (link to external website).