Publication planned for: July 2019
format: Paperback
isbn: 9781108406369
The unique feature of this compact student's introduction to MathematicaR and the Wolfram Language? is that the order of the material closely follows a standard mathematics curriculum. As a result, it provides a brief introduction to those aspects of the Mathematica software program most useful to students. Used as a supplementary text, it will help bridge the gap between Mathematica and the mathematics in the course, and will serve as an excellent tutorial for former students. There have been significant changes to Mathematica since the second edition, and all chapters have now been updated to account for new features in the software, including natural language queries and the vast stores of real-world data that are now integrated through the cloud. This third edition also includes many new exercises and a chapter on 3D printing that showcases the new computational geometry capabilities that will equip readers to print in 3D.
Updated chapters cover the newest developments in the software, including natural language queries and the vast stores of real-world data now integrated through the cloud
Clearly presents software commands and procedures alongside mathematical ideas to demonstrate how Mathematica can illuminate high school and university mathematics
The book does not assume that the reader is an expert in the underlying mathematics
Part of Cambridge Studies in Advanced Mathematics
Publication planned for: September 2019
format: Hardback
isbn: 9781108473200
This book provides an introduction to modern homotopy theory through the lens of higher categories after Joyal and Lurie, giving access to methods used at the forefront of research in algebraic topology and algebraic geometry in the twenty-first century. The text starts from scratch ? revisiting results from classical homotopy theory such as Serre's long exact sequence, Quillen's theorems A and B, Grothendieck's smooth/proper base change formulas and the construction of the Kan-Quillen model structure on simplicial sets ? and develops an alternative to a significant part of Lurie's definitive reference Higher Topos Theory, with new constructions and proofs, in particular, the Yoneda Lemma and Kan extensions. The strong emphasis on homotopical algebra provides clear insights into classical constructions such as calculus of fractions, homotopy limits and derived functors. For graduate students and researchers from neighbouring fields, this book is a user-friendly guide to advanced tools that the theory provides for application.
Starts from scratch, so students with basic prerequisites can jump in
Sticks with one presentation of the theory, to focus on building intuition and developing tools
Treats Kan extensions and homotopical methods in depth, equipping the reader to use the theory in his/her own research
Part of Cambridge Tracts in Mathematics
Publication planned for: June 2019
format: Hardback
isbn: 9781108472081
This study of Schrodinger equations with power-type nonlinearity provides a great deal of insight into other dispersive partial differential equations and geometric partial differential equations. It presents important proofs, using tools from harmonic analysis, microlocal analysis, functional analysis, and topology. This includes a new proof of Keel?Tao endpoint Strichartz estimates, and a new proof of Bourgain's result for radial, energy-critical NLS. It also provides a detailed presentation of scattering results for energy-critical and mass-critical equations. This book is suitable as the basis for a one-semester course, and serves as a useful introduction to nonlinear Schrodinger equations for those with a background in harmonic analysis, functional analysis, and partial differential equations.
Readers will find that the study of semilinear Schrodinger equations is useful in its own right, having many applications in physics
Covers a very active area of research in partial differential equations
This book is one of the first to present proofs of scattering for the mass-critical NLS problem
Part of Cambridge Texts in Applied Mathematics
Publication planned for: June 2019
format: Hardback
isbn: 9781107065871
Exploring the origins and evolution of magnetic fields in planets, stars and galaxies, this book gives a basic introduction to magnetohydrodynamics and surveys the observational data, with particular focus on geomagnetism and solar magnetism. Pioneering laboratory experiments that seek to replicate particular aspects of fluid dynamo action are also described. The authors provide a complete treatment of laminar dynamo theory, and of the mean-field electrodynamics that incorporates the effects of random waves and turbulence. Both dynamo theory and its counterpart, the theory of magnetic relaxation, are covered. Topological constraints associated with conservation of magnetic helicity are thoroughly explored and major challenges are addressed in areas such as fast-dynamo theory, accretion-disc dynamo theory and the theory of magnetostrophic turbulence. The book is aimed at graduate-level students in mathematics, physics, earth sciences and astrophysics, and will be a valuable resource for researchers at all levels.
Includes the most recent theoretical and experimental developments in the field
This book is an ideal introduction for students who are new to dynamo theory
Surveys observations on planetary and stellar magnetism, giving motivation for the theoretical developments