AVAILABILITY: Not yet published - available from September 2020
FORMAT: Paperback ISBN: 9781108789875
DescriptionContentsResourcesCoursesAbout the Authors
Learning to program isn't just learning the details of a programming language: to become a good programmer you have to become expert at debugging, testing, writing clear code and generally unsticking yourself when you get stuck, while to do well in a programming course you have to learn to score highly in coursework and exams. Featuring tips, stories and explanations of key terms, this book teaches these skills explicitly. Examples in Python, Java and Haskell are included, helping you to gain transferable programming skills whichever language you are learning. Intended for students in Higher or Further Education studying early programming courses, it will help you succeed in, and get the most out of, your course, and support you in developing the software engineering habits that lead to good programs.
Students will establish the habits that will make them good programmers and help them enjoy programming, without unnecessary stress
Is multi-lingual and contains examples in Java, Python and Haskell, helping students transfer what they learn in the context of one language to the context of their next language
Structured with many examples, tips, stories and explanations of terminology, given in visually distinct panels to appeal to the busy reader
1. Introduction
2. What Are Good Programs?
3. How to Get Started
4. How to Understand Your Language
5. How to Use the Best Tools
6. How to Make Sure You Don't Lose Your Program
7. How to Test Your Program
8. How to Make Your Program Clear
9. How to Debug Your Program
10. How to Improve Your Program
11. How to Get Help (without Cheating)
12. How to Score Well in Coursework
13. How to Score Well in a Programming Exam
14. How to Choose a Programming Language
15. How to Go Beyond This Book
References
Index.
AVAILABILITY: Not yet published - available from January 2021
FORMAT: Hardback ISBN: 9781108479523 FORMAT: Paperback ISBN: 9781108789981
Probability theory has diverse applications in a plethora of fields, including physics, engineering, computer science, chemistry, biology and economics. This book will familiarize students with various applications of probability theory, stochastic modeling and random processes, using examples from all these disciplines and more. The reader learns via case studies and begins to recognize the sort of problems that are best tackled probabilistically. The emphasis is on conceptual understanding, the development of intuition and gaining insight, keeping technicalities to a minimum. Nevertheless, a glimpse into the depth of the topics is provided, preparing students for more specialized texts while assuming only an undergraduate-level background in mathematics. The wide range of areas covered - never before discussed together in a unified fashion – includes Markov processes and random walks, Langevin and Fokker–Planck equations, noise, generalized central limit theorem and extreme values statistics, random matrix theory and percolation theory.
Explains the power of probability theory both as a conceptual framework and as a tool across mathematics and physics
Avoids using unnecessary technicalities, keeping the mathematical prerequisites to a minimum
Contains numerous and diverse examples of interdisciplinary applications of probability theory
1. Introduction
2. Random walks
3. Langevin and Focker–Planck equations and their applications
4. Escape over a barrier
5. Noise
6. Generalized central limit theorem and extreme value statistics
7. Anomalous diff usion
8. Random matrix theory
9. Percolation theory
Appendix A. Review of basic probability concepts and common distributions
Appendix B. A brief linear algebra reminder, and some Gaussian integrals
Appendix C. Contour integration and Fourier transform refresher
Appendix D. Review of Newtonian mechanics, basic statistical mechanics and Hessians
Appendix E. Minimizing functionals, the divergence theorem and saddle point approximations
Appendix F. Notation, notation...
References
Index.
EMS Monographs in Mathematics
ISBN print 978-3-03719-209-2,
DOI 10.4171/209
July 2020, 235 pages, hardcover, 16.5 x 23.5 cm.
This book is dedicated to equivariant mathematics, specifically the study of additive categories of objects with actions of finite groups. The framework of Mackey 2-functors axiomatizes the variance of such categories as a function of the group. In other words, it provides a categorification of the widely used notion of Mackey functor, familiar to representation theorists and topologists.
The book contains an extended catalogue of examples of such Mackey 2-functors that are already in use in many mathematical fields from algebra to topology, from geometry to KK-theory. Among the first results of the theory, the ambidexterity theorem gives a way to construct further examples and the separable monadicity theorem explains how the value of a Mackey 2-functor at a subgroup can be carved out of the value at a larger group, by a construction that generalizes ordinary localization in the same way that the étale topology generalizes the Zariski topology. The second part of the book provides a motivic approach to Mackey 2-functors, 2-categorifying the well-known span construction of Dress and Lindner. This motivic theory culminates with the following application: The idempotents of Yoshida’s crossed Burnside ring are the universal source of block decompositions.
The book is self-contained, with appendices providing extensive background and terminology. It is written for graduate students and more advanced researchers interested in category theory, representation theory and topology.
Keywords: Groupoids, Mackey formula, equivariant, 2-functors, derivators, ambidexterity, separable monadicity, spans, string diagrams, motivic
EMS Tracts in Mathematics Vol. 33
ISBN print 978-3-03719-206-1
DOI 10.4171/206
July 2020, 333 pages, hardcover, 17 x 24 cm.
The expansion of scientific knowledge and the development of technology are strongly connected with quantitative analysis of mathematical models. Accuracy and reliability are the key properties we wish to understand and control.
This book presents a unified approach to the analysis of accuracy of deterministic mathematical models described by variational problems and partial differential equations of elliptic type. It is based on new mathematical methods developed to estimate the distance between a solution of a boundary value problem and any function in the admissible functional class associated with the problem in question. The theory is presented for a wide class of elliptic variational problems. It is applied to the investigation of modelling errors arising in dimension reduction, homogenization, simplification, and various conversion methods (penalization, linearization, regularization, etc.). A collection of examples illustrates the performance of error estimates.
Keywords: Modelling error, a posteriori error majorant, model simplification, dimension reduction, homogenization, conversion of models
EMS Series of Lectures in Mathematics
ISBN print 978-3-03719-210-8,
DOI 10.4171/210
June 2020, 143 pages, softcover, 17 x 24 cm.
Τhe classification of complex algebraic surfaces is a very classical subject which goes back to the old Italian school of algebraic geometry with Enriques and Castelnuovo. However, the exposition in the present book is modern and follows Mori's approach to the classification of algebraic varieties. The text includes the P12 theorem, the Sarkisov programme in the surface case and the Noether–Castelnuovo theorem in its classical version.
This book serves as a relatively quick and handy introduction to the theory of algebraic surfaces and is intended for readers with a good knowledge of basic algebraic geometry. Although an acquaintance with the basic parts of books like Principles of Algebraic Geometry by Griffiths and Harris or Algebraic Geometry by Hartshorne should be sufficient, the author strove to make the text as self-contained as possible and, for this reason, a first chapter is devoted to a quick exposition of some preliminaries.
Keywords: Algebraic surfaces, classification
A publication of the Société Mathématique de France
This is the second of two volumes that celebrate the memory of Jean-Christophe Yoccoz.
These volumes present research articles on various aspects of the theory of dynamical systems and related topics that were dear to him.
Graduate students and research mathematicians.
Astérisque, Volume: 416;
2020; 340 pp; Softcover
MSC: Primary 32; 37; 53; 60; 70;
Print ISBN: 978-2-85629-917-3
ISBN: 978-1-119-67164-0 October 2020 352 Pages
The objective of this book is two-fold. The first objective is to construct, as much as possible, stable finite element schemes without affecting accuracy. The second objective is to derive convergence of the numerical schemes up to maximal available regularity of the exact solution. The first two chapters of the book cover existence, uniqueness and stability as well as the working environment, such as vector and function spaces and principle mathematical inequalities. Chapters 3 and 4 cover the approximation procedure with piecewise linears, interpolation, numerical integration and numerical solution of linear system of equations. Chapters 5 through 7 are devoted to the finite element approximations for the one-space dimensional, boundary value problems, initial value problems, and initial-boundary value problems. Finally, Chapters 8 through 10 are an extension of Chapters 3 and 5-7 to higher spatial dimensions. This book is a great resource for upper undergraduate...