Author: Publisher: TheBookEdition
ISBN: 2958142531
Category :
Languages : en
Pages : 341
Book Description
Author: Publisher: TheBookEdition
ISBN: 2958142531
Category :
Languages : en
Pages : 341
Book Description
Mathematics for Machine Learning
Author: Marc Peter DeisenrothPublisher: Cambridge University Press
ISBN: 1108569323
Category : Computers
Languages : en
Pages : 392
Book Description
The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.
An Introduction to Extremal Kahler Metrics
Author: Gábor SzékelyhidiPublisher: American Mathematical Soc.
ISBN: 1470410478
Category : Mathematics
Languages : en
Pages : 210
Book Description
A basic problem in differential geometry is to find canonical metrics on manifolds. The best known example of this is the classical uniformization theorem for Riemann surfaces. Extremal metrics were introduced by Calabi as an attempt at finding a higher-dimensional generalization of this result, in the setting of Kähler geometry. This book gives an introduction to the study of extremal Kähler metrics and in particular to the conjectural picture relating the existence of extremal metrics on projective manifolds to the stability of the underlying manifold in the sense of algebraic geometry. The book addresses some of the basic ideas on both the analytic and the algebraic sides of this picture. An overview is given of much of the necessary background material, such as basic Kähler geometry, moment maps, and geometric invariant theory. Beyond the basic definitions and properties of extremal metrics, several highlights of the theory are discussed at a level accessible to graduate students: Yau's theorem on the existence of Kähler-Einstein metrics, the Bergman kernel expansion due to Tian, Donaldson's lower bound for the Calabi energy, and Arezzo-Pacard's existence theorem for constant scalar curvature Kähler metrics on blow-ups.
Exercises And Problems In Linear Algebra
Author: John M ErdmanPublisher: World Scientific
ISBN: 9811220425
Category : Mathematics
Languages : en
Pages : 220
Book Description
This book contains an extensive collection of exercises and problems that address relevant topics in linear algebra. Topics that the author finds missing or inadequately covered in most existing books are also included. The exercises will be both interesting and helpful to an average student. Some are fairly routine calculations, while others require serious thought.The format of the questions makes them suitable for teachers to use in quizzes and assigned homework. Some of the problems may provide excellent topics for presentation and discussions. Furthermore, answers are given for all odd-numbered exercises which will be extremely useful for self-directed learners. In each chapter, there is a short background section which includes important definitions and statements of theorems to provide context for the following exercises and problems.
Graphs and Matrices
Author: Ravindra B. BapatPublisher: Springer
ISBN: 1447165691
Category : Mathematics
Languages : en
Pages : 197
Book Description
This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reorganized. Whilst this book will be invaluable to students and researchers in graph theory and combinatorial matrix theory, it will also benefit readers in the sciences and engineering.
Disputing Citizenship
Author: Clarke, JohnPublisher: Policy Press
ISBN: 1447312546
Category : Political Science
Languages : en
Pages : 224
Book Description
Available Open Access under CC-BY-NC licence. Citizenship is always in dispute – in practice as well as in theory – but conventional perspectives do not address why the concept of citizenship is so contentious. This unique book presents a new perspective on citizenship by treating it as a continuing focus of dispute.The authors dispute the way citizenship is normally conceived and analysed within the social sciences, developing a view of citizenship as always emerging from struggle. This view is advanced through an exploration of the entanglements of politics, culture and power that are both embodied and contested in forms and practices of citizenship. This compelling view of citizenship emerges from the international and interdisciplinary collaboration of the four authors, drawing on the diverse disputes over citizenship in their countries of origin (Brazil, France, the UK and the US). The book is essential reading for anyone interested in the field of citizenship, no matter what their geographical, political or academic location.
Noncommutative Geometry and Particle Physics
Author: Walter D. van SuijlekomPublisher: Springer
ISBN: 9401791627
Category : Science
Languages : en
Pages : 246
Book Description
This book provides an introduction to noncommutative geometry and presents a number of its recent applications to particle physics. It is intended for graduate students in mathematics/theoretical physics who are new to the field of noncommutative geometry, as well as for researchers in mathematics/theoretical physics with an interest in the physical applications of noncommutative geometry. In the first part, we introduce the main concepts and techniques by studying finite noncommutative spaces, providing a “light” approach to noncommutative geometry. We then proceed with the general framework by defining and analyzing noncommutative spin manifolds and deriving some main results on them, such as the local index formula. In the second part, we show how noncommutative spin manifolds naturally give rise to gauge theories, applying this principle to specific examples. We subsequently geometrically derive abelian and non-abelian Yang-Mills gauge theories, and eventually the full Standard Model of particle physics, and conclude by explaining how noncommutative geometry might indicate how to proceed beyond the Standard Model.
Semigroup Methods for Evolution Equations on Networks
Author: Delio MugnoloPublisher: Springer
ISBN: 3319046217
Category : Science
Languages : en
Pages : 294
Book Description
This concise text is based on a series of lectures held only a few years ago and originally intended as an introduction to known results on linear hyperbolic and parabolic equations. Yet the topic of differential equations on graphs, ramified spaces, and more general network-like objects has recently gained significant momentum and, well beyond the confines of mathematics, there is a lively interdisciplinary discourse on all aspects of so-called complex networks. Such network-like structures can be found in virtually all branches of science, engineering and the humanities, and future research thus calls for solid theoretical foundations. This book is specifically devoted to the study of evolution equations – i.e., of time-dependent differential equations such as the heat equation, the wave equation, or the Schrödinger equation (quantum graphs) – bearing in mind that the majority of the literature in the last ten years on the subject of differential equations of graphs has been devoted to elliptic equations and related spectral problems. Moreover, for tackling the most general settings - e.g. encoded in the transmission conditions in the network nodes - one classical and elegant tool is that of operator semigroups. This book is simultaneously a very concise introduction to this theory and a handbook on its applications to differential equations on networks. With a more interdisciplinary readership in mind, full proofs of mathematical statements have been frequently omitted in favor of keeping the text as concise, fluid and self-contained as possible. In addition, a brief chapter devoted to the field of neurodynamics of the brain cortex provides a concrete link to ongoing applied research.
French Rococo Ébénisterie in the J. Paul Getty Museum
Author: Gillian WilsonPublisher: J. Paul Getty Museum
ISBN: 9781606066300
Category : Design
Languages : en
Pages : 0
Book Description
The first comprehensive catalogue of the Getty Museum’s significant collection of French Rococo ébénisterie furniture. This catalogue focuses on French ébénisterie furniture in the Rococo style dating from 1735 to 1760. These splendid objects directly reflect the tastes of the Museum’s founder, J. Paul Getty, who started collecting in this area in 1938 and continued until his death in 1976. The Museum’s collection is particularly rich in examples created by the most talented cabinet masters then active in Paris, including Bernard van Risenburgh II (after 1696–ca. 1766), Jacques Dubois (1694–1763), and Jean-François Oeben (1721–1763). Working for members of the French royal family and aristocracy, these craftsmen excelled at producing veneered and marquetried pieces of furniture (tables, cabinets, and chests of drawers) fashionable for their lavish surfaces, refined gilt-bronze mounts, and elaborate design. These objects were renowned throughout Europe at a time when Paris was considered the capital of good taste. The entry on each work comprises both a curatorial section, with description and commentary, and a conservation report, with construction diagrams. An introduction by Anne-Lise Desmas traces the collection’s acquisition history, and two technical essays by Arlen Heginbotham present methodologies and findings on the analysis of gilt-bronze mounts and lacquer. The free online edition of this open-access publication is available at www.getty.edu/publications/rococo/ and includes zoomable, high-resolution photography. Also available are free PDF, EPUB, and Kindle/MOBI downloads of the book, and JPG downloads of the main catalogue images.
Markov Chains
Author: D. RevuzPublisher: Elsevier
ISBN: 0080880223
Category : Mathematics
Languages : en
Pages : 389
Book Description
This is the revised and augmented edition of a now classic book which is an introduction to sub-Markovian kernels on general measurable spaces and their associated homogeneous Markov chains. The first part, an expository text on the foundations of the subject, is intended for post-graduate students. A study of potential theory, the basic classification of chains according to their asymptotic behaviour and the celebrated Chacon-Ornstein theorem are examined in detail.The second part of the book is at a more advanced level and includes a treatment of random walks on general locally compact abelian groups. Further chapters develop renewal theory, an introduction to Martin boundary and the study of chains recurrent in the Harris sense. Finally, the last chapter deals with the construction of chains starting from a kernel satisfying some kind of maximum principle.
