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Catalogue complet

J Robert Buchanan: First Course In
Partial Differential Equations, A

First Course In Partial Differential Equations, A

While the field of Deep Learning has been advancing at frightening speeds during the last ten years, we do not have a plausible theoretical explanation of its success yet. One can safely say that Deep Learning works, but nobody really understands why. Nevertheless, starting around five years before now, a decent number of theoretical papers specifically concerning neural nets started to emerge at top machine learning venues. This makes us think that the core of Deep Learning theory has already started to crystallize.The goal of the present book is to present these core concepts of Deep Learning theory to readers so that they could directly dive into recent papers of this area. For this purpose, each chapter elaborates a simple model or a classical result in details first and then discusses possible generalizations and more recent developments of the same idea.We have to warn the reader that the present book is not a mathematical manuscript. Not all results here are stated as formal theorems and not all theorems are provided with complete and rigorous proofs. Many of the theorems of the book are proven up to some technical lemmas, while for some there is only a proof sketch. This conforms with the main idea of the book: present and illustrate concepts rather than reproduce all the results.The book, in its present form, covers the following topics: uniform generalization bounds, PAC-bayesian generalization bounds, double descent phenomena, infinitely-wide networks, implicit bias of gradient descent, loss landscape, gradient descent convergence guarantees, and initialization strategies.

Elements Of Deep Learning Theory

This book presents a comprehensive treatment of pricing and hedging soccer betting contracts using the modern techniques of probability, statistics, finance, and portfolio management. It introduces betting in general and then addresses the probabilistic intuition needed in the more complex world of soccer betting. The author presents an innovative perspective by thinking about betting odds in terms of the expected number of goals of both teams. In addition, when the betting market is in play, the book treats betting before the game and during the game separately.

Science of Soccer Statistics

Soccermetrics

An Introduction to the Finite Element Method with the Variational Approach offers a comprehensive solution to the gaps often found in introductory texts on the Finite Element Method (FEM). The book provides a thorough introduction to the fundamental principles of linear and time-independent FEM within the variational framework. It meticulously covers the derivation of 1-D FEM equations based on variational functionals, encompassing both linear and higher-order elements, and shape functions driven by convergence criteria. Furthermore, it explores 1-D numerical integration, outlines coding procedures, and provides insights into handling material nonlinearity and time-dependent scenarios. Expanding into 2-D problems, the book offers derivations of 2-D FEM equations tailored to diverse engineering disciplines, including Steady-State Heat Conduction, Solid Mechanics (covering torsion, plane strain/axisymmetric cases, and the bending, stability, and vibrations of thin plates), as well as Fluid Mechanics (addressing incompressible inviscid and viscous fluids). It includes detailed discussions on element continuity, numerical integration techniques, and even includes 2-D codes for selected problems. The book concludes by delving into recent advancements in FEM, with a specific focus on applications in machine learning and isogeometric analysis.

An Introduction to the Finite Element Method with the Variational Approach

This text focuses on the parts of stochastic theory that are particularly relevant to applications. It begins with a description of Brownian motion and the associated stochastic calculus, including the relationship to partial differential equations. It then solves stochastic differential equations by a variety of methods. The author also studies in detail the one-dimensional case. The book concludes with a treatment of semigroups and generators, applying the theory of Harris chains to diffusions as well as weak convergence of Markov chains to diffusions.

An Elementary Introduction Emphasizing Applications

Stochastic Calculus

The aim of this textbook is to improve students' ability to formulate economic problems and provide essential mathematical tools for analysis across various contexts. This book presents the author's current understanding of mathematics, shaped by several years of teaching this subject as well as enriched through interactions with his students. To aid students in their learning, the book is written in a manner that better highlights key concepts and provides additional clarity when possible. In this way, it is hoped that students will feel more guided in their study of mathematics and its applications in microeconomics.

Essential Mathematics For Microeconomics: A Student's Guide To Key Mathematical Techniques

De Gruyter Series in Applied and Numerical Mathematics

Advanced Computational Approaches for Rarefied Flows

Beyond Navier-Stokes

Series in Materials Science and Engineering

This book provides an introduction to the geometrical and topological methods that have become essential tools for soft condensed matter physicists. The emphasis is on providing mathematical tools in clear but precise language, focusing on fundamental concepts using real examples to illustrate for readers in vivid, three-dimensional fashion. The motivation is clearly provided using problems from soft condensed matter, from the packing of colloids to liquid crystals and thermal fluctuations of lipid membranes.

Geometry and Topology of Soft Materials

Radon Series on Computational and Applied Mathematics

Hilbert Space Methods for the Theory of Electromagnetism

Maxwell’s Equations

Boundary Value Problems and Partial Differential Equations

Storytelling with Data Box Set

De Gruyter Studies in Mathematical Physics

Mirror symmetry is one of the most exciting ideas in mathematics to emerge in the last two decades. It was introduced in physics as a duality between superconformal field theories. This book discusses this rapidly developing aspect of string theory.

Laurent Polynomials in Mirror Symmetry

First Course In Partial Differential Equations, A

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