Format: Hardback, 348 pages, height x width: 235x155 mm, 7 Illustrations, color; 5 Illustrations,
black and white; XIV, 348 p. 12 illus., 7 illus. in color., 1 Hardback
Series: Infosys Science Foundation Series
Pub. Date: 08-Feb-2025
ISBN-13: 9789819792016
This book, Dierential Geometry: Manifolds, Bundles and Characteristic Classes (Book I-A), is the rst in a captivating series of four books presenting a choice of topics, among fundamental and more advanced, in dierential geometry (DG), such as manifolds and tensor calculus, dierentiable actions and principal bundles, parallel displacement and exponential mappings, holonomy, complex line bundles and characteristic classes. The inclusion of an appendix on a few elements of algebraic topology provides a didactical guide towards the more advanced Algebraic Topology literature. The subsequent three books of the series are:
Dierential Geometry: Riemannian Geometry and Isometric Immersions (Book I-B)
Chapter 1 Manifolds and Tensor Calculus.
Chapter 2 Differentiable
Actions and Principal Bundles.
Chapter 3 Infinite dimensional Differential
Geometry.
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Format: Hardback, 205 pages, height x width: 240x168 mm, 5 Illustrations, color; 1 Illustrations,
black and white; XVIII, 205 p. 6 illus., 5 illus. in color., 1 Hardback
Series: Synthesis Lectures on Mathematics & Statistics
Pub. Date: 21-Jan-2025
ISBN-13: 9783031766718
Author Biography
Goodreads reviews
This book presents a broad range of regression models including count regression models, constrained and penalised regression models such as ridge, LASSO, and elasticnet regression that are used in various applied science fields. The author describes the historical development of the least squares principle, simple linear regression, and Polynomial regression. In addition, logistic regression and multiple linear regression are discussed at length. A novel method to estimate the slope of linear regression is presented along with an emphasis on the importance of numeric problems
Table of Contents
Types of Regression.- Simple Liner Regression.- Logistic Regression.- Multiple Linear Regression.- Applications of Regression.
Format: Paperback / softback, 334 pages, height x width: 235x155 mm, 20 Illustrations, color;
93 Illustrations, black and white; X, 334 p. 113 illus., 20 illus. in color., 1 Paperback / softback
Pub. Date: 21-Feb-2025
ISBN-13: 9783031740657
This book is part biographical account, part novel, and part popular science. The basic facts are historically true, but many episodes have additionally been dramatized with plausible content that brings the personal story to life in the style of a novel or movie script. This genre of a dramatized biography" of scientists was first created by the author 45 years ago and became a great success selling over half a million copies in China, where it has been in particular demand for teaching.
But this is not the whole story: In addition, the book explains, in a serious yet accessible manner, the basics of Einsteins scientific work, especially its impact on contemporary cosmology, astronomy, and physics. As an experienced teacher of relativity and astronomy for high-school and university students, the author knows how to make profound scientific subjects accessible, and his presentation is as fascinating as a detective story. Readers will learn not only about the historical setting but also about the challenges and frustrations faced by Einstein, about his breakthroughs and triumphs, as well as the far-reaching significance of his theory of relativity, quantum mechanics, and other scientific achievements. The reader will come to understand why, of all the billions of people living in the twentieth century, Albert Einstein was singled out as the Person of the Century.
1. Germany.-
2. Switzerland.-
3. A Revolution in Physics.-
4. The Special Theory of Relativity.-
5. The Rising Star.
Format: Hardback, 460 pages, height x width: 235x155 mm, XXII, 460 p., 1 Hardback
Pub. Date: 04-Dec-2024
ISBN-13: 9783031758010
This book presents a collection of high-quality papers in applied and numerical mathematics, as well as approximation theory, all closely related to Wolfgang Dahmen’s scientific contributions. Compiled in honor of his 75th birthday, the papers are written by leading experts and cover topics including nonlinear approximation theory, numerical analysis of partial differential equations, learning theory, and electron microscopy. A unifying theme throughout the collection is the emphasis on a solid mathematical foundation, which serves as the basis for the most efficient numerical algorithms used to simulate complex phenomena.
Ronald A. DeVore and Angela Kunoth, Prologue to Multiscale, Nonlinear
and Adaptive Approximation II.- Ronald A. DeVore and Angela Kunoth,
Introduction: Wolfgang Dahmens mathematical work (as of 2009).- Markus
Bachmayr and Albert Cohen, Multilevel Representations of Random Fields and
Sparse Approximations of Solutions to Random PDEs.- Hassan Ballout and Yvon
Maday and Christophe Prudhomme, Nonlinear compressive reduced basis
approximation for multi-parameter elliptic problem.- Ido Ben Shaul and Shai
Dekel, Sparse Besov Space Analysis of Representations in Machine Learning.-
Benjamin Berkels and Peter Binev, Joint Denoising and Line Distortion
Correction for Raster-Scanned Image Series.- Dietrich Braess and Wolfgang
Hackbusch, The Approximation of Cauchy-Stieltjes and Laplace-Stieltjes
Functions.- Andrea Bonito and Diane Guignard, Approximating Partial
Differential Equations without Boundary Conditions.- Albert Cohen and Ronald
DeVore and Eitan Tadmor, Constructions of Bounded Solutions of div u= f in
Critical Spaces.- Jan-Christopher Cohrs and Benjamin Berkels, On the
importance of the -regularization of the distribution-dependent MumfordShah
model for hyperspectral image segmentation.- Ronald DeVore, Guergana Petrova
and Przemysaw Wojtaszczyk, A Note on Best n-term Approximation for
Generalized Wiener Classes.- Lars Grasedyck, Sebastian Kramer and Dieter
Moser, Stable Truncation and Root-Independent Normalization of Tree Tensor
Networks.- Diane Guignard and Olga Mula, Tree-Based Nonlinear Reduced
Modeling.- Helmut Harbrecht and Michael Multerer, Samplets: Wavelet Concepts
for Scattered Data.- Michael Herty, Adrian Kolb, and Siegfried Muller, A
novel multilevel approach for the efficient computation of random hyperbolic
conservation laws.- Kamen G. Ivanov, Gerard Kerkyacharian, George Kyriazis,
and Pencho Petrushev, On the Construction of Bases and Frames with
Applications.- Angela Kunoth and Mathias Oster and Reinhold Schneider,
Towards a Continuous Mathematical Model for the Analysis of Classes of Deep
Neural Networks.- Dominique Picard, Unstoppable Mathematicians.- Reinhold
Schneider and Mathias Oster, Some Thoughts on Compositional Tensor Networks.-
Rob Stevenson, Efficient least squares discretizations for Unique
Continuation and Cauchy problems.
Format: Paperback / softback, 168 pages, height x width: 235x155 mm, X, 168 p., 1 Paperback / softback
Series: Compact Textbooks in Mathematics
Pub. Date: 23-Jan-2025
ISBN-13: 9783031771590
This textbook gives an introduction to optimization tools which arise around the Weierstrass theorem about the minimum of a lower semicontinuous function. Starting from a Euclidean space, it moves further into the infinite dimensional setting towards the direct variational method, going through differentiation and introducing relevant background information on the way.
Exercises accompany the text and include observations, remarks, and examples that help understand the presented material. Although some basic knowledge of functional analysis is assumed, covering Hilbert and Banach spaces and the Lebesgue integration, the required background material is covered throughout the text, and literature suggestions are provided. For less experienced readers, a summary of some optimization techniques is also included.
The book will appeal to both students and instructors in specialized courses on optimization, wishing to learn more about variational methods.
1. The Weierstrass Theorem - the origin of optimization.- 2. Some
basics from functional analysis and function spaces.- 3. Differentiation in
infinite dimensional spaces.- 4. On the Weierstrass Theorem in infinite
dimensional spaces.- 5. Applications to multiple integrals.
Format: Hardback, 308 pages, height x width: 235x155 mm, 74 Illustrations, color; 1 Illustrations, black and white; X, 308 p. 75 illus., 74 illus. in color., 1 Hardback
Pub. Date: 08-Feb-2025
ISBN-13: 9783031750229
This book constructs input finite dimensional (FD) models that are amendable for numerical calculations and provides accurate representations for responses of dynamical systems to these inputs, i.e., numerical solutions of stochastic equations. It establishes conditions under which numerical solutions of these equations deliver accurate estimates of extreme responses of dynamical systems that are needed to, for example, predict extreme weather events and design reliable aircrafts. It is intended to serve a broad audience including graduate students, researchers, engineers, scientists and applied mathematicians interested in the formulation and solutions of complex stochastic problems.
Introduction.-, Primer of probability theory.- , Random vectors and
processes.- , Convergence of random elements.- , Extremes of random processes
by finite dimensional (FD) models.- , Extremes of solutions of stochastic
differential equations by finite dimensional (FD) models.
Format: Paperback / softback, 360 pages, height x width: 235x155 mm, 82 Illustrations, color; 18 Illustrations,
black and white; Approx. 360 p. 100 illus., 82 illus. in color., 1 Paperback / softback
Series: Mathematics Study Resources 17
Pub. Date: 15-Mar-2025
ISBN-13: 9783658463120
With this book, which is based on the third edition of a book first written in German about random walks, the author succeeds in a remarkably playful manner in captivating the reader with numerous surprising random phenomena and non-standard limit theorems related to simple random walks and related topics. The work stands out with its consistently problem-oriented, lively presentation, which is further enhanced by 100 illustrative images. The text includes 53 self-assessment questions, with answers provided at the end of each chapter.
Additionally, 74 exercises with solutions assist in understanding the material deeply. The text frequently engages in concrete model-building, and the resulting findings are thoroughly discussed and interconnected. Students who have tested this work in introductory seminars on stochastics were particularly fascinated by the interplay of geometric arguments (reflection principle), combinatorics, elementary stochastics, and analysis.
This book is a translation of an original German edition. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.
1 Introduction.- 2 The Simple Symmetric Random Walk on Z.- 3 Bridges:
The Tied-down Random Walk.- 4 Asymmetric Random Walks on Z and Related
Topics.- 5 Random Walks on the Integer Lattice Zd.- 6 Outlook.- 7 Tools from
Stochastics, Combinatorics, and Analysis.- Solutions to the
Exercises.- Bibliography