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New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in Mathbb{R}^{n}

New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in Mathbb{R}^{n}
Author: Antonio Alarcón
Publisher:
Total Pages: 77
Release: 2020
Genre: Electronic books
ISBN: 9781470458126

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The aim of this work is to adapt the complex analytic methods originating in modern Oka theory to the study of non-orientable conformal minimal surfaces in \mathbb{R}^n for any n\ge 3. These methods, which the authors develop essentially from the first principles, enable them to prove that the space of conformal minimal immersions of a given bordered non-orientable surface to \mathbb{R}^n is a real analytic Banach manifold, obtain approximation results of Runge-Mergelyan type for conformal minimal immersions from non-orientable surfaces, and show general position theorems for non-orientable co.


Minimal Surfaces from a Complex Analytic Viewpoint

Minimal Surfaces from a Complex Analytic Viewpoint
Author: Antonio Alarcón
Publisher: Springer Nature
Total Pages: 430
Release: 2021-03-10
Genre: Mathematics
ISBN: 3030690563

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This monograph offers the first systematic treatment of the theory of minimal surfaces in Euclidean spaces by complex analytic methods, many of which have been developed in recent decades as part of the theory of Oka manifolds (the h-principle in complex analysis). It places particular emphasis on the study of the global theory of minimal surfaces with a given complex structure. Advanced methods of holomorphic approximation, interpolation, and homotopy classification of manifold-valued maps, along with elements of convex integration theory, are implemented for the first time in the theory of minimal surfaces. The text also presents newly developed methods for constructing minimal surfaces in minimally convex domains of Rn, based on the Riemann–Hilbert boundary value problem adapted to minimal surfaces and holomorphic null curves. These methods also provide major advances in the classical Calabi–Yau problem, yielding in particular minimal surfaces with the conformal structure of any given bordered Riemann surface. Offering new directions in the field and several challenging open problems, the primary audience of the book are researchers (including postdocs and PhD students) in differential geometry and complex analysis. Although not primarily intended as a textbook, two introductory chapters surveying background material and the classical theory of minimal surfaces also make it suitable for preparing Masters or PhD level courses.


Deep Learning Architectures

Deep Learning Architectures
Author: Ovidiu Calin
Publisher: Springer Nature
Total Pages: 760
Release: 2020-02-13
Genre: Mathematics
ISBN: 3030367215

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This book describes how neural networks operate from the mathematical point of view. As a result, neural networks can be interpreted both as function universal approximators and information processors. The book bridges the gap between ideas and concepts of neural networks, which are used nowadays at an intuitive level, and the precise modern mathematical language, presenting the best practices of the former and enjoying the robustness and elegance of the latter. This book can be used in a graduate course in deep learning, with the first few parts being accessible to senior undergraduates. In addition, the book will be of wide interest to machine learning researchers who are interested in a theoretical understanding of the subject.


Integral Bases

Integral Bases
Author: William Edward Hodgson Berwick
Publisher:
Total Pages: 112
Release: 1927
Genre: Algebraic number theory
ISBN:

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Field and Galois Theory

Field and Galois Theory
Author: Patrick Morandi
Publisher: Springer Science & Business Media
Total Pages: 294
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461240409

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In the fall of 1990, I taught Math 581 at New Mexico State University for the first time. This course on field theory is the first semester of the year-long graduate algebra course here at NMSU. In the back of my mind, I thought it would be nice someday to write a book on field theory, one of my favorite mathematical subjects, and I wrote a crude form of lecture notes that semester. Those notes sat undisturbed for three years until late in 1993 when I finally made the decision to turn the notes into a book. The notes were greatly expanded and rewritten, and they were in a form sufficient to be used as the text for Math 581 when I taught it again in the fall of 1994. Part of my desire to write a textbook was due to the nonstandard format of our graduate algebra sequence. The first semester of our sequence is field theory. Our graduate students generally pick up group and ring theory in a senior-level course prior to taking field theory. Since we start with field theory, we would have to jump into the middle of most graduate algebra textbooks. This can make reading the text difficult by not knowing what the author did before the field theory chapters. Therefore, a book devoted to field theory is desirable for us as a text. While there are a number of field theory books around, most of these were less complete than I wanted.


Hands-On Mathematics for Deep Learning

Hands-On Mathematics for Deep Learning
Author: Jay Dawani
Publisher: Packt Publishing Ltd
Total Pages: 347
Release: 2020-06-12
Genre: Computers
ISBN: 183864184X

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A comprehensive guide to getting well-versed with the mathematical techniques for building modern deep learning architectures Key FeaturesUnderstand linear algebra, calculus, gradient algorithms, and other concepts essential for training deep neural networksLearn the mathematical concepts needed to understand how deep learning models functionUse deep learning for solving problems related to vision, image, text, and sequence applicationsBook Description Most programmers and data scientists struggle with mathematics, having either overlooked or forgotten core mathematical concepts. This book uses Python libraries to help you understand the math required to build deep learning (DL) models. You'll begin by learning about core mathematical and modern computational techniques used to design and implement DL algorithms. This book will cover essential topics, such as linear algebra, eigenvalues and eigenvectors, the singular value decomposition concept, and gradient algorithms, to help you understand how to train deep neural networks. Later chapters focus on important neural networks, such as the linear neural network and multilayer perceptrons, with a primary focus on helping you learn how each model works. As you advance, you will delve into the math used for regularization, multi-layered DL, forward propagation, optimization, and backpropagation techniques to understand what it takes to build full-fledged DL models. Finally, you’ll explore CNN, recurrent neural network (RNN), and GAN models and their application. By the end of this book, you'll have built a strong foundation in neural networks and DL mathematical concepts, which will help you to confidently research and build custom models in DL. What you will learnUnderstand the key mathematical concepts for building neural network modelsDiscover core multivariable calculus conceptsImprove the performance of deep learning models using optimization techniquesCover optimization algorithms, from basic stochastic gradient descent (SGD) to the advanced Adam optimizerUnderstand computational graphs and their importance in DLExplore the backpropagation algorithm to reduce output errorCover DL algorithms such as convolutional neural networks (CNNs), sequence models, and generative adversarial networks (GANs)Who this book is for This book is for data scientists, machine learning developers, aspiring deep learning developers, or anyone who wants to understand the foundation of deep learning by learning the math behind it. Working knowledge of the Python programming language and machine learning basics is required.


Introduction to Stochastic Processes

Introduction to Stochastic Processes
Author: Gregory F. Lawler
Publisher: CRC Press
Total Pages: 249
Release: 2018-10-03
Genre: Mathematics
ISBN: 1482286114

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Emphasizing fundamental mathematical ideas rather than proofs, Introduction to Stochastic Processes, Second Edition provides quick access to important foundations of probability theory applicable to problems in many fields. Assuming that you have a reasonable level of computer literacy, the ability to write simple programs, and the access to software for linear algebra computations, the author approaches the problems and theorems with a focus on stochastic processes evolving with time, rather than a particular emphasis on measure theory. For those lacking in exposure to linear differential and difference equations, the author begins with a brief introduction to these concepts. He proceeds to discuss Markov chains, optimal stopping, martingales, and Brownian motion. The book concludes with a chapter on stochastic integration. The author supplies many basic, general examples and provides exercises at the end of each chapter. New to the Second Edition: Expanded chapter on stochastic integration that introduces modern mathematical finance Introduction of Girsanov transformation and the Feynman-Kac formula Expanded discussion of Itô's formula and the Black-Scholes formula for pricing options New topics such as Doob's maximal inequality and a discussion on self similarity in the chapter on Brownian motion Applicable to the fields of mathematics, statistics, and engineering as well as computer science, economics, business, biological science, psychology, and engineering, this concise introduction is an excellent resource both for students and professionals.


First Year Calculus (First Edition)

First Year Calculus (First Edition)
Author: Michael Dougherty
Publisher: Cognella Academic Publishing
Total Pages:
Release: 2019-05-03
Genre:
ISBN: 9781516542284

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First Semester Calculus for Students of Mathematics and Related Disciplines equips students with a working knowledge of the fundamental principles of calculus. The book provides an engaging and accessible entry point into a critical field of study. It prepares students for more advanced courses in calculus and also helps them understand how to apply basic principles of calculus to solve problems within a wide range of disciplines, including business, biology, engineering, science, liberal arts, and mathematics. The text employs rigorous treatment of early calculus topics and detailed explanations to facilitate greater understanding and connection with the material. Over the course of five chapters, students learn about symbolic logic, continuity and limits, derivatives, mathematical and real-world applications of derivatives, and antiderivatives and their applications. Throughout, students are provided with rich guidance and copious opportunities to deepen their personal understanding of the subject matter. Highly readable and applicable, First Semester Calculus for Students of Mathematics and Related Disciplines is an ideal resource for a variety of courses that apply concepts of calculus to solve mathematical and real-world problems.


Deep Learning: Concepts and Architectures

Deep Learning: Concepts and Architectures
Author: Witold Pedrycz
Publisher: Springer Nature
Total Pages: 342
Release: 2019-10-29
Genre: Technology & Engineering
ISBN: 3030317560

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This book introduces readers to the fundamental concepts of deep learning and offers practical insights into how this learning paradigm supports automatic mechanisms of structural knowledge representation. It discusses a number of multilayer architectures giving rise to tangible and functionally meaningful pieces of knowledge, and shows how the structural developments have become essential to the successful delivery of competitive practical solutions to real-world problems. The book also demonstrates how the architectural developments, which arise in the setting of deep learning, support detailed learning and refinements to the system design. Featuring detailed descriptions of the current trends in the design and analysis of deep learning topologies, the book offers practical guidelines and presents competitive solutions to various areas of language modeling, graph representation, and forecasting.


Cycles in Graphs

Cycles in Graphs
Author: B.R. Alspach
Publisher: Elsevier
Total Pages: 483
Release: 1985-08-01
Genre: Mathematics
ISBN: 0080872263

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This volume deals with a variety of problems involving cycles in graphs and circuits in digraphs. Leading researchers in this area present here 3 survey papers and 42 papers containing new results. There is also a collection of unsolved problems.