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Siu Yum-Tong: Introduction to Several
Complex Variables

Introduction to Several Complex Variables

Your training data has as much to do with the success of your data project as the algorithms themselves--most failures in deep learning systems relate to training data. But while training data is the foundation for successful machine learning, there are few comprehensive resources to help you ace the process. This hands-on guide explains how to work with and scale training data. Data science professionals and machine learning engineers will gain a solid understanding of the concepts, tools, and processes needed to: <ul> <li>Design, deploy, and ship training data for production-grade deep learning applications </li><li>Integrate with a growing ecosystem of tools </li><li>Recognize and correct new training data-based failure modes </li><li>Improve existing system performance and avoid development risks </li><li>Confidently use automation and acceleration approaches to more effectively create training data </li><li>Avoid data loss by structuring metadata around created datasets </li><li>Clearly explain training data concepts to subject matter experts and other shareholders </li><li>Successfully maintain, operate, and improve your system </li></ul>

Training Data for Machine Learning

CRC Press/Chapman and Hall Handbooks in Mathematics Series

This handbook concerns the subject of holomorphic function spaces and operators acting on them. Topics include Bergman spaces, Hardy spaces, Besov/Sobolev spaces, Fock spaces, and the space of Dirichlet series. Operators discussed in the book include Toeplitz operators, Hankel operators, composition operators, and Cowen-Douglas class operators.

Handbook of Analytic Operator Theory

Starting Category Theory

This new 25th anniversary edition of Visual Complex Analysis introduces this powerful method combining complex numbers with ordinary calculus, and includes new introductory content and brand-new captions that fully explain the geometrical reasoning.

This new 25th anniversary edition of Visual Complex Analysis introduces this powerful method combining complex numbers with ordinary calculus, and includes new introductory content and brand-new captions that fully explain the geometrical reasoning.

25th Anniversary Edition

Visual Complex Analysis

Series on Knots & Everything

A classic knot is an embedded simple loop in 3-dimensional space. It can be described as a 4-valent planar graph or network in the horizontal plane, with the vertices or crossings corresponding to double points of a projection. At this stage we have the shadow of the knot defined by the projection. We can reconstruct the knot by lifting the crossings into two points in space, one above the other. This information is preserved at the vertices by cutting the arc which appears to go under the over crossing arc. We can then act on this diagram of the knot using the famous Reidemeister moves to mimic the motion of the knot in space. The result is classic combinatorial knot theory. In recent years, many different types of knot theories have been considered where the information stored at the crossings determines how the Reidemeister moves are used, if at all.

In this book, we look at all these new theories systematically in a way which any third-year undergraduate mathematics student would understand. This book can form the basis of an undergraduate course or as an entry point for a postgraduate studying topology.

Combinatorial Knot Theory

This is a concise book that introduces students to the basics of logical thinking and important mathematical structures that are critical for a solid understanding of logical formalisms themselves as well as for building the necessary background to tackle other fields that are based on these logical principles. Despite its compact and small size, it includes many solved problems and quite a few end-of-section exercises that will help readers consolidate their understanding of the material.


This textbook is essential reading for anyone interested in the logical foundations of Informatics, Computer Science, Data Science, Artificial Intelligence, and other related areas. Written with undergraduate students in these disciplines in mind, this book can very well serve the needs of interested and curious readers who wish to get a grasp of the logical principles upon which these fields are built. This book does not require readers to possess math skills beyond those learned in high school.

Mathematical Foundations Of Information Sciences

Chapman & Hall/CRC Monographs and Research Notes in Mathematics

Convex Analysis in Polynomial Spaces with Applications

"This rigorous introduction to the fundamental ideas of convexity and their use in optimization offers a unifying approach for both discrete and continuous applications. Students and researchers in optimization, operations research, computer science, and applied mathematics will appreciate the book's 300+ exercises and coverage of new developments"--

This rigorous introduction to the fundamental ideas of convexity and their use in optimization offers a unifying approach for both discrete and continuous applications. Students and researchers in optimization, operations research, computer science, and applied mathematics will appreciate the book's 300+ exercises and coverage of new developments.

Convexity and its Applications in Discrete and Continuous Optimization

This book provides a comprehensive exploration of generalization in deep learning, focusing on both theoretical foundations and practical strategies. It delves deeply into how machine learning models, particularly deep neural networks, achieve robust performance on unseen data.

Theoretical Foundations and Practical Strategies

Deep Learning Generalization

One of the central highlights of this work is the exploration of the Yoneda lemma and its profound implications, during which intuitive explanations are provided, as well as detailed proofs, and specific examples. This book covers aspects of category theory often considered advanced in a clear and intuitive way, with rigorous mathematical proofs. It investigates universal properties, coherence, the relationship between categories and graphs, and treats monads and comonads on an equal footing, providing theorems, interpretations and concrete examples. Finally, this text contains an introduction to monoidal categories and to strong and commutative monads, which are essential tools in current research but seldom found in other textbooks.


Starting Category Theory serves as an accessible and comprehensive introduction to the fundamental concepts of category theory. Originally crafted as lecture notes for an undergraduate course, it has been developed to be equally well-suited for individuals pursuing self-study. Most crucially, it deliberately caters to those who are new to category theory, not requiring readers to have a background in pure mathematics, but only a basic understanding of linear algebra.

Textbooks in Mathematics

The idea of complex numbers dates back at least 300 years-to Gauss and Euler, among others. Today complex analysis is a central part of modern analytical thinking. It is used in engineering, physics, mathematics, astrophysics, and many other fields. It provides powerful tools for doing mathematical analysis, and often yields pleasing and unanticipated answers.


This book makes the subject of complex analysis accessible to a broad audience. The complex numbers are a somewhat mysterious number system that seems to come out of the blue. It is important for students to see that this is really a very concrete set of objects that has very concrete and meaningful applications. 





Features:









This new edition is a substantial rewrite, focusing on the accessibility, applied, and visual aspect of complex analysis





This book has an exceptionally large number of examples and a large number of figures. 








The topic is presented as a natural outgrowth of the calculus. It is not a new language, or a new way of thinking.








Incisive applications appear throughout the book.








Partial differential equations are used as a unifying theme.

Complex Variables: A Physical Approach with Applications, Second Edition offers a notable revision. The emphasis remains on theory and practice. The first part of the text focuses on the fundamental concepts. The author then moves on to a detailed look at how complex variables are used in the real world.

A Physical Approach with Applications

Complex Variables

Introduction to Several Complex Variables

Bibliografische Angaben

Schlagworte

Bibliografische Angaben

Schlagworte

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