Density Functional Theory. A Practical Introduction

Explore the foundations and modern applications of Galois theory Galois theory is widely regarded as one of the most elegant areas of mathematics. A Classical Introduction to Galois Theory develops the topic from a historical perspective, with an emphasis on the solvability of polynomials by radicals. The book provides a gradual transition from the computational methods typical of early literature on the subject to the more abstract approach that characterizes most contemporary expositions. The author provides an easily-accessible presentation of fundamental notions such as roots of unity, minimal polynomials, primitive elements, radical extensions, fixed fields, groups of automorphisms, and solvable series. As a result, their role in modern treatments of Galois theory is clearly illuminated for readers. Classical theorems by Abel, Galois, Gauss, Kronecker, Lagrange, and Ruffini are presented, and the power of Galois theory as both a theoretical and computational tool is illustrated through: A study of the solvability of polynomials of prime degree Development of the theory of periods of roots of unity Derivation of the classical formulas for solving general quadratic, cubic, and quartic polynomials by radicals Throughout the book, key theorems are proved in two ways, once using a classical approach and then again utilizing modern methods. Numerous worked examples showcase the discussed techniques, and background material on groups and fields is provided, supplying readers with a self-contained discussion of the topic. A Classical Introduction to Galois Theory is an excellent resource for courses on abstract algebra at the upper-undergraduate level. The book is also appealing to anyone interested in understanding the origins of Galois theory, why it was created, and how it has evolved into the discipline it is today.

A practical handbook for chemists performing bond forming reactions, this book features useful information on the synthesis of common functional groups in organic chemistry. • Details modern functional group synthesis through carbon-heteroelement (N, O, P, S, B, halogen) bond forming reactions with a focus on operational simplicity and sustainability. • Summarizes key and recent developments – which are otherwise scattered across journal literature – into a single source • Contains over 100 detailed preparations of common functional groups • Included 25 troubleshooting guides with suggestions and potential solutions to common problems. • Complements the text in enhanced ebook editions with tutorial videos where the author provides an introduction to microwave assisted chemistry

Explains the theory behind basic computer vision and provides a bridge from the theory to practical implementation using the industry standard OpenCV libraries Computer Vision is a rapidly expanding area and it is becoming progressively easier for developers to make use of this field due to the ready availability of high quality libraries (such as OpenCV 2). This text is intended to facilitate the practical use of computer vision with the goal being to bridge the gap between the theory and the practical implementation of computer vision. The book will explain how to use the relevant OpenCV library routines and will be accompanied by a full working program including the code snippets from the text. This textbook is a heavily illustrated, practical introduction to an exciting field, the applications of which are becoming almost ubiquitous. We are now surrounded by cameras, for example cameras on computers & tablets/ cameras built into our mobile phones/ cameras in games consoles; cameras imaging difficult modalities (such as ultrasound, X-ray, MRI) in hospitals, and surveillance cameras. This book is concerned with helping the next generation of computer developers to make use of all these images in order to develop systems which are more intuitive and interact with us in more intelligent ways. Explains the theory behind basic computer vision and provides a bridge from the theory to practical implementation using the industry standard OpenCV libraries Offers an introduction to computer vision, with enough theory to make clear how the various algorithms work but with an emphasis on practical programming issues Provides enough material for a one semester course in computer vision at senior undergraduate and Masters levels Includes the basics of cameras and images and image processing to remove noise, before moving on to topics such as image histogramming; binary imaging; video processing to detect and model moving objects; geometric operations & camera models; edge detection; features detection; recognition in images Contains a large number of vision application problems to provide students with the opportunity to solve real problems. Images or videos for these problems are provided in the resources associated with this book which include an enhanced eBook

Gain a deep, intuitive and technical understanding of practical options theory The main challenges in successful options trading are conceptual, not mathematical. Volatility: Practical Options Theory provides financial professionals, academics, students and others with an intuitive as well as technical understanding of both the basic and advanced ideas in options theory to a level that facilitates practical options trading. The approach taken in this book will prove particularly valuable to options traders and other practitioners tasked with making pricing and risk management decisions in an environment where time constraints mean that simplicity and intuition are of greater value than mathematical formalism. The most important areas of options theory, namely implied volatility, delta hedging, time value and the so-called options greeks are explored based on intuitive economic arguments alone before turning to formal models such as the seminal Black-Scholes-Merton model. The reader will understand how the model free approach and mathematical models are related to each other, their underlying theoretical assumptions and their implications to level that facilitates practical implementation. There are several excellent mathematical descriptions of options theory, but few focus on a translational approach to convert the theory into practice. This book emphasizes the translational aspect, while first building an intuitive, technical understanding that allows market makers, portfolio managers, investment managers, risk managers, and other traders to work more effectively within—and beyond—the bounds of everyday practice. Gain a deeper understanding of the assumptions underlying options theory Translate theoretical ideas into practice Develop a more accurate intuition for better time-constrained decision making This book allows its readers to gain more than a superficial understanding of the mechanisms at work in options markets. Volatility gives its readers the edge by providing a true bedrock foundation upon which practical knowledge becomes stronger.

A guide to economics, statistics and finance that explores the mathematical foundations underling econometric methods An Introduction to Econometric Theory offers a text to help in the mastery of the mathematics that underlie econometric methods and includes a detailed study of matrix algebra and distribution theory. Designed to be an accessible resource, the text explains in clear language why things are being done, and how previous material informs a current argument. The style is deliberately informal with numbered theorems and lemmas avoided. However, very few technical results are quoted without some form of explanation, demonstration or proof. The author – a noted expert in the field – covers a wealth of topics including: simple regression, basic matrix algebra, the general linear model, distribution theory, the normal distribution, properties of least squares, unbiasedness and efficiency, eigenvalues, statistical inference in regression, t and F tests, the partitioned regression, specification analysis, random regressor theory, introduction to asymptotics and maximum likelihood. Each of the chapters is supplied with a collection of exercises, some of which are straightforward and others more challenging. This important text: Presents a guide for teaching econometric methods to undergraduate and graduate students of economics, statistics or finance Offers proven classroom-tested material Contains sets of exercises that accompany each chapter Includes a companion website that hosts additional materials, solution manual and lecture slides Written for undergraduates and graduate students of economics, statistics or finance, An Introduction to Econometric Theory is an essential beginner’s guide to the underpinnings of econometrics.

The origins and significance of electron density in the chemical, biological, and materials sciences Electron density is one of the fundamental concepts underlying modern chemistry and one of the key determinants of molecular structure and stability. It is also the basic variable of density functional theory, which has made possible, in recent years, the application of the mathematical theory of quantum physics to chemical and biological systems. With an equal emphasis on computational and philosophical questions, A Matter of Density: Exploring the Electron Density Concept in the Chemical, Biological, and Materials Sciences addresses the foundations, analysis, and applications of this pivotal chemical concept. The first part of the book presents a coherent and logically connected treatment of the theoretical foundations of the electron density concept. Discussion includes the use of probabilities in statistical physics; the origins of quantum mechanics; the philosophical questions at the heart of quantum theory, like quantum entanglement; and methods for the experimental determination of electron density distributions. The remainder of the book deals with applications of the electron density concept in the chemical, biological, and materials sciences. Contributors offer insights on how a deep understanding of the origins of chemical reactivity can be gleaned from the concepts of density functional theory. Also discussed are the applications of electron density in molecular similarity analysis and electron density-derived molecular descriptors, such as electrostatic potentials and local ionization energies. This section concludes with some applications of modern density functional theory to surfaces and interfaces. An essential reference for students as well as quantum and computational chemists, physical chemists, and physicists, this book offers an unparalleled look at the development of the concept of electron density from its inception to its role in density functional theory, which led to the 1998 Nobel Prize in Chemistry.

A thought-provoking look at statistical learning theory and its role in understanding human learning and inductive reasoning A joint endeavor from leading researchers in the fields of philosophy and electrical engineering, An Elementary Introduction to Statistical Learning Theory is a comprehensive and accessible primer on the rapidly evolving fields of statistical pattern recognition and statistical learning theory. Explaining these areas at a level and in a way that is not often found in other books on the topic, the authors present the basic theory behind contemporary machine learning and uniquely utilize its foundations as a framework for philosophical thinking about inductive inference. Promoting the fundamental goal of statistical learning, knowing what is achievable and what is not, this book demonstrates the value of a systematic methodology when used along with the needed techniques for evaluating the performance of a learning system. First, an introduction to machine learning is presented that includes brief discussions of applications such as image recognition, speech recognition, medical diagnostics, and statistical arbitrage. To enhance accessibility, two chapters on relevant aspects of probability theory are provided. Subsequent chapters feature coverage of topics such as the pattern recognition problem, optimal Bayes decision rule, the nearest neighbor rule, kernel rules, neural networks, support vector machines, and boosting. Appendices throughout the book explore the relationship between the discussed material and related topics from mathematics, philosophy, psychology, and statistics, drawing insightful connections between problems in these areas and statistical learning theory. All chapters conclude with a summary section, a set of practice questions, and a reference sections that supplies historical notes and additional resources for further study. An Elementary Introduction to Statistical Learning Theory is an excellent book for courses on statistical learning theory, pattern recognition, and machine learning at the upper-undergraduate and graduate levels. It also serves as an introductory reference for researchers and practitioners in the fields of engineering, computer science, philosophy, and cognitive science that would like to further their knowledge of the topic.

The first book focusing on one of the hottest new topics in Internet of Things systems research and development Studies estimate that by 2020 we will have a vast Internet of Things (IoT) network comprising 26 billion connected devices, including everything from light bulbs to refrigerators, coffee makers to cars. From the beginning, the concept of cyber-physical systems (CPS), or the sensing and control of physical phenomena through networks of devices that work together to achieve common goals, has been implicit in the IoT enterprise. This book focuses on the increasingly hot topic of Human-in-the-loop Cyber-Physical Systems (HiTLCPS)—CPSs that incorporate human responses in IoT equation. Why have we not yet integrated the human component into CPSs? What are the major challenges to achieving HiTLCPS? How can we take advantage of ubiquitous sensing platforms, such as smartphones and personal devices to achieve that goal? While mature HiTLCPS designs have yet to be achieved, or a general consensus reached on underlying HiTLCPS requirements, principles, and theory, researchers and developers worldwide are on the cusp of realizing them. With contributions from researchers at the cutting edge of HiTLCPS R&D, this book addresses many of these questions from the theoretical and practical points of view. An essential primer on a rapidly emerging Internet-of-Things concept, focusing on human-centric applications Discusses new topics which, until now, have only been available in research papers scattered throughout the world literature Addressed fundamental concepts in depth while providing practical insights into the development of complete HiTLCPS systems Includes a companion website containing full source-code for all of the applications described This book is an indispensable resource for researchers and app developers eager to explore HiTL concepts and include them into their designs. It is also an excellent primer for advanced undergraduates and graduate students studying IoT, CPS, and HiTLCPS.

A computational perspective on partial order and lattice theory, focusing on algorithms and their applications This book provides a uniform treatment of the theory and applications of lattice theory. The applications covered include tracking dependency in distributed systems, combinatorics, detecting global predicates in distributed systems, set families, and integer partitions. The book presents algorithmic proofs of theorems whenever possible. These proofs are written in the calculational style advocated by Dijkstra, with arguments explicitly spelled out step by step. The author’s intent is for readers to learn not only the proofs, but the heuristics that guide said proofs. Introduction to Lattice Theory with Computer Science Applications: Examines; posets, Dilworth’s theorem, merging algorithms, lattices, lattice completion, morphisms, modular and distributive lattices, slicing, interval orders, tractable posets, lattice enumeration algorithms, and dimension theory Provides end of chapter exercises to help readers retain newfound knowledge on each subject Includes supplementary material at www.ece.utexas.edu/~garg Introduction to Lattice Theory with Computer Science Applications is written for students of computer science, as well as practicing mathematicians.

Imparts the similarities and differences between ratified and condensed matter, classical and quantum systems as well as real and ideal gases. Presents the quasi-thermodynamic theory of gas-liquid interface and its application for density profile calculation within the van der Waals theory of surface tension. Uses inductive logic to lead readers from observation and facts to personal interpretation and from specific conclusions to general ones.