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A Short Course in Quantum Information Theory: An Approach From Theoretical Physics (Lecture Notes in Physics #827)
by Lajos DiosiThis short and concise primer takes the vantage point of theoretical physics and the unity of physics. It sets out to strip the burgeoning field of quantum information science to its basics by linking it to universal concepts in physics. An extensive lecture rather than a comprehensive textbook, this volume is based on courses delivered over several years to advanced undergraduate and beginning graduate students, but essentially it addresses anyone with a working knowledge of basic quantum physics. Readers will find these lectures a most adequate entry point for theoretical studies in this field. For the second edition, the authors has succeeded in adding many new topics while sticking to the conciseness of the overall approach. A new chapter on qubit thermodynamics has been added, while new sections and subsections have been incorporated in various chapter to deal with weak and time-continuous measurements, period-finding quantum algorithms and quantum error corrections. From the reviews of the first edition: "The best things about this book are its brevity and clarity. In around 100 pages it provides a tutorial introduction to quantum information theory, including problems and solutions. ... it's worth a look if you want to quickly get up to speed with the language and central concepts of quantum information theory, including the background classical information theory." (Craig Savage, Australian Physics, Vol. 44 (2), 2007)
A Short Course on Topological Insulators: Band Structure and Edge States in One and Two Dimensions (Lecture Notes in Physics #919)
by János K. Asbóth László Oroszlány András PályiThis course-based primer provides newcomers to the field with a concise introduction to some of the core topics in the emerging field of topological insulators. The aim is to provide a basic understanding of edge states, bulk topological invariants, and of the bulk--boundary correspondence with as simple mathematical tools as possible. The present approach uses noninteracting lattice models of topological insulators, building gradually on these to arrive from the simplest one-dimensional case (the Su-Schrieffer-Heeger model for polyacetylene) to two-dimensional time-reversal invariant topological insulators (the Bernevig-Hughes-Zhang model for HgTe). In each case the discussion of simple toy models is followed by the formulation of the general arguments regarding topological insulators. The only prerequisite for the reader is a working knowledge in quantum mechanics, the relevant solid state physics background is provided as part of this self-contained text, which is complemented by end-of-chapter problems.
A Short Introduction to Mathematical Concepts in Physics
by Jim NapolitanoMathematics is the language of physics and yet, mathematics is an enormous subject. This textbook provides an accessible and concise introduction to mathematical physics for undergraduate students taking a one semester course. It assumes the reader has studied a year of introductory physics and three semesters of basic calculus, including some vector calculus, but no formal training in differential equations or matrix algebra. It equips readers with the skills and foundational knowledge they need for courses that follow in classical mechanics, electromagnetism, quantum mechanics, and thermal physics. This book exposes students early on to the kinds of mathematical manipulations they will need in upper-level courses in physics. It can also serve as a useful reference for their further studies. Key features: Accompanied by homework problems and a solutions manual for instructors, available upon qualifying course adoption Bridges the gap between calculus and physics, explaining fundamental mathematics (differentiation, integration, infinite series) in physical terms Explores quick extensions into mathematics useful in physics, not typically taught in math courses, including the Gamma Function, hyperbolic functions, Gaussian integrals, Legendre polynomials, functions of a complex variable, and probability distribution functions
A Short Introduction to Partial Differential Equations (CMS/CAIMS Books in Mathematics #11)
by Arian NovruziThis book provides a short introduction to partial differential equations (PDEs). It is primarily addressed to graduate students and researchers, who are new to PDEs. The book offers a user-friendly approach to the analysis of PDEs, by combining elementary techniques and fundamental modern methods. The author focuses the analysis on four prototypes of PDEs, and presents two approaches for each of them. The first approach consists of the method of analytical and classical solutions, and the second approach consists of the method of weak (variational) solutions. In connection with the approach of weak solutions, the book also provides an introduction to distributions, Fourier transform and Sobolev spaces. The book ends with an appendix chapter, which complements the previous chapters with proofs, examples and remarks. This book can be used for an intense one-semester, or normal two-semester, PDE course. The reader is expected to have knowledge of linear algebra and of differential equations, a good background in real and complex calculus and a modest background in analysis and topology. The book has many examples, which help to better understand the concepts, highlight the key ideas and emphasize the sharpness of results, as well as a section of problems at the end of each chapter.
A Shrinking Society: Post-Demographic Transition in Japan (SpringerBriefs in Population Studies)
by Toshihiko HaraThis is the book to focus on a new phenomenon emerging in the twenty-first century: the rapidly aging and decreasing population of a well-developed country, namely, Japan. The meaning of this phenomenon has been successfully clarified as the possible historical consequence of the demographic transition from high birth and death rates to low ones. Japan has entered the post-demographic transitional phase and will be the fastest-shrinking society in the world, leading other Asian countries that are experiencing the same drastic changes. The author used the historical statistics, compiled by the Statistic Bureau, Ministry of Internal Affairs and Communications in 2006 and population projections for released in 2012 by the National Institute of Population and Social Security Research, to show the past and future development of the dependency ratio from 1891 to 2060. Then, utilizing the population life table and net reproduction rate, the effects of increasing life expectancy and declining fertility on the dependency ratio were observed separately. Finally, the historical relationships among women's survival rates at reproductive age, the theoretical fertility rate to maintain the replacement level and the recorded total fertility rate (TFR) were analyzed. Historical observation showed TFR adapting to the theoretical level of fertility with a certain time lag and corresponding to women's survival rates at reproductive age. Women's increasing lifespan and survival rates could have influenced decision making to minimize the risk of childbearing. Even if the theoretical fertility rate meets the replacement level, women's views of minimizing the risk may remain unchanged because for women the cost-benefit imbalance in childbearing is still too high in Japan. Based on the findings, the author discusses the sustainability of Japanese society in relation to national finances, social security reform, family policies, immigration policies and community polices.
A Signal Theoretic Introduction to Random Processes
by Roy M. HowardA fresh introduction to random processes utilizing signal theory By incorporating a signal theory basis, A Signal Theoretic Introduction to Random Processes presents a unique introduction to random processes with an emphasis on the important random phenomena encountered in the electronic and communications engineering field. The strong mathematical and signal theory basis provides clarity and precision in the statement of results. The book also features: A coherent account of the mathematical fundamentals and signal theory that underpin the presented material Unique, in-depth coverage of material not typically found in introductory books Emphasis on modeling and notation that facilitates development of random process theory Coverage of the prototypical random phenomena encountered in electrical engineering Detailed proofs of results A related website with solutions to the problems found at the end of each chapter A Signal Theoretic Introduction to Random Processes is a useful textbook for upper-undergraduate and graduate-level courses in applied mathematics as well as electrical and communications engineering departments. The book is also an excellent reference for research engineers and scientists who need to characterize random phenomena in their research. provides details the prototypical random processes that are fundamental to electrical, electronic, and communication engineering. Consequently, chapter 7-10 coverage includes details of the characterization of random phenomena from an engineering perspective: probability mass function/probability density function evolution, autocorrelation function, and power spectral density. Chapter 11 features an introduction to order statistics, which provides the background for a discussion of the Poisson point random process in Chapter 12. Chapter 13 introduces birth-death random processes and then Chapter 14 provides an introduction to first passage time theory.
A Simple Guide to Technology and Analytics
by Brian J. EvansEveryday technology is constantly changing, and it’s hard to keep up with it at times. What is all this talk about automation, STEM, analytics and super-computers, and how will it really affect my daily life at work and in the home? This book is a simple guide to everyday technology and analytics written in plain language. It starts with explaining how computer networks are increasing in speed so fast that we can do more in less time than ever before. It explains the analytical jargon in plain English and why robotics in the home will be aided by the new technology of the quantum computer. Richly furnished with over 200 illustrations, photos and with minimal equations, A Simple Guide to Technology and Analytics is a ready reference book for those times when you don’t really understand the technology and analytics being talked about. It explains complicated topics such as automated character recognition in a very simple way, and has simple exercises for the reader to fully understand the technology (with answers at the back). It even has explanations on how home appliances work, which are very useful the next time you go shopping for a microwave or TV. Even the Glossary at the back can be used as a quick look-up explanation for those on the go.
A Simple Introduction to Python (Chapman & Hall/CRC The Python Series)
by Stephen LynchA Simple Introduction to Python is aimed at pre-university students and complete novices to programming. The whole book has been created using Jupyter notebooks. After introducing Python as a powerful calculator, simple programming constructs are covered, and the NumPy, MatPlotLib and SymPy modules (libraries) are introduced. Python is then used for Mathematics, Cryptography, Artificial Intelligence, Data Science and Object Oriented Programming.The reader is shown how to program using the integrated development environments: Python IDLE, Spyder, Jupyter notebooks, and through cloud computing with Google Colab.Features: No prior experience in programming is required. Demonstrates how to format Jupyter notebooks for publication on the Web. Full solutions to exercises are available as a Jupyter notebook on the Web. All Jupyter notebook solution files can be downloaded through GitHub. GitHub Repository of Data Files and a Jupyter Solution notebook: https://github.com/proflynch/A-Simple-Introduction-to-PythonJupyter Solution notebook web page: https://drstephenlynch.github.io/webpages/A-Simple-Introduction-to-Python-Solutions.html
A Simple Introduction to the Mixed Finite Element Method: Theory and Applications (SpringerBriefs in Mathematics)
by Gabriel N. GaticaThe main purpose of this book is to provide a simple and accessible introduction to the mixed finite element method as a fundamental tool to numerically solve a wide class of boundary value problems arising in physics and engineering sciences. The book is based on material that was taught in corresponding undergraduate and graduate courses at the Universidad de Concepcion, Concepcion, Chile, during the last 7 years. As compared with several other classical books in the subject, the main features of the present one have to do, on one hand, with an attempt of presenting and explaining most of the details in the proofs and in the different applications. In particular several results and aspects of the corresponding analysis that are usually available only in papers or proceedings are included here.
A Source Book in Mathematics
by David Eugene SmithThis work presents, in English translation, the great discoveries in mathematics from the Renaissance to the end of the nineteenth century. You are able to read the writings of Newton, Leibniz, Pascal, Riemann, Bernoulli, and others, exactly as the world saw them for the first time. Succinct selections from 125 different treatises and articles, most of them unavailable elsewhere in English, offer a vivid, firsthand story of the growth of mathematics.
A Spectral Theory Of Noncommuting Operators
by Rongwei YangThe main goal of this book is to describe various aspects of the theory of joint spectra for matrices and linear operators. It is suitable for a graduate-level topic course in spectral theory and/or representation theory. The first three chapters can also be adopted for an advanced course in linear algebra. Centered around the concept of projective spectrum, the book presents a coherent treatment of fundamental elements from a wide range of mathematical disciplines, such as complex analysis, complex dynamics, differential geometry, functional analysis, group theory, and Lie algebras. Researchers and students, particularly those who aspire to gain a bigger picture of mathematics, will find this book both informative and resourceful.
A Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation (Lecture Notes in Mathematics #2229)
by Sebastian KleinThis book develops a spectral theory for the integrable system of 2-dimensional, simply periodic, complex-valued solutions u of the sinh-Gordon equation. Such solutions (if real-valued) correspond to certain constant mean curvature surfaces in Euclidean 3-space. Spectral data for such solutions are defined (following ideas of Hitchin and Bobenko) and the space of spectral data is described by an asymptotic characterization. Using methods of asymptotic estimates, the inverse problem for the spectral data is solved along a line, i.e. the solution u is reconstructed on a line from the spectral data. Finally, a Jacobi variety and Abel map for the spectral curve are constructed and used to describe the change of the spectral data under translation of the solution u. The book's primary audience will be research mathematicians interested in the theory of infinite-dimensional integrable systems, or in the geometry of constant mean curvature surfaces.
A Star in My Orange: Looking for Nature's Shapes
by Dana Meachen RauThis book introduces the child to different geometric shapes seen in nature.
A Stata Companion to Political Analysis (Third Edition)
by Philip H. PollockWith this Third Edition, students quickly learn Stata with step-by-step instructions, more than 50 exercises, customized data sets, annotated screen shots, boxes that highlight Stata's capabilities, and guidance on using Stata to read raw data.
A Statistical Guide for the Ethically Perplexed
by Howard Wainer Lawrence HubertExploring the intersection of ethics and statistics, this comprehensive guide illustrates the proper use of probabilistic and statistical reasoning in the behavioral, social, and biomedical sciences. Lauded for their contributions to statistics, psychology, and psychometrics, the authors make statistical methods relevant to readers' day-to-day lives by including real historical situations that demonstrate the role of statistics in reasoning and decision making. In addition, seven U.S. Supreme Court decisions reflect the influence of statistical and psychometric reasoning and interpretation/misinterpretation.
A Statistical Mechanical Interpretation of Algorithmic Information Theory (SpringerBriefs in Mathematical Physics #36)
by Kohtaro TadakiThis book is the first one that provides a solid bridge between algorithmic information theory and statistical mechanics. Algorithmic information theory (AIT) is a theory of program size and recently is also known as algorithmic randomness. AIT provides a framework for characterizing the notion of randomness for an individual object and for studying it closely and comprehensively. In this book, a statistical mechanical interpretation of AIT is introduced while explaining the basic notions and results of AIT to the reader who has an acquaintance with an elementary theory of computation.A simplification of the setting of AIT is the noiseless source coding in information theory. First, in the book, a statistical mechanical interpretation of the noiseless source coding scheme is introduced. It can be seen that the notions in statistical mechanics such as entropy, temperature, and thermal equilibrium are translated into the context of noiseless source coding in a natural manner. Then, the framework of AIT is introduced. On this basis, the introduction of a statistical mechanical interpretation of AIT is begun. Namely, the notion of thermodynamic quantities, such as free energy, energy, and entropy, is introduced into AIT. In the interpretation, the temperature is shown to be equal to the partial randomness of the values of all these thermodynamic quantities, where the notion of partial randomness is a stronger representation of the compression rate measured by means of program-size complexity. Additionally, it is demonstrated that this situation holds for the temperature itself as a thermodynamic quantity. That is, for each of all the thermodynamic quantities above, the computability of its value at temperature T gives a sufficient condition for T to be a fixed point on partial randomness.In this groundbreaking book, the current status of the interpretation from both mathematical and physical points of view is reported. For example, a total statistical mechanical interpretation of AIT that actualizes a perfect correspondence to normal statistical mechanics can be developed by identifying a microcanonical ensemble in the framework of AIT. As a result, the statistical mechanical meaning of the thermodynamic quantities of AIT is clarified. In the book, the close relationship of the interpretation to Landauer's principle is pointed out.
A Step by Step Approach to the Modeling of Chemical Engineering Processes
by Liliane Maria Ferrareso LonaThis book treats modeling and simulation in a simple way, that builds on the existing knowledge and intuition of students. They will learn how to build a model and solve it using Excel.Most chemical engineering students feel a shiver down the spine when they see a set of complex mathematical equations generated from the modeling of a chemical engineering system. This is because they usually do not understand how to achieve this mathematical model, or they do not know how to solve the equations system without spending a lot of time and effort.Trying to understand how to generate a set of mathematical equations to represent a physical system (to model) and solve these equations (to simulate) is not a simple task. A model, most of the time, takes into account all phenomena studied during a Chemical Engineering course. In the same way, there is a multitude of numerical methods that can be used to solve the same set of equations generated from the modeling, and many different computational languages can be adopted to implement the numerical methods. As a consequence of this comprehensiveness and combinatorial explosion of possibilities, most books that deal with this subject are very extensive and embracing, making need for a lot of time and effort to go through this subject. It is expected that with this book the chemical engineering student and the future chemical engineer feel motivated to solve different practical problems involving chemical processes, knowing they can do that in an easy and fast way, with no need of expensive software.
A Step-by-Step Guide to Exploratory Factor Analysis with SPSS
by Marley W. WatkinsThis is a concise, easy-to-use, step-by-step guide for applied researchers conducting exploratory factor analysis (EFA) using SPSS.
A Step-by-Step Guide to Exploratory Factor Analysis with Stata
by Marley W. WatkinsThis is a concise, easy to use, step-by-step guide for applied researchers conducting exploratory factor analysis (EFA) using Stata. In this book, Dr. Watkins systematically reviews each decision step in EFA with screen shots of Stata code and recommends evidence-based best practice procedures. This is an eminently applied, practical approach with few or no formulas and is aimed at readers with little to no mathematical background. Dr. Watkins maintains an accessible tone throughout and uses minimal jargon and formula to help facilitate grasp of the key issues users will face when applying EFA, along with how to implement, interpret, and report results. Copious scholarly references and quotations are included to support the reader in responding to editorial reviews. This is a valuable resource for upper level undergraduate and postgraduate students, as well as for more experienced researchers undertaking multivariate or structure equation modeling courses across the behavioral, medical, and social sciences.
A Stitch in Line: Mathematics and One-Stitch Sashiko (AK Peters/CRC Recreational Mathematics Series)
by Katherine SeatonA Stitch in Line: Mathematics and One-Stitch Sashiko provides readers with instructions for creating hitomezashi items with minimum outlay. The reader is guided through the practical steps involved in creating each design, and then the mathematics which underpins it is explained in a friendly, accessible way. This is a fantastic book for anyone who is interested in recreational mathematics and/or fibre arts and can be a useful resource for teaching and learning mathematical concepts in a fun and engaging format. Features Numerous full-colour photographs of hitomezashi stitch patterns which have been mathematically designed. Suitable for readers of all mathematical levels and backgrounds — no prior knowledge is automatically assumed. A compressed encoding for recording and designing hitomezashi patterns to be stitched or drawn. Accessible explanations and explorations of mathematical concepts inherent in, or illustrated by, hitomezashi patterns.
A Strange Wilderness: The Lives of the Great Mathematicians
by Amir D. Aczel“Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost.”-- Mathematics historian W. S. Anglin From the internationally bestselling author of Fermats Last Theorem comes a landmark publication on the eccentric lives of the foremost mathematicians in history..From Archimedes eureka moment to Alexander Grothendiecks seclusion in the Pyrenees, bestselling author Amir Aczel selects the most compelling stories in the history of mathematics, creating a colorful narrative that explores the quirky personalities behind some of the most groundbreaking, enduring theorems. This is not your dry “college textbook” account of mathematical history; it bristles with tales of duels, battlefield heroism, flamboyant arrogance, pranks, secret societies, imprisonment, feuds, theft, and some very costly errors of judgment. (Clearly, genius doesnt guarantee street smarts.) Ultimately, readers will come away entertained, and with a newfound appreciation of the tenacity, complexity, eccentricity, and brilliance of the mathematical genius.
A Strategy for Using Multicriteria Analysis in Decision-Making: A Guide for Simple and Complex Environmental Projects
by Nolberto MunierThis book develops a whole strategy for decision-making, with the full participation of the decision-maker and utilizing continuous feedback. It introduces the use of the very well-known and proven methodology, linear programming, but specially adapted for this purpose. For this, it incorporates a method to include subjective concepts, as well as the possibility of working with many different and even contradictory objectives. The book is liberally populated with diverse case studies to illustrate the concepts. This practical guide will be of interest to anyone undertaking analysis and decision-making, on both simple and complex projects, and who is looking for a strategy to organize, classify, and evaluate the large amount of information required to make an informed decision. The strategy includes methods to analyze the results and extract conclusions from them.
A Student's Guide to Fourier Transforms
by J. F. JamesFourier transform theory is of central importance in a vast range of applications in physical science, engineering, and applied mathematics. This new edition of a successful student text provides a concise introduction to the theory and practice of Fourier transforms, using qualitative arguments wherever possible and avoiding unnecessary mathematics. After a brief description of the basic ideas and theorems, the power of the technique is then illustrated by referring to particular applications in optics, spectroscopy, electronics and telecommunications. The rarely discussed but important field of multi-dimensional Fourier theory is covered, including a description of computer-aided tomography (CAT-scanning). The final chapter discusses digital methods, with particular attention to the fast Fourier transform. Throughout, discussion of these applications is reinforced by the inclusion of worked examples. The book assumes no previous knowledge of the subject, and will be invaluable to students of physics, electrical and electronic engineering, and computer science.
A Student's Guide to Geophysical Equations
by William LowrieThe advent of accessible student computing packages has meant that geophysics students can now easily manipulate datasets and gain first-hand modeling experience - essential in developing an intuitive understanding of the physics of the Earth. Yet to gain a more in-depth understanding of physical theory, and to develop new models and solutions, it is necessary to be able to derive the relevant equations from first principles. This compact, handy book fills a gap left by most modern geophysics textbooks, which generally do not have space to derive all of the important formulae, showing the intermediate steps. This guide presents full derivations for the classical equations of gravitation, gravity, tides, earth rotation, heat, geomagnetism and foundational seismology, illustrated with simple schematic diagrams. It supports students through the successive steps and explains the logical sequence of a derivation - facilitating self-study and helping students to tackle homework exercises and prepare for exams.
A Student's Guide to Lagrangians and Hamiltonians
by Patrick HamillA concise but rigorous treatment of variational techniques, focussing primarily on Lagrangian and Hamiltonian systems, this book is ideal for physics, engineering and mathematics students. The book begins by applying Lagrange's equations to a number of mechanical systems. It introduces the concepts of generalized coordinates and generalized momentum. Following this the book turns to the calculus of variations to derive the Euler–Lagrange equations. It introduces Hamilton's principle and uses this throughout the book to derive further results. The Hamiltonian, Hamilton's equations, canonical transformations, Poisson brackets and Hamilton–Jacobi theory are considered next. The book concludes by discussing continuous Lagrangians and Hamiltonians and how they are related to field theory. Written in clear, simple language and featuring numerous worked examples and exercises to help students master the material, this book is a valuable supplement to courses in mechanics.