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Mathematics of Quantum Computation
by Goong Chen Ranee K. BrylinskiAmong the most exciting developments in science today is the design and construction of the quantum computer. Its realization will be the result of multidisciplinary efforts, but ultimately, it is mathematics that lies at the heart of theoretical quantum computer science.Mathematics of Quantum Computation brings together leading computer sc
Mathematics of Quantum Computing: An Introduction
by Wolfgang SchererThis textbook presents the elementary aspects of quantum computing in a mathematical form. It is intended as core or supplementary reading for physicists, mathematicians, and computer scientists taking a first course on quantum computing. It starts by introducing the basic mathematics required for quantum mechanics, and then goes on to present, in detail, the notions of quantum mechanics, entanglement, quantum gates, and quantum algorithms, of which Shor's factorisation and Grover's search algorithm are discussed extensively. In addition, the algorithms for the Abelian Hidden Subgroup and Discrete Logarithm problems are presented and the latter is used to show how the Bitcoin digital signature may be compromised. It also addresses the problem of error correction as well as giving a detailed exposition of adiabatic quantum computing. The book contains around 140 exercises for the student, covering all of the topics treated, together with an appendix of solutions.
The Mathematics of the Uncertain: A Tribute To Pedro Gil (Studies In Systems, Decision And Control #142)
by Eduardo Gil Eva Gil Juan Gil María Ángeles GilThis book is a tribute to Professor Pedro Gil, who created the Department of Statistics, OR and TM at the University of Oviedo, and a former President of the Spanish Society of Statistics and OR (SEIO). In more than eighty original contributions, it illustrates the extent to which Mathematics can help manage uncertainty, a factor that is inherent to real life. Today it goes without saying that, in order to model experiments and systems and to analyze related outcomes and data, it is necessary to consider formal ideas and develop scientific approaches and techniques for dealing with uncertainty. Mathematics is crucial in this endeavor, as this book demonstrates. As Professor Pedro Gil highlighted twenty years ago, there are several well-known mathematical branches for this purpose, including Mathematics of chance (Probability and Statistics),Mathematics of communication (Information Theory), andMathematics of imprecision (Fuzzy Sets Theory and others).These branches often intertwine, since different sources of uncertainty can coexist, and they are not exhaustive. While most of the papers presented here address the three aforementioned fields, some hail from other Mathematical disciplines such as Operations Research; others, in turn, put the spotlight on real-world studies and applications. The intended audience of this book is mainly statisticians, mathematicians and computer scientists, but practitioners in these areas will certainly also find the book a very interesting read.
The Mathematics Teacher in the Digital Era: An International Perspective on Technology Focused Professional Development (Mathematics Education in the Digital Era #2)
by Nathalie Sinclair Alison Clark-Wilson Ornella RobuttiThis volume addresses the key issue of the initial education and lifelong professional learning of teachers of mathematics to enable them to realize the affordances of educational technology for mathematics. With invited contributions from leading scholars in the field, this volume contains a blend of research articles and descriptive texts.In the opening chapter John Mason invites the reader to engage in a number of mathematics tasks that highlight important features of technology-mediated mathematical activity. This is followed by three main sections:An overview of current practices in teachers’ use of digital technologies in the classroom and explorations of the possibilities for developing more effective practices drawing on a range of research perspectives (including grounded theory, enactivism and Valsiner’s zone theory).A set of chapters that share many common constructs (such as instrumental orchestration, instrumental distance and double instrumental genesis) and research settings that have emerged from the French research community, but have also been taken up by other colleagues.Meta-level considerations of research in the domain by contrasting different approaches and proposing connecting or uniting elements
Mathematik für Informatik und Data Science: Eine fundierte Einführung in Logik, Analysis, Lineare Algebra und Stochastik für Künstliche Intelligenz und Maschinelles Lernen (Studienbücher Informatik)
by Andreas KnoblauchDieses Buch liefert eine kompakte aber fundierte Darstellung der wichtigsten Gebiete der Mathematik für Informatik, die insbesondere für Data Science, Künstliche Intelligenz und Maschinelles Lernen notwendig sind. Inhaltlich gehören dazu Grundlagen zu Logik und Beweisen, ein- und mehrdimensionale Analysis mit Differential- und Integralrechnung, Lineare Algebra mit Vektor- und Matrixrechnung, linearen Gleichungssystemen, Koordinatentransformationen, Eigenvektoren sowie Wahrscheinlichkeitsrechnung mit Grundlagen der Kombinatorik, Statistik und Informationstheorie. Trotz der kompakten Darstellung werden alle Konzepte und Sätze sorgfältig eingeführt und bewiesen. Nichts soll vom Himmel fallen, sondern aus Axiomen und elementaren Prinzipien hergeleitet werden. Ziel ist es beim Studierenden das befriedigende Gefühl zu erzeugen, alles von Grund auf verstanden zu haben, und nichts nur „glauben“ zu müssen.
Mathematik für Informatiker: Ein praxisbezogenes Lehrbuch
by Peter HartmannDieses Buch enthält den Mathematikstoff, der für das Informatikstudium in anwendungsorientierten Bachelorstudiengängen benötigt wird. Der Inhalt entspringt der langjährigen Lehrerfahrung des Autors.Das heißt:Sie finden immer wieder Anwendungen aus der Informatik.Sie lernen nicht nur mathematische Methoden, es werden auch die Denkweisen der Mathematik vermittelt, die eine Grundlage zum Verständnis der Informatik bilden.Beweise werden dann geführt, wenn Sie daraus etwas lernen können, nicht um des Beweisens willen.Mathematik ist für viele Studierende zunächst ein notwendiges Übel. Das Buch zeigt durch ausführliche Motivation, durch viele Beispiele, durch das ständige Aufzeigen von Querbezügen zwischen Mathematik und Informatik, dass Mathematik nicht nur nützlich ist, sondern interessant sein kann und manchmal auch Spaß macht.
Mathematik für Informatiker für Dummies (Für Dummies)
by Hans-Jürgen Steffens Christian Zöllner Kathrin MühlmannIst der Mathematik-Schein auch für Sie die größte Hürde im Studium? Dabei brauchen Sie als Informatiker solide mathematische Grundkenntnisse, um Algorithmen zu verstehen und mit Anwendern aus Naturwissenschaft und Technik auf Augenhöhe zu kommunizieren. Dieses Buch vermittelt Ihnen auf verständliche Weise und immer mit Querbezügen zur Informatik die mathematischen Grundlagen, die alle Informatiker benötigen: Aussagenlogik, Rekursion, Induktion, Relationen, Analysis, Wahrscheinlichkeitsrechnung, Statistik und lineare Algebra. Keine Sorge: Es werden lediglich Schulkenntnisse in Mathematik vorausgesetzt.
Mathematik für Ingenieure: Eine anschauliche Einführung für das praxisorientierte Studium
by Thomas Rießinger"Mathematik in entspannter Atmosphäre" ist das Leitbild dieses leicht verständlichen Lehrbuchs. Im Erzählstil und mit vielen Beispielen beleuchtet der Autor nicht nur die Höhere Mathematik, sondern er stellt auch den Lehrstoff in Bezug zu den Anwendungen. Die gesamte für den Ingenieurstudenten wichtige Mathematik wird in einem Band behandelt. Dies gelingt durch Verzicht auf abstrakte Höhen und durch eine prüfungsgerechte Stoffauswahl, die sich streng an den Bedürfnissen des späteren Ingenieurs ausrichtet. Das Buch kann vorlesungsbegleitend oder zum Selbststudium eingesetzt werden. Die 159 Übungsaufgaben mit Lösungen unterstützen das Einüben des Lehrstoffs und sind im Band "Übungsaufgaben zur Mathematik für Ingenieure" ausführlich durchgerechnet. Der "Brückenkurs" auf http://extras.springer.com/2013/978-3-642-36858-5 erleichtert Anfängern den Einstieg.
Mathematik für Ingenieure
by Thomas Rießinger"Mathematik in entspannter Atmosphäre" ist das Leitbild dieses leicht verständlichen Lehrbuchs. Im Erzählstil und mit vielen Beispielen beleuchtet der Autor nicht nur die Höhere Mathematik, sondern er stellt auch den Lehrstoff in Bezug zu den Anwendungen. Die gesamte für den Ingenieurstudenten wichtige Mathematik wird in einem Band behandelt. Dies gelingt durch Verzicht auf abstrakte Höhen und durch eine prüfungsgerechte Stoffauswahl, die sich streng an den Bedürfnissen des späteren Ingenieurs ausrichtet. Das Buch kann vorlesungsbegleitend oder zum Selbststudium eingesetzt werden. Die 159 Übungsaufgaben mit Lösungen unterstützen das Einüben des Lehrstoffs und sind im Band "Übungsaufgaben zur Mathematik für Ingenieure" ausführlich durchgerechnet.Der "Brückenkurs" beim Buch auf springer.com erleichtert Anfängern den Einstieg.
Mathematik kompakt
by Rainer Schwenkert Yvonne StryDas kompakte einbändige Werk bietet eine aktuelle Stoffauswahl mit Themen wie Wahrscheinlichkeitsrechnung und Statistik, dafür wird auf überflüssige Beweise verzichtet. Die Autoren präsentieren den gesamten Stoff in einem anschaulichen, aufgelockerten Stil - mit Zusammenfassungen und Verständnistests zu jedem Kapitel, Randnotizen für die schnelle Orientierung, Beispielen und Anwendungen sowie zahlreichen Übungsaufgaben mit Lösungen. Ergänzendes Material wie Folien und kommentierte Lösungen stehen im Internet zum Download bereit.
Mathematische Grundlagen der Informatik: Mathematisches Denken und Beweisen - Eine Einführung
by Christoph Meinel Martin MundhenkDie mathematischen Grundlagen der Informatik werden anhand von Definitionen und Beispielen anschaulich eingeführt. Ziel des Buches, nun in einer korrigierten und aktualisierten Fassung, ist es, systematisch die für die Informatik typischen und grundlegenden mathematischen Denkweisen vorzustellen – ohne dabei auf besondere, die übliche Schulmathematik übersteigende Vorkenntnisse aufzubauen.
Mathematische Grundlagen des überwachten maschinellen Lernens: Optimierungstheoretische Methoden
by Konrad EngelDieses Buch behandelt die gängigsten Methoden zur Klassifikation von digitalisierten Objekten. Jedem Objekt ist ein Punkt im Euklidischen Raum passender Dimension zugeordnet. Das Lernen basiert auf einer Menge von Punkten, für die die zugehörige Klasse bekannt ist. Eine Reduktion der Dimension sowie elementare und anspruchsvollere Methoden zur Ermittlung schnell berechenbarer Funktionen, mit denen man aus einem Punkt die zugehörige Klasse mit einer möglichst geringen Fehlerrate ableiten kann, werden hergeleitet und in einer einheitlichen Herangehensweise begründet. Die recht elementaren Beweise werden im Wesentlichen mit Mitteln der Linearen Algebra geführt, nur für die neuronalen Netze wird etwas Analysis benötigt.Die Produktfamilie WissensExpress bietet Ihnen Lehr- und Lernbücher in kompakter Form. Die Bücher liefern schnell und verständlich fundiertes Wissen.
Mathematische Methoden der Bioinformatik - Eine Einführung
by Werner TimischlGroße Datenmengen lassen sich ohne den Einsatz von einschlägigen Softwareprodukten kaum bearbeiten. Mit den bereitgestellten Algorithmen können Daten statistisch ausgewertet und Optimierungsaufgaben oder kombinatorische Problemstellungen gelöst werden. Auch wenn dies zumeist im „Black Box“-Verfahren geschieht, ist es doch hilfreich, etwa bei der Auswahl der Algorithmen oder bei der Einschätzung der erforderlichen Zeit-Ressourcen, die hinter den Algorithmen steckenden mathematischen Ideen zu kennen. Das Buch lädt Biologen und Mediziner ein, sich mit den mathematischen Grundlagen von ausgewählten Algorithmen der Bioinformatik vertraut zu machen. Es ist eine Einführung mit vielen durchgerechneten Beispielen und zahlreichen Aufgaben mit ausführlichen Lösungen zum Einüben der mathematischen Inhalte. Inhaltliche Schwerpunkte sind Matrizen, lineare Gleichungssysteme, Rekursionen, Abzähltechniken, diskrete dynamische Optimierung, Markov-Ketten, Hidden Markov-Modelle und distanzbasierte Klassifikationsverfahren.
Matheuristics: Algorithms and Implementations (EURO Advanced Tutorials on Operational Research)
by Vittorio Maniezzo Marco Antonio Boschetti Thomas StützleThis book is the first comprehensive tutorial on matheuristics. Matheuristics are based on mathematical extensions of previously known heuristics, mainly metaheuristics, and on original, area-specific approaches. This tutorial provides a detailed discussion of both contributions, presenting the pseudocodes of over 40 algorithms, abundant literature references, and for each case a step-by-step description of a sample run on a common Generalized Assignment Problem example. C++ source codes of all algorithms are available in an associated SW repository.
Mathletics: How Gamblers, Managers, and Fans Use Mathematics in Sports, Second Edition
by Wayne L. Winston Konstantinos Pelechrinis Scott NestlerHow to use math to improve performance and predict outcomes in professional sportsMathletics reveals the mathematical methods top coaches and managers use to evaluate players and improve team performance, and gives math enthusiasts the practical skills they need to enhance their understanding and enjoyment of their favorite sports—and maybe even gain the outside edge to winning bets. This second edition features new data, new players and teams, and new chapters on soccer, e-sports, golf, volleyball, gambling Calcuttas, analysis of camera data, Bayesian inference, ridge regression, and other statistical techniques. After reading Mathletics, you will understand why baseball teams should almost never bunt; why football overtime systems are unfair; why points, rebounds, and assists aren’t enough to determine who’s the NBA’s best player; and more.
Maths For Computing: A Beginner's Guide (Undergraduate Topics in Computer Science)
by Quentin Charatan Aaron KansThis introductory textbook covers all the mathematical concepts necessary for a computing degree, limiting coverage only to the material needed for the fundamentals of computing rather than delving into the higher mathematical concepts. Key features include: Gears content toward students who are less confident in mathematics Provides exercises, with solutions, at the end of each chapter Teaches topics using everyday language Includes numerous worked examples in every chapter Uses familiar scenarios to introduce mathematical concepts Discusses the relevance of each chapter topic to the world of computing Core topics covered include: Set and groups Matrices Relations and functions Logic and proofs Combinatorics Probability Graph theory The book is written for students embarking on an undergraduate or foundation degree course in computer science (or related discipline) and aims to provide the basic skills and knowledge of discrete mathematics required for such a course. Whereas many textbooks tend to teach this subject in a way that is more suitable for mathematicians, this text specifically targets first-year students on computing courses and aims to teach only the basic material that they will need for their computing degree. Dr Quentin Charatan is a former Principal Lecturer and now visiting lecturer at the University of East London, UK. Dr Aaron Kans is the Head of the Computer Science and Digital Technologies Department in the School of Architecture, Computing & Engineering at the same institution.
MATLAB and Simulink Crash Course for Engineers
by Eklas HossainMATLAB and Simulink Crash Course for Engineers is a reader-friendly introductory guide to the features, functions, and applications of MATLAB and Simulink. The book provides readers with real-world examples, exercises, and applications, and offers highly illustrated, step-by-step demonstrations of techniques for the modelling and simulation of complex systems. MATLAB coverage includes vectors and matrices, programs and functions, complex numbers, visualization, solving equations, numerical methods, optimization problems, and graphical user interfaces. The Simulink coverage includes commonly used Simulink blocks, control system simulation, electrical circuit analysis, electric power systems, power electronics, and renewable energy technology. This powerful tutorial is a great resource for students, engineers, and other busy technical professionals who need to quickly acquire a solid understanding of MATLAB and Simulink.
MATLAB and Simulink in Action: Programming, Scientific Computing and Simulation
by Dingyü Xue Feng PanThe textbook is intended for teaching MATLAB language and its applications. The book is composed of three parts: MATLAB programming, scientific computing with MATLAB, and system simulation with Simulink. Since MATLAB is widely used in all fields of science and engineering, a good introduction to the language can not only help students learn how to use it to solve practical problems, but also provide them with the skills to use MATLAB independently in their later courses and research. The three parts of the book are well-balanced and tailored to the needs of engineering students, and the mathematical problems commonly encountered in engineering can be easily solved using MATLAB. This textbook is suitable for undergraduate and graduate students majoring in science and engineering.
MATLAB Deep Learning
by Phil KimThis book consists of six chapters, which can be grouped into three subjects. The first subject is Machine Learning and takes place in Chapter 1. Deep Learning stems from Machine Learning. This implies that if you want to understand the essence of Deep Learning, you have to know the philosophy behind Machine Learning to some extent. Chapter 1 starts with the relationship between Machine Learning and Deep Learning, followed by problem solving strategies and fundamental limitations of Machine Learning. The detailed techniques are not introduced yet. Instead, fundamental concepts that applies to both the neural network and Deep Learning will be covered. The second subject is artificial neural network. Chapters 2-4 focuses on this subject. As Deep Learning is a type of Machine Learning that employs a neural network, the neural network is inseparable from Deep Learning. Chapter 2 starts with the fundamentals of the neural network: principles of its operation, architecture, and learning rules. It also provides the reason that the simple single-layer architecture evolved to the complex multi-layer architecture. Chapter 3 presents the backpropagation algorithm, which is an important and representative learning rule of the neural network and also employed in Deep Learning. This chapter explains how cost functions and learning rules are related and which cost functions are widely employed in Deep Learning. Chapter 4 introduces how to apply the neural network to classification problems. We have allocated a separate section for classification because it is currently the most prevailing application of Machine Learning. For example, image recognition, one of the primary applications of Deep Learning, is a classification problem. The third topic is Deep Learning. It is the main topic of this book as well. Deep Learning is covered in Chapters 5 and 6. Chapter 5 introduces the drivers that enables Deep Learning to yield excellent performance. For a better understanding, it starts with the history of barriers and solutions of Deep Learning. Chapter 6 covers the convolution neural network, which is representative of Deep Learning techniques. The convolution neural network is second-to-none in terms of image recognition. This chapter starts with an introduction of the basic concept and architecture of the convolution neural network as it compares with the previous image recognition algorithms. It is followed by an explanation of the roles and operations of the convolution layer and pooling layer, which act as essential components of the convolution neural network. The chapter concludes with an example of digit image recognition using the convolution neural network and investigates the evolution of the image throughout the layers.
MATLAB for Brain and Cognitive Scientists
by Mike X CohenAn introduction to a popular programming language for neuroscience research, taking the reader from beginning to intermediate and advanced levels of MATLAB programming.MATLAB is one of the most popular programming languages for neuroscience and psychology research. Its balance of usability, visualization, and widespread use makes it one of the most powerful tools in a scientist's toolbox. In this book, Mike Cohen teaches brain scientists how to program in MATLAB, with a focus on applications most commonly used in neuroscience and psychology. Although most MATLAB tutorials will abandon users at the beginner's level, leaving them to sink or swim, MATLAB for Brain and Cognitive Scientists takes readers from beginning to intermediate and advanced levels of MATLAB programming, helping them gain real expertise in applications that they will use in their work.The book offers a mix of instructive text and rigorous explanations of MATLAB code along with programming tips and tricks. The goal is to teach the reader how to program data analyses in neuroscience and psychology. Readers will learn not only how to but also how not to program, with examples of bad code that they are invited to correct or improve. Chapters end with exercises that test and develop the skills taught in each chapter. Interviews with neuroscientists and cognitive scientists who have made significant contributions their field using MATLAB appear throughout the book. MATLAB for Brain and Cognitive Scientists is an essential resource for both students and instructors, in the classroom or for independent study.
MATLAB For Dummies
by John Paul Mueller Jim SizemoreGo from total MATLAB newbie to plotting graphs and solving equations in a flash! MATLAB is one of the most powerful and commonly used tools in the STEM field. But did you know it doesn’t take an advanced degree or a ton of computer experience to learn it? MATLAB For Dummies is the roadmap you’ve been looking for to simplify and explain this feature-filled tool. This handy reference walks you through every step of the way as you learn the MATLAB language and environment inside-and-out. Starting with straightforward basics before moving on to more advanced material like Live Functions and Live Scripts, this easy-to-read guide shows you how to make your way around MATLAB with screenshots and newly updated procedures. It includes: A comprehensive introduction to installing MATLAB, using its interface, and creating and saving your first file Fully updated to include the 2020 and 2021 updates to MATLAB, with all-new screenshots and up-to-date procedures Enhanced debugging procedures and use of the Symbolic Math Toolbox Brand new instruction on working with Live Scripts and Live Functions, designing classes, creating apps, and building projects Intuitive walkthroughs for MATLAB’s advanced features, including importing and exporting data and publishing your work Perfect for STEM students and new professionals ready to master one of the most powerful tools in the fields of engineering, mathematics, and computing, MATLAB For Dummies is the simplest way to go from complete newbie to power user faster than you would have thought possible.
MATLAB for Engineering and the Life Sciences (Synthesis Lectures on Engineering, Science, and Technology)
by Joe TranquilloThis book is a self-guided tour of MATLAB for engineers and life scientists. It introduces the most commonly used programming techniques through biologically inspired examples. Although the text is written for undergraduates, graduate students and academics, as well as those in industry, will find value in learning MATLAB. The book takes the emphasis off of learning syntax so that the reader can focus more on algorithmic thinking. Although it is not assumed that the reader has taken differential equations or a linear algebra class, there are short introductions to many of these concepts. Following a short history of computing, the MATLAB environment is introduced. Next, vectors and matrices are discussed, followed by matrix-vector operations. The core programming elements of MATLAB are introduced in three successive chapters on scripts, loops, and conditional logic. The last three chapters outline how to manage the input and output of data, create professional quality graphics and find and use MATLAB toolboxes. Throughout, biomedical and life science examples are used to illustrate MATLAB's capabilities.
MATLAB for Neuroscientists: An Introduction to Scientific Computing in MATLAB
by Pascal Wallisch Michael E. Lusignan Marc D. Benayoun Tanya I. Baker Adam Seth Dickey Nicholas G. HatsopoulosMATLAB for Neuroscientists serves as the only complete study manual and teaching resource for MATLAB, the globally accepted standard for scientific computing, in the neurosciences and psychology. This unique introduction can be used to learn the entire empirical and experimental process (including stimulus generation, experimental control, data collection, data analysis, modeling, and more), and the 2nd Edition continues to ensure that a wide variety of computational problems can be addressed in a single programming environment. This updated edition features additional material on the creation of visual stimuli, advanced psychophysics, analysis of LFP data, choice probabilities, synchrony, and advanced spectral analysis. Users at a variety of levels―advanced undergraduates, beginning graduate students, and researchers looking to modernize their skills―will learn to design and implement their own analytical tools, and gain the fluency required to meet the computational needs of neuroscience practitioners.
MATLAB for Psychologists
by Alessandro Soranzo Mauro Borgo Massimo GrassiThe matrix laboratory interactive computing environment--MATLAB--has brought creativity to research in diverse disciplines, particularly in designing and programming experiments. More commonly used in mathematics and the sciences, it also lends itself to a variety of applications across the field of psychology. For the novice looking to use it in experimental psychology research, though, becoming familiar with MATLAB can be a daunting task. MATLAB for Psychologists expertly guides readers through the component steps, skills, and operations of the software, with plentiful graphics and examples to match the reader's comfort level. Using an extended illustration, this concise volume explains the program's usefulness at any point in an experiment, without the limits imposed by other types of software. And the authors demonstrate the responsiveness of MATLAB to the individual's research needs, whether the task is programming experiments, creating sensory stimuli, running simulations, or calculating statistics for data analysis. Key features of the coverage: Thinking in a matrix way.Handling and plotting data.Guidelines for improved programming, sound, and imaging.Statistical analysis and signal detection theory indexes.The Graphical User Interface.The Psychophysics Toolbox.MATLAB for Psychologists serves a wide audience of advanced undergraduate and graduate level psychology students, professors, and researchers as well as lab technicians involved in programming psychology experiments.
Matlab für Dummies (Für Dummies)
by Jim SizemoreOb Naturwissenschaftler, Mathematiker, Ingenieur oder Datenwissenschaftler - mit MATLAB haben Sie ein mächtiges Tool in der Hand, das Ihnen die Arbeit mit Ihren Daten erleichtert. Aber wie das mit manch mächtigen Dingen so ist - es ist auch ganz schön kompliziert. Aber keine Sorge! Jim Sizemore führt Sie in diesem Buch Schritt für Schritt an das Programm heran - von der Installation und den ersten Skripten bis hin zu aufwändigen Berechnungen, der Erstellung von Grafiken und effizienter Fehlerbehebung. Sie werden begeistert sein, was Sie mit MATLAB alles anstellen können.