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Figurierte Zahlen: Veranschaulichung als heuristische Strategie
by Jochen ZiegenbalgDieses Buch behandelt die Visualisierung als Methode des mathematischen Problemlösens, Begründens und Beweisens: Konkrete Beispiele zur Veranschaulichung durch mathematische Figuren und Bilder bieten einen faszinierenden Einblick in das Argumentieren anhand strukturierter und strukturierender Figuren zur Betrachtung von Zahlen und Zahlenfolgen. Die historischen Wurzeln dieses mathematischen Handwerkszeugs werden dabei so weit wie möglich einbezogen. Die Beispiele sind in der Regel konstruktiver Natur; gelegentlich wird, wo angebracht, die algorithmische Erschließung durch Hinweise auf die Programmierung mit Hilfe von Computeralgebra Systemen ergänzt. Das Buch richtet sich an Studierende und Lehrende an Schulen und Hochschulen, sowie an alle an der Elementarmathematik interessierten Nichtspezialisten, die das mathematische Arbeiten einmal außerhalb der von den Bildungsinstitutionen vorgezeichneten Pfade kennenlernen wollen. Es liefert insbesondere Lehrkräften und Lehramtsstudierenden wertvolle Anregungen, etwa zur Förderung mathematisch interessierter Schülerinnen und Schüler. In der 2. Auflage ist mit den mathematisch fundamentalen und historisch bedeutsamen Themen Wechselwegnahme, Teilbarkeit, Euklidischer Algorithmus, Inkommensurabilität und Kettenbrüche ein neues, für Visualisierungen gut geeignetes Kapitel hinzugekommen. Bereits bestehende Kapitel wurde durch Abschnitte über Trapezzahlen, ungerade Quadratzahlen und zentrierte Polygonalzahlen ergänzt.
Figuring It Out
by Nuno CratoThis is a book of mathematical stories -- funny and puzzling mathematical stories. They tell of villains who try to steal secrets, heroes who encode their messages, and mathematicians who spend years on end searching for the best way to pile oranges. There are also stories about highway confusions occurring when the rules of Cartesian geometry are ignored, small-change errors due to ignorance of ancient paradoxes, and mistakes in calendars arising from poor numerical approximations. This book is about the power and beauty of mathematics. It shows mathematics in action, explained in a way that everybody can understand. It is a book for enticing youngsters and inspiring teachers. Nuno Crato is a leading science writer and mathematician, whose entertaining essays have won a number of international awards.
Figuring Out Fluency - Addition and Subtraction With Fractions and Decimals: A Classroom Companion (Corwin Mathematics Series)
by John J. SanGiovanni Jennifer M. Bay-Williams Sherri L. Martinie Jennifer SuhBecause fluency practice is not a worksheet. Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. It is not about speed or recall. Real fluency is about choosing strategies that are efficient, flexible, lead to accurate solutions, and are appropriate for the given situation. Developing fluency is also a matter of equity and access for all learners. The landmark book Figuring Out Fluency in Mathematics Teaching and Learning offered educators the inspiration to develop a deeper understanding of procedural fluency, along with a plethora of pragmatic tools for shifting classrooms toward a fluency approach. Now, teachers have the chance to apply that inspiration through explicit instruction and practice every day with the classroom companion Figuring Out Fluency: Addition and Subtraction with Fractions and Decimals. With this book, teachers can: Dive deeper into the Significant Strategies for fluency explained in the anchor book Learn how these strategies grow from and relate to the basic fact strategies children learn Access over 100 strategy-aligned and classroom-ready activities for fluency instruction and practice in adding and subtracting fractions and decimals, including worked examples, routines, games, and centers Find activities for assessing all components of addition and subtraction fluency for fractions and decimals, plus support for engaging families Download all of the needed support tools, game boards, and other resources from the companion website for immediate implementation. Give each and every student the knowledge and power to become skilled and confident mathematical thinkers and doers.
Figuring Out Fluency - Addition and Subtraction With Fractions and Decimals: A Classroom Companion (Corwin Mathematics Series)
by John J. SanGiovanni Jennifer M. Bay-Williams Sherri L. Martinie Jennifer SuhBecause fluency practice is not a worksheet. Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. It is not about speed or recall. Real fluency is about choosing strategies that are efficient, flexible, lead to accurate solutions, and are appropriate for the given situation. Developing fluency is also a matter of equity and access for all learners. The landmark book Figuring Out Fluency in Mathematics Teaching and Learning offered educators the inspiration to develop a deeper understanding of procedural fluency, along with a plethora of pragmatic tools for shifting classrooms toward a fluency approach. Now, teachers have the chance to apply that inspiration through explicit instruction and practice every day with the classroom companion Figuring Out Fluency: Addition and Subtraction with Fractions and Decimals. With this book, teachers can: Dive deeper into the Significant Strategies for fluency explained in the anchor book Learn how these strategies grow from and relate to the basic fact strategies children learn Access over 100 strategy-aligned and classroom-ready activities for fluency instruction and practice in adding and subtracting fractions and decimals, including worked examples, routines, games, and centers Find activities for assessing all components of addition and subtraction fluency for fractions and decimals, plus support for engaging families Download all of the needed support tools, game boards, and other resources from the companion website for immediate implementation. Give each and every student the knowledge and power to become skilled and confident mathematical thinkers and doers.
Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8: Moving Beyond Basic Facts and Memorization (Corwin Mathematics Series)
by Jennifer M. Bay-Williams John J. SanGiovanniBecause fluency practice is not a worksheet. Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. Real fluency involves reasoning and creativity, and it varies by the situation at hand. Figuring Out Fluency in Mathematics Teaching and Learning offers educators the inspiration to develop a deeper understanding of procedural fluency, along with a plethora of pragmatic tools for shifting classrooms toward a fluency approach. In a friendly and accessible style, this hands-on guide empowers educators to support students in acquiring the repertoire of reasoning strategies necessary to becoming versatile and nimble mathematical thinkers. It includes: "Seven Significant Strategies" to teach to students as they work toward procedural fluency. Activities, fluency routines, and games that encourage learning the efficiency, flexibility, and accuracy essential to real fluency. Reflection questions, connections to mathematical standards, and techniques for assessing all components of fluency. Suggestions for engaging families in understanding and supporting fluency. Fluency is more than a toolbox of strategies to choose from; it’s also a matter of equity and access for all learners. Give your students the knowledge and power to become confident mathematical thinkers.
Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8: Moving Beyond Basic Facts and Memorization (Corwin Mathematics Series)
by Jennifer M. Bay-Williams John J. SanGiovanniBecause fluency practice is not a worksheet. Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. Real fluency involves reasoning and creativity, and it varies by the situation at hand. Figuring Out Fluency in Mathematics Teaching and Learning offers educators the inspiration to develop a deeper understanding of procedural fluency, along with a plethora of pragmatic tools for shifting classrooms toward a fluency approach. In a friendly and accessible style, this hands-on guide empowers educators to support students in acquiring the repertoire of reasoning strategies necessary to becoming versatile and nimble mathematical thinkers. It includes: "Seven Significant Strategies" to teach to students as they work toward procedural fluency. Activities, fluency routines, and games that encourage learning the efficiency, flexibility, and accuracy essential to real fluency. Reflection questions, connections to mathematical standards, and techniques for assessing all components of fluency. Suggestions for engaging families in understanding and supporting fluency. Fluency is more than a toolbox of strategies to choose from; it’s also a matter of equity and access for all learners. Give your students the knowledge and power to become confident mathematical thinkers.
FileMaker Pro 13: The Missing Manual
by Susan Prosser Stuart GripmanYou don’t need a technical background to build powerful databases with FileMaker Pro 13. This crystal-clear guide covers all new FileMaker Pro 13 features, such as its improved layout tools and enhanced mobile support. Whether you’re running a business, printing a catalog, or planning a wedding, you’ll learn how to customize your database to run on a PC, Mac, Web browser, or iOS device.The important stuff you need to know:Get started. Tour FileMaker Pro’s features and create your first database in minutes.Access data anywhere. Use FileMaker Go on your iPad or iPhone—or share data on the Web.Dive into relational data. Solve problems quickly by connecting and combining data tables.Create professional documents. Publish reports, invoices, catalogs, and other documents with ease.Harness processing power. Use calculations and scripts to crunch numbers, search text, and automate tasks.Add visual power and clarity. Create colorful charts to illustrate and summarize your data.Share your database on a secure server. Add the high-level features of FileMaker Pro Advanced and FileMaker Pro Server.
Filling and Wrapping, Three-Dimensional Measurement
by Glenda Lappan James T. Fey William M. Fitzgerald Susan N. Friel Elizabeth Difanis PhillipsNIMAC-sourced textbook
Filling and Wrapping: Three-Dimensional Measurement
by Glenda Lappan James T. Fey Susan N. Friel Elizabeth Difanis PhillipsNIMAC-sourced textbook
Filling and Wrapping: Three-Dimensional Measurement
by Phillips Fey Friel LappanGlenda Lap pan is a University Distinguished Professor in the Program in Mathematics Education (PRIME) and the Department of Mathematics at Michigan State University. Her research and development interests are in the connected areas of students' learning of mathematics and mathematics teachers' professional growth and change related to the development and enactment of K-12 curriculum materials. Elizabeth Difanis Phillips is a Senior Academic Specialist in the Program in Mathematics Education (PRIME) and the Department of Mathematics at Michigan State University. She is interested in teaching and learning mathematics for both teachers and students. These interests have led to curriculum and professional development projects at the middle school and high school levels, as well as projects related to the teaching and learning of algebra across the grades.
Filling and Wrapping: Three-Dimensional Measurements (Texas)
by Inc. Glenda Lappan James T. Fey William M. Fitzgerald Susan N. Friel Elizabeth Difanis Phillips WestWordsNIMAC-sourced textbook
Filtering and Control of Stochastic Jump Hybrid Systems
by Ligang Wu Xiuming Yao Wei Xing ZhengThis book presents recent research work on stochastic jump hybrid systems. Specifically, the considered stochastic jump hybrid systems include Markovian jump Ito stochastic systems, Markovian jump linear-parameter-varying (LPV) systems, Markovian jump singular systems, Markovian jump two-dimensional (2-D) systems, and Markovian jump repeated scalar nonlinear systems. Some sufficient conditions are first established respectively for the stability and performances of those kinds of stochastic jump hybrid systems in terms of solution of linear matrix inequalities (LMIs). Based on the derived analysis conditions, the filtering and control problems are addressed. The book presents up-to-date research developments and novel methodologies on stochastic jump hybrid systems. The contents can be divided into two parts: the first part is focused on robust filter design problem, while the second part is put the emphasis on robust control problem. These methodologies provide a framework for stability and performance analysis, robust controller design, and robust filter design for the considered systems. Solutions to the design problems are presented in terms of LMIs. The book is a timely reflection of the developing area of filtering and control theories for Markovian jump hybrid systems with various kinds of imperfect information. It is a collection of a series of latest research results and therefore serves as a useful textbook for senior and/or graduate students who are interested in knowing 1) the state-of-the-art of linear filtering and control areas, and 2) recent advances in stochastic jump hybrid systems. The readers will also benefit from some new concepts, new models and new methodologies with practical significance in control engineering and signal processing.
Finance with Monte Carlo
by Ronald W. ShonkwilerThis text introduces upper division undergraduate/beginning graduate students in mathematics, finance, or economics, to the core topics of a beginning course in finance/financial engineering. Particular emphasis is placed on exploiting the power of the Monte Carlo method to illustrate and explore financial principles. Monte Carlo is the uniquely appropriate tool for modeling the random factors that drive financial markets and simulating their implications. The Monte Carlo method is introduced early and it is used in conjunction with the geometric Brownian motion model (GBM) to illustrate and analyze the topics covered in the remainder of the text. Placing focus on Monte Carlo methods allows for students to travel a short road from theory to practical applications. Coverage includes investment science, mean-variance portfolio theory, option pricing principles, exotic options, option trading strategies, jump diffusion and exponential Lévy alternative models, and the Kelly criterion for maximizing investment growth. Novel features: inclusion of both portfolio theory and contingent claim analysis in a single text pricing methodology for exotic options expectation analysis of option trading strategies pricing models that transcend the Black-Scholes framework optimizing investment allocations concepts thoroughly explored through numerous simulation exercises numerous worked examples and illustrations The mathematical background required is a year and one-half course in calculus, matrix algebra covering solutions of linear systems, and a knowledge of probability including expectation, densities and the normal distribution. A refresher for these topics is presented in the Appendices. The programming background needed is how to code branching, loops and subroutines in some mathematical or general purpose language. The mathematical background required is a year and one-half course in calculus, matrix algebra covering solutions of linear systems, and a knowledge of probability including expectation, densities and the normal distribution. A refresher for these topics is presented in the Appendices. The programming background needed is how to code branching, loops and subroutines in some mathematical or general purpose language. Also by the author: (with F. Mendivil) Explorations in Monte Carlo, ©2009, ISBN: 978-0-387-87836-2; (with J. Herod) Mathematical Biology: An Introduction with Maple and Matlab, Second edition, ©2009, ISBN: 978-0-387-70983-3.
Financial Algebra
by Robert Gerver Richard SgroiBy combining algebraic and graphical approaches with practical business and personal finance applications, South-Western's FINANCIAL ALGEBRA, motivates high school students to explore algebraic thinking patterns and functions in a financial context. FINANCIAL ALGEBRA will help your students achieve success by offering an applications based learning approach incorporating Algebra I, Algebra II, and Geometry topics. Authors Gerver and Sgroi have spent more than 25 years working with students of all ability levels and they have found the most success when connecting math to the real world. FINANCIAL ALGEBRA encourages students to be actively involved in applying mathematical ideas to their everyday lives.
Financial Algebra: Advanced Algebra With Financial Applications
by Robert Gerver Richard SgroiBy combining algebraic and graphical approaches with practical business and personal finance applications, South-Western's FINANCIAL ALGEBRA, motivates high school students to explore algebraic thinking patterns and functions in a financial context.
Financial Algebra: Advanced Algebra With Financial Applications (Financial Algebra Ser.)
by Robert Gerver Richard SgroiNIMAC-sourced textbook
Financial Algebra: Student Workbook
by Robert K. Gerver Richard J. SgroiThe Student Workbook offers additional resources for mastering algebraic concepts within a financial context.
Financial Calculus
by Martin Baxter Andrew RennieFinance provides a dramatic example of the successful application of advanced mathematical techniques to the practical problem of pricing financial derivatives. This self-contained 2002 text is designed for first courses in financial calculus aimed at students with a good background in mathematics. Key concepts such as martingales and change of measure are introduced in the discrete time framework, allowing an accessible account of Brownian motion and stochastic calculus: proofs in the continuous-time world follow naturally. The Black-Scholes pricing formula is first derived in the simplest financial context. The second half of the book is then devoted to increasing the financial sophistication of the models and instruments. The final chapter introduces more advanced topics including stock price models with jumps, and stochastic volatility. A valuable feature is the large number of exercises and examples, designed to test technique and illustrate how the methods and concepts can be applied to realistic financial questions.
Financial Data Analytics with Machine Learning, Optimization and Statistics (Wiley Finance)
by Phillip Yam Sam Chen Ka Chun CheungAn essential introduction to data analytics and Machine Learning techniques in the business sector In Financial Data Analytics with Machine Learning, Optimization and Statistics, a team consisting of a distinguished applied mathematician and statistician, experienced actuarial professionals and working data analysts delivers an expertly balanced combination of traditional financial statistics, effective machine learning tools, and mathematics. The book focuses on contemporary techniques used for data analytics in the financial sector and the insurance industry with an emphasis on mathematical understanding and statistical principles and connects them with common and practical financial problems. Each chapter is equipped with derivations and proofs—especially of key results—and includes several realistic examples which stem from common financial contexts. The computer algorithms in the book are implemented using Python and R, two of the most widely used programming languages for applied science and in academia and industry, so that readers can implement the relevant models and use the programs themselves. The book begins with a brief introduction to basic sampling theory and the fundamentals of simulation techniques, followed by a comparison between R and Python. It then discusses statistical diagnosis for financial security data and introduces some common tools in financial forensics such as Benford's Law, Zipf's Law, and anomaly detection. The statistical estimation and Expectation-Maximization (EM) & Majorization-Minimization (MM) algorithms are also covered. The book next focuses on univariate and multivariate dynamic volatility and correlation forecasting, and emphasis is placed on the celebrated Kelly's formula, followed by a brief introduction to quantitative risk management and dependence modelling for extremal events. A practical topic on numerical finance for traditional option pricing and Greek computations immediately follows as well as other important topics in financial data-driven aspects, such as Principal Component Analysis (PCA) and recommender systems with their applications, as well as advanced regression learners such as kernel regression and logistic regression, with discussions on model assessment methods such as simple Receiver Operating Characteristic (ROC) curves and Area Under Curve (AUC) for typical classification problems. The book then moves on to other commonly used machine learning tools like linear classifiers such as perceptrons and their generalization, the multilayered counterpart (MLP), Support Vector Machines (SVM), as well as Classification and Regression Trees (CART) and Random Forests. Subsequent chapters focus on linear Bayesian learning, including well-received credibility theory in actuarial science and functional kernel regression, and non-linear Bayesian learning, such as the Naïve Bayes classifier and the Comonotone-Independence Bayesian Classifier (CIBer) recently independently developed by the authors and used successfully in InsurTech. After an in-depth discussion on cluster analyses such as K-means clustering and its inversion, the K-nearest neighbor (KNN) method, the book concludes by introducing some useful deep neural networks for FinTech, like the potential use of the Long-Short Term Memory model (LSTM) for stock price prediction. This book can help readers become well-equipped with the following skills: To evaluate financial and insurance data quality, and use the distilled knowledge obtained from the data after applying data analytic tools to make timely financial decisions To apply effective data dimension reduction tools to enhance supervised learning To describe and select suitable data analytic tools as introduced above for a given dataset depending upon classification or regression prediction purpose The book covers the competencies tested by several professional examinations, such as the Predictive Analytics Exam offered by the Society of Actuaries, and the Institute and Faculty of Actu
Financial Data Analytics with R: Monte-Carlo Validation
by Jenny K. ChenFinancial Data Analysis with R: Monte-Carlo Validation is a comprehensive exploration of statistical methodologies and their applications in finance. Readers are taken on a journey in each chapter through practical explanations and examples, enabling them to develop a solid foundation of these methods in R and their applications in finance.This book serves as an indispensable resource for finance professionals, analysts, and enthusiasts seeking to harness the power of data-driven decision-making.The book goes beyond just teaching statistical methods in R and incorporates a unique section of informative Monte-Carlo simulations. These Monte-Carlo simulations are uniquely designed to showcase the reader the potential consequences and misleading conclusions that can arise when fundamental model assumptions are violated. Through step-by-step tutorials and realworld cases, readers will learn how and why model assumptions are important to follow.With a focus on practicality, Financial Data Analysis with R: Monte-Carlo Validation equips readers with the skills to construct and validate financial models using R. The Monte-Carlo simulation exercises provide a unique opportunity to understand the methods further, making this book an essential tool for anyone involved in financial analysis, investment strategy, or risk management. Whether you are a seasoned professional or a newcomer to the world of financial analytics, this book serves as a guiding light, empowering you to navigate the landscape of finance with precision and confidence.Key Features: An extensive compilation of commonly used financial data analytics methods from fundamental to advanced levels Learn how to model and analyze financial data with step-by-step illustrations in R and ready-to-use publicly available data Includes Monte-Carlo simulations uniquely designed to showcase the reader the potential consequences and misleading conclusions that arise when fundamental model assumptions are violated Data and computer programs are available for readers to replicate and implement the models and methods themselves
Financial Data Resampling for Machine Learning Based Trading: Application to Cryptocurrency Markets (SpringerBriefs in Applied Sciences and Technology)
by Rui Neves Tomé Almeida BorgesThis book presents a system that combines the expertise of four algorithms, namely Gradient Tree Boosting, Logistic Regression, Random Forest and Support Vector Classifier to trade with several cryptocurrencies. A new method for resampling financial data is presented as alternative to the classical time sampled data commonly used in financial market trading. The new resampling method uses a closing value threshold to resample the data creating a signal better suited for financial trading, thus achieving higher returns without increased risk. The performance of the algorithm with the new resampling method and the classical time sampled data are compared and the advantages of using the system developed in this work are highlighted.
Financial Derivative and Energy Market Valuation
by Michael MastroA road map for implementing quantitative financial modelsFinancial Derivative and Energy Market Valuation brings the application of financial models to a higher level by helping readers capture the true behavior of energy markets and related financial derivatives. The book provides readers with a range of statistical and quantitative techniques and demonstrates how to implement the presented concepts and methods in Matlab®.Featuring an unparalleled level of detail, this unique work provides the underlying theory and various advanced topics without requiring a prior high-level understanding of mathematics or finance. In addition to a self-contained treatment of applied topics such as modern Fourier-based analysis and affine transforms, Financial Derivative and Energy Market Valuation also:* Provides the derivation, numerical implementation, and documentation of the corresponding Matlab for each topic* Extends seminal works developed over the last four decades to derive and utilize present-day financial models* Shows how to use applied methods such as fast Fourier transforms to generate statistical distributions for option pricing* Includes all Matlab code for readers wishing to replicate the figures found throughout the bookThorough, practical, and easy to use, Financial Derivative and Energy Market Valuation is a first-rate guide for readers who want to learn how to use advanced numerical methods to implement and apply state-of-the-art financial models. The book is also ideal for graduate-level courses in quantitative finance, mathematical finance, and financial engineering.
Financial Econometrics
by Peijie WangThis book which provides an overview of contemporary topics related to the modelling of financial time series, is set against a backdrop of rapid expansions of interest in both the models themselves and the financial problems to which they are applied.This excellent textbook covers all the major developments in the area in recent years in an informative as well as succinct way.Refreshingly, every chapter has a section of two or more examples and a section of empirical literature, offering the reader the opportunity to practice the kind of research going on in the area. This approach helps the reader develop interest, confidence and momentum in learning contemporary econometric topics
Financial Econometrics (Routledge Advanced Texts In Economics And Finance Ser.)
by Peijie WangThis book provides an essential toolkit for all students wishing to know more about the modelling and analysis of financial data. Applications of econometric techniques are becoming increasingly common in the world of finance and this second edition of an established text covers the following key themes:- unit roots, cointegration and other develop
Financial Econometrics Modeling: Derivatives Pricing, Hedge Funds and Term Structure Models
by Greg N. Gregoriou Razvan PascalauThis book proposes new tools and models to price options, assess market volatility, and investigate the market efficiency hypothesis. In particular, it considers new models for hedge funds and derivatives of derivatives, and adds to the literature of testing for the efficiency of markets both theoretically and empirically.