Das vorliegende Buch verdankt seine Entstehung dem Bedurfnis nach einer ubersichtlichen Einleitung in die Wahr scheinlichkeitsrechnung und einer klaren Darstellung ihrer Hauptsatze, welches sich mir aufdrangte, als ich vor langerer Zeit von einem jungen, auch mathematisch gebildeten Philosophen gebeten wurde, ihn in diese Rechnung einzufuhren. Trotz der Wichtigkeit, welche dieser Zweig der Mathematik besitzt, trotz der Bedeutung seiner Anwendungen auch auf rein wissenschaft lichem Gebiete zufolge der auf ihm basierenden Ausgleichungs rechnung von Beobachtungen fehlte es doch an einem Lehr buche, welches eine erste Einfuhrung ermoglichte. Das mit Recht geruhmte Werk von Hag e n: "Grundzuge der W ahr scheinlichkeitsrechnung" enthalt diese Grundzuge nicht, sondern ihren weiteren Ausbau in der Methode der kleinsten Quadrate und deren Anwendungen. Nur die ersten zwanzig Seiten sind den Hauptsatzen der Wahrscheinlichkeitsreclmung gewidmet; diese enthalten aber lediglich einen Abdruck der zehn Principien, welche La Place in seinem "E88ai Philo8ophique SU1' Les P1'O ba bilite8" als die hauptsachlichsten Resultate des Calculs hinstellt. Obwohl sie mit erlauternden Bemerkungen versehen sind, konnen sie doch eine methodische Einleitung nicht er setzen, ja, sie wirken auf den Anfanger durch die Benutzung von nicht definierten Begriffen, wie den der Ursache, sogar verwirrend ein. IV Den erwahnten Mangel einer methodischen Einleitung soll das vorliegende Buchlein ersetzen; dagegen schien es nicht notig, die Anwendungen der entwi'ckelten Principien auf die Ausgleichungsrechnung zu g'eben, weil hieruber vortreffliche Werke in genugender Anzahl existieren, z. B. das erwahnte von Hagen und die grundlegenden Darstellungen von Ga. uss."

Take your financial skills to the next level by mastering cutting-edge mathematical and statistical financial applications Key Features Explore advanced financial models used by the industry and ways of solving them using Python Build state-of-the-art infrastructure for modeling, visualization, trading, and more Empower your financial applications by applying machine learning and deep learning Book DescriptionThe second edition of Mastering Python for Finance will guide you through carrying out complex financial calculations practiced in the industry of finance by using next-generation methodologies. You will master the Python ecosystem by leveraging publicly available tools to successfully perform research studies and modeling, and learn to manage risks with the help of advanced examples. You will start by setting up your Jupyter notebook to implement the tasks throughout the book. You will learn to make efficient and powerful data-driven financial decisions using popular libraries such as TensorFlow, Keras, Numpy, SciPy, and sklearn. You will also learn how to build financial applications by mastering concepts such as stocks, options, interest rates and their derivatives, and risk analytics using computational methods. With these foundations, you will learn to apply statistical analysis to time series data, and understand how time series data is useful for implementing an event-driven backtesting system and for working with high-frequency data in building an algorithmic trading platform. Finally, you will explore machine learning and deep learning techniques that are applied in finance. By the end of this book, you will be able to apply Python to different paradigms in the financial industry and perform efficient data analysis. What you will learn Solve linear and nonlinear models representing various financial problems Perform principal component analysis on the DOW index and its components Analyze, predict, and forecast stationary and non-stationary time series processes Create an event-driven backtesting tool and measure your strategies Build a high-frequency algorithmic trading platform with Python Replicate the CBOT VIX index with SPX options for studying VIX-based strategies Perform regression-based and classification-based machine learning tasks for prediction Use TensorFlow and Keras in deep learning neural network architecture Who this book is forIf you are a financial or data analyst or a software developer in the financial industry who is interested in using advanced Python techniques for quantitative methods in finance, this is the book you need! You will also find this book useful if you want to extend the functionalities of your existing financial applications by using smart machine learning techniques. Prior experience in Python is required.

Discover easy-to-follow solutions and techniques to help you to implement applied mathematical concepts such as probability, calculus, and equations using Python's numeric and scientific libraries Key Features Compute complex mathematical problems using programming logic with the help of step-by-step recipes Learn how to utilize Python's libraries for computation, mathematical modeling, and statistics Discover simple yet effective techniques for solving mathematical equations and apply them in real-world statistics Book DescriptionPython, one of the world's most popular programming languages, has a number of powerful packages to help you tackle complex mathematical problems in a simple and efficient way. These core capabilities help programmers pave the way for building exciting applications in various domains, such as machine learning and data science, using knowledge in the computational mathematics domain. The book teaches you how to solve problems faced in a wide variety of mathematical fields, including calculus, probability, statistics and data science, graph theory, optimization, and geometry. You'll start by developing core skills and learning about packages covered in Python's scientific stack, including NumPy, SciPy, and Matplotlib. As you advance, you'll get to grips with more advanced topics of calculus, probability, and networks (graph theory). After you gain a solid understanding of these topics, you'll discover Python's applications in data science and statistics, forecasting, geometry, and optimization. The final chapters will take you through a collection of miscellaneous problems, including working with specific data formats and accelerating code. By the end of this book, you'll have an arsenal of practical coding solutions that can be used and modified to solve a wide range of practical problems in computational mathematics and data science. What you will learn Get familiar with basic packages, tools, and libraries in Python for solving mathematical problems Explore various techniques that will help you to solve computational mathematical problems Understand the core concepts of applied mathematics and how you can apply them in computer science Discover how to choose the most suitable package, tool, or technique to solve a certain problem Implement basic mathematical plotting, change plot styles, and add labels to the plots using Matplotlib Get to grips with probability theory with the Bayesian inference and Markov Chain Monte Carlo (MCMC) methods Who this book is forThis book is for professional programmers and students looking to solve mathematical problems computationally using Python. Advanced mathematics knowledge is not a requirement, but a basic knowledge of mathematics will help you to get the most out of this book. The book assumes familiarity with Python concepts of data structures.

Employ the essential and hands-on tools and functions of MATLAB's ordinary differential equation (ODE) and partial differential equation (PDE) packages, which are explained and demonstrated via interactive examples and case studies. This book contains dozens of simulations and solved problems via m-files/scripts and Simulink models which help you to learn programming and modeling of more difficult, complex problems that involve the use of ODEs and PDEs. You'll become efficient with many of the built-in tools and functions of MATLAB/Simulink while solving more complex engineering and scientific computing problems that require and use differential equations. Practical MATLAB Modeling with Simulink explains various practical issues of programming and modelling. After reading and using this book, you'll be proficient at using MATLAB and applying the source code from the book's examples as templates for your own projects in data science or engineering. What You Will Learn Model complex problems using MATLAB and Simulink Gain the programming and modeling essentials of MATLAB using ODEs and PDEs Use numerical methods to solve 1st and 2nd order ODEs Solve stiff, higher order, coupled, and implicit ODEs Employ numerical methods to solve 1st and 2nd order linear PDEs Solve stiff, higher order, coupled, and implicit PDEs Who This Book Is For Engineers, programmers, data scientists, and students majoring in engineering, applied/industrial math, data science, and scientific computing. This book continues where Apress' Beginning MATLAB and Simulink leaves off.

Build efficient forecasting models using traditional time series models and machine learning algorithms. Key Features Perform time series analysis and forecasting using R packages such as Forecast and h2o Develop models and find patterns to create visualizations using the TSstudio and plotly packages Master statistics and implement time-series methods using examples mentioned Book DescriptionTime series analysis is the art of extracting meaningful insights from, and revealing patterns in, time series data using statistical and data visualization approaches. These insights and patterns can then be utilized to explore past events and forecast future values in the series. This book explores the basics of time series analysis with R and lays the foundations you need to build forecasting models. You will learn how to preprocess raw time series data and clean and manipulate data with packages such as stats, lubridate, xts, and zoo. You will analyze data and extract meaningful information from it using both descriptive statistics and rich data visualization tools in R such as the TSstudio, plotly, and ggplot2 packages. The later section of the book delves into traditional forecasting models such as time series linear regression, exponential smoothing (Holt, Holt-Winter, and more) and Auto-Regressive Integrated Moving Average (ARIMA) models with the stats and forecast packages. You'll also cover advanced time series regression models with machine learning algorithms such as Random Forest and Gradient Boosting Machine using the h2o package. By the end of this book, you will have the skills needed to explore your data, identify patterns, and build a forecasting model using various traditional and machine learning methods. What you will learn Visualize time series data and derive better insights Explore auto-correlation and master statistical techniques Use time series analysis tools from the stats, TSstudio, and forecast packages Explore and identify seasonal and correlation patterns Work with different time series formats in R Explore time series models such as ARIMA, Holt-Winters, and more Evaluate high-performance forecasting solutions Who this book is forHands-On Time Series Analysis with R is ideal for data analysts, data scientists, and all R developers who are looking to perform time series analysis to predict outcomes effectively. A basic knowledge of statistics is required; some knowledge in R is expected, but not mandatory.