Mathematical Problems in Data Science

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Publisher : Springer
ISBN 13 : 3319251279
Total Pages : 219 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Mathematical Problems in Data Science by : Li M. Chen

Download or read book Mathematical Problems in Data Science written by Li M. Chen and published by Springer. This book was released on 2015-12-15 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes current problems in data science and Big Data. Key topics are data classification, Graph Cut, the Laplacian Matrix, Google Page Rank, efficient algorithms, hardness of problems, different types of big data, geometric data structures, topological data processing, and various learning methods. For unsolved problems such as incomplete data relation and reconstruction, the book includes possible solutions and both statistical and computational methods for data analysis. Initial chapters focus on exploring the properties of incomplete data sets and partial-connectedness among data points or data sets. Discussions also cover the completion problem of Netflix matrix; machine learning method on massive data sets; image segmentation and video search. This book introduces software tools for data science and Big Data such MapReduce, Hadoop, and Spark. This book contains three parts. The first part explores the fundamental tools of data science. It includes basic graph theoretical methods, statistical and AI methods for massive data sets. In second part, chapters focus on the procedural treatment of data science problems including machine learning methods, mathematical image and video processing, topological data analysis, and statistical methods. The final section provides case studies on special topics in variational learning, manifold learning, business and financial data rec overy, geometric search, and computing models. Mathematical Problems in Data Science is a valuable resource for researchers and professionals working in data science, information systems and networks. Advanced-level students studying computer science, electrical engineering and mathematics will also find the content helpful.

Foundations of Data Science

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Publisher : Cambridge University Press
ISBN 13 : 1108617360
Total Pages : 433 pages
Book Rating : 4.1/5 (86 download)

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Book Synopsis Foundations of Data Science by : Avrim Blum

Download or read book Foundations of Data Science written by Avrim Blum and published by Cambridge University Press. This book was released on 2020-01-23 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the mathematical and algorithmic foundations of data science, including machine learning, high-dimensional geometry, and analysis of large networks. Topics include the counterintuitive nature of data in high dimensions, important linear algebraic techniques such as singular value decomposition, the theory of random walks and Markov chains, the fundamentals of and important algorithms for machine learning, algorithms and analysis for clustering, probabilistic models for large networks, representation learning including topic modelling and non-negative matrix factorization, wavelets and compressed sensing. Important probabilistic techniques are developed including the law of large numbers, tail inequalities, analysis of random projections, generalization guarantees in machine learning, and moment methods for analysis of phase transitions in large random graphs. Additionally, important structural and complexity measures are discussed such as matrix norms and VC-dimension. This book is suitable for both undergraduate and graduate courses in the design and analysis of algorithms for data.

Data Science and Machine Learning

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Publisher : CRC Press
ISBN 13 : 1000730778
Total Pages : 538 pages
Book Rating : 4.0/5 (7 download)

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Book Synopsis Data Science and Machine Learning by : Dirk P. Kroese

Download or read book Data Science and Machine Learning written by Dirk P. Kroese and published by CRC Press. This book was released on 2019-11-20 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on mathematical understanding Presentation is self-contained, accessible, and comprehensive Full color throughout Extensive list of exercises and worked-out examples Many concrete algorithms with actual code

Math for Programmers

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Publisher : Manning Publications
ISBN 13 : 1617295353
Total Pages : 686 pages
Book Rating : 4.6/5 (172 download)

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Book Synopsis Math for Programmers by : Paul Orland

Download or read book Math for Programmers written by Paul Orland and published by Manning Publications. This book was released on 2021-01-12 with total page 686 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Math for Programmers you’ll explore important mathematical concepts through hands-on coding. Filled with graphics and more than 300 exercises and mini-projects, this book unlocks the door to interesting–and lucrative!–careers in some of today’s hottest fields. As you tackle the basics of linear algebra, calculus, and machine learning, you’ll master the key Python libraries used to turn them into real-world software applications. Summary To score a job in data science, machine learning, computer graphics, and cryptography, you need to bring strong math skills to the party. Math for Programmers teaches the math you need for these hot careers, concentrating on what you need to know as a developer. Filled with lots of helpful graphics and more than 200 exercises and mini-projects, this book unlocks the door to interesting–and lucrative!–careers in some of today’s hottest programming fields. Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the technology Skip the mathematical jargon: This one-of-a-kind book uses Python to teach the math you need to build games, simulations, 3D graphics, and machine learning algorithms. Discover how algebra and calculus come alive when you see them in code! About the book In Math for Programmers you’ll explore important mathematical concepts through hands-on coding. Filled with graphics and more than 300 exercises and mini-projects, this book unlocks the door to interesting–and lucrative!–careers in some of today’s hottest fields. As you tackle the basics of linear algebra, calculus, and machine learning, you’ll master the key Python libraries used to turn them into real-world software applications. What's inside Vector geometry for computer graphics Matrices and linear transformations Core concepts from calculus Simulation and optimization Image and audio processing Machine learning algorithms for regression and classification About the reader For programmers with basic skills in algebra. About the author Paul Orland is a programmer, software entrepreneur, and math enthusiast. He is co-founder of Tachyus, a start-up building predictive analytics software for the energy industry. You can find him online at www.paulor.land. Table of Contents 1 Learning math with code PART I - VECTORS AND GRAPHICS 2 Drawing with 2D vectors 3 Ascending to the 3D world 4 Transforming vectors and graphics 5 Computing transformations with matrices 6 Generalizing to higher dimensions 7 Solving systems of linear equations PART 2 - CALCULUS AND PHYSICAL SIMULATION 8 Understanding rates of change 9 Simulating moving objects 10 Working with symbolic expressions 11 Simulating force fields 12 Optimizing a physical system 13 Analyzing sound waves with a Fourier series PART 3 - MACHINE LEARNING APPLICATIONS 14 Fitting functions to data 15 Classifying data with logistic regression 16 Training neural networks

Data Science

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Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110697823
Total Pages : 489 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Data Science by : Ivo D. Dinov

Download or read book Data Science written by Ivo D. Dinov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-12-06 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: The amount of new information is constantly increasing, faster than our ability to fully interpret and utilize it to improve human experiences. Addressing this asymmetry requires novel and revolutionary scientific methods and effective human and artificial intelligence interfaces. By lifting the concept of time from a positive real number to a 2D complex time (kime), this book uncovers a connection between artificial intelligence (AI), data science, and quantum mechanics. It proposes a new mathematical foundation for data science based on raising the 4D spacetime to a higher dimension where longitudinal data (e.g., time-series) are represented as manifolds (e.g., kime-surfaces). This new framework enables the development of innovative data science analytical methods for model-based and model-free scientific inference, derived computed phenotyping, and statistical forecasting. The book provides a transdisciplinary bridge and a pragmatic mechanism to translate quantum mechanical principles, such as particles and wavefunctions, into data science concepts, such as datum and inference-functions. It includes many open mathematical problems that still need to be solved, technological challenges that need to be tackled, and computational statistics algorithms that have to be fully developed and validated. Spacekime analytics provide mechanisms to effectively handle, process, and interpret large, heterogeneous, and continuously-tracked digital information from multiple sources. The authors propose computational methods, probability model-based techniques, and analytical strategies to estimate, approximate, or simulate the complex time phases (kime directions). This allows transforming time-varying data, such as time-series observations, into higher-dimensional manifolds representing complex-valued and kime-indexed surfaces (kime-surfaces). The book includes many illustrations of model-based and model-free spacekime analytic techniques applied to economic forecasting, identification of functional brain activation, and high-dimensional cohort phenotyping. Specific case-study examples include unsupervised clustering using the Michigan Consumer Sentiment Index (MCSI), model-based inference using functional magnetic resonance imaging (fMRI) data, and model-free inference using the UK Biobank data archive. The material includes mathematical, inferential, computational, and philosophical topics such as Heisenberg uncertainty principle and alternative approaches to large sample theory, where a few spacetime observations can be amplified by a series of derived, estimated, or simulated kime-phases. The authors extend Newton-Leibniz calculus of integration and differentiation to the spacekime manifold and discuss possible solutions to some of the "problems of time". The coverage also includes 5D spacekime formulations of classical 4D spacetime mathematical equations describing natural laws of physics, as well as, statistical articulation of spacekime analytics in a Bayesian inference framework. The steady increase of the volume and complexity of observed and recorded digital information drives the urgent need to develop novel data analytical strategies. Spacekime analytics represents one new data-analytic approach, which provides a mechanism to understand compound phenomena that are observed as multiplex longitudinal processes and computationally tracked by proxy measures. This book may be of interest to academic scholars, graduate students, postdoctoral fellows, artificial intelligence and machine learning engineers, biostatisticians, econometricians, and data analysts. Some of the material may also resonate with philosophers, futurists, astrophysicists, space industry technicians, biomedical researchers, health practitioners, and the general public.

Mathematics for Machine Learning

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Publisher : Cambridge University Press
ISBN 13 : 1108569323
Total Pages : 392 pages
Book Rating : 4.1/5 (85 download)

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Book Synopsis Mathematics for Machine Learning by : Marc Peter Deisenroth

Download or read book Mathematics for Machine Learning written by Marc Peter Deisenroth and published by Cambridge University Press. This book was released on 2020-04-23 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.

Mathematics of Big Data

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Publisher : MIT Press
ISBN 13 : 0262347911
Total Pages : 443 pages
Book Rating : 4.2/5 (623 download)

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Book Synopsis Mathematics of Big Data by : Jeremy Kepner

Download or read book Mathematics of Big Data written by Jeremy Kepner and published by MIT Press. This book was released on 2018-08-07 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book to present the common mathematical foundations of big data analysis across a range of applications and technologies. Today, the volume, velocity, and variety of data are increasing rapidly across a range of fields, including Internet search, healthcare, finance, social media, wireless devices, and cybersecurity. Indeed, these data are growing at a rate beyond our capacity to analyze them. The tools—including spreadsheets, databases, matrices, and graphs—developed to address this challenge all reflect the need to store and operate on data as whole sets rather than as individual elements. This book presents the common mathematical foundations of these data sets that apply across many applications and technologies. Associative arrays unify and simplify data, allowing readers to look past the differences among the various tools and leverage their mathematical similarities in order to solve the hardest big data challenges. The book first introduces the concept of the associative array in practical terms, presents the associative array manipulation system D4M (Dynamic Distributed Dimensional Data Model), and describes the application of associative arrays to graph analysis and machine learning. It provides a mathematically rigorous definition of associative arrays and describes the properties of associative arrays that arise from this definition. Finally, the book shows how concepts of linearity can be extended to encompass associative arrays. Mathematics of Big Data can be used as a textbook or reference by engineers, scientists, mathematicians, computer scientists, and software engineers who analyze big data.

Mathematical Foundations for Data Analysis

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Publisher : Springer Nature
ISBN 13 : 3030623416
Total Pages : 299 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Mathematical Foundations for Data Analysis by : Jeff M. Phillips

Download or read book Mathematical Foundations for Data Analysis written by Jeff M. Phillips and published by Springer Nature. This book was released on 2021-03-29 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook, suitable for an early undergraduate up to a graduate course, provides an overview of many basic principles and techniques needed for modern data analysis. In particular, this book was designed and written as preparation for students planning to take rigorous Machine Learning and Data Mining courses. It introduces key conceptual tools necessary for data analysis, including concentration of measure and PAC bounds, cross validation, gradient descent, and principal component analysis. It also surveys basic techniques in supervised (regression and classification) and unsupervised learning (dimensionality reduction and clustering) through an accessible, simplified presentation. Students are recommended to have some background in calculus, probability, and linear algebra. Some familiarity with programming and algorithms is useful to understand advanced topics on computational techniques.

The Mathematics of Data

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Publisher : American Mathematical Soc.
ISBN 13 : 1470435756
Total Pages : 340 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Mathematics of Data by : Michael W. Mahoney

Download or read book The Mathematics of Data written by Michael W. Mahoney and published by American Mathematical Soc.. This book was released on 2018-11-15 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nothing provided

Mathematical Foundations of Big Data Analytics

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Publisher : Springer Nature
ISBN 13 : 3662625210
Total Pages : 273 pages
Book Rating : 4.6/5 (626 download)

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Book Synopsis Mathematical Foundations of Big Data Analytics by : Vladimir Shikhman

Download or read book Mathematical Foundations of Big Data Analytics written by Vladimir Shikhman and published by Springer Nature. This book was released on 2021-02-11 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this textbook, basic mathematical models used in Big Data Analytics are presented and application-oriented references to relevant practical issues are made. Necessary mathematical tools are examined and applied to current problems of data analysis, such as brand loyalty, portfolio selection, credit investigation, quality control, product clustering, asset pricing etc. – mainly in an economic context. In addition, we discuss interdisciplinary applications to biology, linguistics, sociology, electrical engineering, computer science and artificial intelligence. For the models, we make use of a wide range of mathematics – from basic disciplines of numerical linear algebra, statistics and optimization to more specialized game, graph and even complexity theories. By doing so, we cover all relevant techniques commonly used in Big Data Analytics.Each chapter starts with a concrete practical problem whose primary aim is to motivate the study of a particular Big Data Analytics technique. Next, mathematical results follow – including important definitions, auxiliary statements and conclusions arising. Case-studies help to deepen the acquired knowledge by applying it in an interdisciplinary context. Exercises serve to improve understanding of the underlying theory. Complete solutions for exercises can be consulted by the interested reader at the end of the textbook; for some which have to be solved numerically, we provide descriptions of algorithms in Python code as supplementary material.This textbook has been recommended and developed for university courses in Germany, Austria and Switzerland.

Data Science for Mathematicians

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Publisher : CRC Press
ISBN 13 : 0429675682
Total Pages : 545 pages
Book Rating : 4.4/5 (296 download)

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Book Synopsis Data Science for Mathematicians by : Nathan Carter

Download or read book Data Science for Mathematicians written by Nathan Carter and published by CRC Press. This book was released on 2020-09-15 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematicians have skills that, if deepened in the right ways, would enable them to use data to answer questions important to them and others, and report those answers in compelling ways. Data science combines parts of mathematics, statistics, computer science. Gaining such power and the ability to teach has reinvigorated the careers of mathematicians. This handbook will assist mathematicians to better understand the opportunities presented by data science. As it applies to the curriculum, research, and career opportunities, data science is a fast-growing field. Contributors from both academics and industry present their views on these opportunities and how to advantage them.

Algorithms for Data Science

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Publisher : Springer
ISBN 13 : 3319457977
Total Pages : 438 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Algorithms for Data Science by : Brian Steele

Download or read book Algorithms for Data Science written by Brian Steele and published by Springer. This book was released on 2016-12-25 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook on practical data analytics unites fundamental principles, algorithms, and data. Algorithms are the keystone of data analytics and the focal point of this textbook. Clear and intuitive explanations of the mathematical and statistical foundations make the algorithms transparent. But practical data analytics requires more than just the foundations. Problems and data are enormously variable and only the most elementary of algorithms can be used without modification. Programming fluency and experience with real and challenging data is indispensable and so the reader is immersed in Python and R and real data analysis. By the end of the book, the reader will have gained the ability to adapt algorithms to new problems and carry out innovative analyses. This book has three parts:(a) Data Reduction: Begins with the concepts of data reduction, data maps, and information extraction. The second chapter introduces associative statistics, the mathematical foundation of scalable algorithms and distributed computing. Practical aspects of distributed computing is the subject of the Hadoop and MapReduce chapter.(b) Extracting Information from Data: Linear regression and data visualization are the principal topics of Part II. The authors dedicate a chapter to the critical domain of Healthcare Analytics for an extended example of practical data analytics. The algorithms and analytics will be of much interest to practitioners interested in utilizing the large and unwieldly data sets of the Centers for Disease Control and Prevention's Behavioral Risk Factor Surveillance System.(c) Predictive Analytics Two foundational and widely used algorithms, k-nearest neighbors and naive Bayes, are developed in detail. A chapter is dedicated to forecasting. The last chapter focuses on streaming data and uses publicly accessible data streams originating from the Twitter API and the NASDAQ stock market in the tutorials. This book is intended for a one- or two-semester course in data analytics for upper-division undergraduate and graduate students in mathematics, statistics, and computer science. The prerequisites are kept low, and students with one or two courses in probability or statistics, an exposure to vectors and matrices, and a programming course will have no difficulty. The core material of every chapter is accessible to all with these prerequisites. The chapters often expand at the close with innovations of interest to practitioners of data science. Each chapter includes exercises of varying levels of difficulty. The text is eminently suitable for self-study and an exceptional resource for practitioners.

Probability and Statistics for Data Science

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Publisher : CRC Press
ISBN 13 : 0429687117
Total Pages : 295 pages
Book Rating : 4.4/5 (296 download)

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Book Synopsis Probability and Statistics for Data Science by : Norman Matloff

Download or read book Probability and Statistics for Data Science written by Norman Matloff and published by CRC Press. This book was released on 2019-06-21 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability and Statistics for Data Science: Math + R + Data covers "math stat"—distributions, expected value, estimation etc.—but takes the phrase "Data Science" in the title quite seriously: * Real datasets are used extensively. * All data analysis is supported by R coding. * Includes many Data Science applications, such as PCA, mixture distributions, random graph models, Hidden Markov models, linear and logistic regression, and neural networks. * Leads the student to think critically about the "how" and "why" of statistics, and to "see the big picture." * Not "theorem/proof"-oriented, but concepts and models are stated in a mathematically precise manner. Prerequisites are calculus, some matrix algebra, and some experience in programming. Norman Matloff is a professor of computer science at the University of California, Davis, and was formerly a statistics professor there. He is on the editorial boards of the Journal of Statistical Software and The R Journal. His book Statistical Regression and Classification: From Linear Models to Machine Learning was the recipient of the Ziegel Award for the best book reviewed in Technometrics in 2017. He is a recipient of his university's Distinguished Teaching Award.

Introduction to Probability

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Publisher : CRC Press
ISBN 13 : 1466575573
Total Pages : 599 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Introduction to Probability by : Joseph K. Blitzstein

Download or read book Introduction to Probability written by Joseph K. Blitzstein and published by CRC Press. This book was released on 2014-07-24 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.

Data Science For Dummies

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Publisher : John Wiley & Sons
ISBN 13 : 1119811619
Total Pages : 436 pages
Book Rating : 4.1/5 (198 download)

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Book Synopsis Data Science For Dummies by : Lillian Pierson

Download or read book Data Science For Dummies written by Lillian Pierson and published by John Wiley & Sons. This book was released on 2021-08-20 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monetize your company’s data and data science expertise without spending a fortune on hiring independent strategy consultants to help What if there was one simple, clear process for ensuring that all your company’s data science projects achieve a high a return on investment? What if you could validate your ideas for future data science projects, and select the one idea that’s most prime for achieving profitability while also moving your company closer to its business vision? There is. Industry-acclaimed data science consultant, Lillian Pierson, shares her proprietary STAR Framework – A simple, proven process for leading profit-forming data science projects. Not sure what data science is yet? Don’t worry! Parts 1 and 2 of Data Science For Dummies will get all the bases covered for you. And if you’re already a data science expert? Then you really won’t want to miss the data science strategy and data monetization gems that are shared in Part 3 onward throughout this book. Data Science For Dummies demonstrates: The only process you’ll ever need to lead profitable data science projects Secret, reverse-engineered data monetization tactics that no one’s talking about The shocking truth about how simple natural language processing can be How to beat the crowd of data professionals by cultivating your own unique blend of data science expertise Whether you’re new to the data science field or already a decade in, you’re sure to learn something new and incredibly valuable from Data Science For Dummies. Discover how to generate massive business wins from your company’s data by picking up your copy today.

High-Dimensional Probability

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Publisher : Cambridge University Press
ISBN 13 : 1108415199
Total Pages : 299 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis High-Dimensional Probability by : Roman Vershynin

Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Doing Math with Python

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Publisher : No Starch Press
ISBN 13 : 1593277199
Total Pages : 265 pages
Book Rating : 4.5/5 (932 download)

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Book Synopsis Doing Math with Python by : Amit Saha

Download or read book Doing Math with Python written by Amit Saha and published by No Starch Press. This book was released on 2015-08-01 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Doing Math with Python shows you how to use Python to delve into high school–level math topics like statistics, geometry, probability, and calculus. You’ll start with simple projects, like a factoring program and a quadratic-equation solver, and then create more complex projects once you’ve gotten the hang of things. Along the way, you’ll discover new ways to explore math and gain valuable programming skills that you’ll use throughout your study of math and computer science. Learn how to: –Describe your data with statistics, and visualize it with line graphs, bar charts, and scatter plots –Explore set theory and probability with programs for coin flips, dicing, and other games of chance –Solve algebra problems using Python’s symbolic math functions –Draw geometric shapes and explore fractals like the Barnsley fern, the Sierpinski triangle, and the Mandelbrot set –Write programs to find derivatives and integrate functions Creative coding challenges and applied examples help you see how you can put your new math and coding skills into practice. You’ll write an inequality solver, plot gravity’s effect on how far a bullet will travel, shuffle a deck of cards, estimate the area of a circle by throwing 100,000 "darts" at a board, explore the relationship between the Fibonacci sequence and the golden ratio, and more. Whether you’re interested in math but have yet to dip into programming or you’re a teacher looking to bring programming into the classroom, you’ll find that Python makes programming easy and practical. Let Python handle the grunt work while you focus on the math. Uses Python 3