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| calculus for data science: Foundations of Data Science Avrim Blum, John Hopcroft, Ravindran Kannan, 2020-01-23 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. |
| calculus for data science: Mathematics for Machine Learning Marc Peter Deisenroth, A. Aldo Faisal, Cheng Soon Ong, 2020-04-23 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. |
| calculus for data science: Probability and Statistics for Data Science Norman Matloff, 2019-06-21 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. |
| calculus for data science: Introduction to Probability Joseph K. Blitzstein, Jessica Hwang, 2014-07-24 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. |
| calculus for data science: Mathematical Foundations for Data Analysis Jeff M. Phillips, 2021-03-29 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. |
| calculus for data science: Data Science for Mathematicians Nathan Carter, 2020-09-15 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. |
| calculus for data science: The Statistics and Calculus with Python Workshop Peter Farrell, Alvaro Fuentes, Ajinkya Sudhir Kolhe, Quan Nguyen, Alexander Joseph Sarver, Marios Tsatsos, 2020-08-18 With examples and activities that help you achieve real results, applying calculus and statistical methods relevant to advanced data science has never been so easy Key FeaturesDiscover how most programmers use the main Python libraries when performing statistics with PythonUse descriptive statistics and visualizations to answer business and scientific questionsSolve complicated calculus problems, such as arc length and solids of revolution using derivatives and integralsBook Description Are you looking to start developing artificial intelligence applications? Do you need a refresher on key mathematical concepts? Full of engaging practical exercises, The Statistics and Calculus with Python Workshop will show you how to apply your understanding of advanced mathematics in the context of Python. The book begins by giving you a high-level overview of the libraries you'll use while performing statistics with Python. As you progress, you'll perform various mathematical tasks using the Python programming language, such as solving algebraic functions with Python starting with basic functions, and then working through transformations and solving equations. Later chapters in the book will cover statistics and calculus concepts and how to use them to solve problems and gain useful insights. Finally, you'll study differential equations with an emphasis on numerical methods and learn about algorithms that directly calculate values of functions. By the end of this book, you'll have learned how to apply essential statistics and calculus concepts to develop robust Python applications that solve business challenges. What you will learnGet to grips with the fundamental mathematical functions in PythonPerform calculations on tabular datasets using pandasUnderstand the differences between polynomials, rational functions, exponential functions, and trigonometric functionsUse algebra techniques for solving systems of equationsSolve real-world problems with probabilitySolve optimization problems with derivatives and integralsWho this book is for If you are a Python programmer who wants to develop intelligent solutions that solve challenging business problems, then this book is for you. To better grasp the concepts explained in this book, you must have a thorough understanding of advanced mathematical concepts, such as Markov chains, Euler's formula, and Runge-Kutta methods as the book only explains how these techniques and concepts can be implemented in Python. |
| calculus for data science: Data Science and Machine Learning Dirk P. Kroese, Zdravko Botev, Thomas Taimre, Radislav Vaisman, 2019-11-20 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 |
| calculus for data science: Data Science from Scratch Joel Grus, 2015-04-14 Data science libraries, frameworks, modules, and toolkits are great for doing data science, but they’re also a good way to dive into the discipline without actually understanding data science. In this book, you’ll learn how many of the most fundamental data science tools and algorithms work by implementing them from scratch. If you have an aptitude for mathematics and some programming skills, author Joel Grus will help you get comfortable with the math and statistics at the core of data science, and with hacking skills you need to get started as a data scientist. Today’s messy glut of data holds answers to questions no one’s even thought to ask. This book provides you with the know-how to dig those answers out. Get a crash course in Python Learn the basics of linear algebra, statistics, and probability—and understand how and when they're used in data science Collect, explore, clean, munge, and manipulate data Dive into the fundamentals of machine learning Implement models such as k-nearest Neighbors, Naive Bayes, linear and logistic regression, decision trees, neural networks, and clustering Explore recommender systems, natural language processing, network analysis, MapReduce, and databases |
| calculus for data science: All of Statistics Larry Wasserman, 2013-12-11 Taken literally, the title All of Statistics is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. The book includes modern topics like non-parametric curve estimation, bootstrapping, and classification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analysing data. |
| calculus for data science: Coding the Matrix Philip N. Klein, 2013-07 An engaging introduction to vectors and matrices and the algorithms that operate on them, intended for the student who knows how to program. Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by doing, writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google's ranking algorithm), and cancer detection from cell features. A companion web site, codingthematrix.com provides data and support code. Most of the assignments can be auto-graded online. Over two hundred illustrations, including a selection of relevant xkcd comics. Chapters: The Function, The Field, The Vector, The Vector Space, The Matrix, The Basis, Dimension, Gaussian Elimination, The Inner Product, Special Bases, The Singular Value Decomposition, The Eigenvector, The Linear Program A new edition of this text, incorporating corrections and an expanded index, has been issued as of September 4, 2013, and will soon be available on Amazon. |
| calculus for data science: Introduction to Deep Learning Sandro Skansi, 2018-02-04 This textbook presents a concise, accessible and engaging first introduction to deep learning, offering a wide range of connectionist models which represent the current state-of-the-art. The text explores the most popular algorithms and architectures in a simple and intuitive style, explaining the mathematical derivations in a step-by-step manner. The content coverage includes convolutional networks, LSTMs, Word2vec, RBMs, DBNs, neural Turing machines, memory networks and autoencoders. Numerous examples in working Python code are provided throughout the book, and the code is also supplied separately at an accompanying website. Topics and features: introduces the fundamentals of machine learning, and the mathematical and computational prerequisites for deep learning; discusses feed-forward neural networks, and explores the modifications to these which can be applied to any neural network; examines convolutional neural networks, and the recurrent connections to a feed-forward neural network; describes the notion of distributed representations, the concept of the autoencoder, and the ideas behind language processing with deep learning; presents a brief history of artificial intelligence and neural networks, and reviews interesting open research problems in deep learning and connectionism. This clearly written and lively primer on deep learning is essential reading for graduate and advanced undergraduate students of computer science, cognitive science and mathematics, as well as fields such as linguistics, logic, philosophy, and psychology. |
| calculus for data science: Introduction to Stochastic Calculus with Applications Fima C. Klebaner, 2005 This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author. |
| calculus for data science: Calculus for Machine Learning Jason Brownlee, Stefania Cristina, Mehreen Saeed, 2022-02-23 Calculus seems to be obscure, but it is everywhere. In machine learning, while we rarely write code on differentiation or integration, the algorithms we use have theoretical roots in calculus. If you ever wondered how to understand the calculus part when you listen to people explaining the theory behind a machine learning algorithm, this new Ebook, in the friendly Machine Learning Mastery style that you’re used to, is all you need. Using clear explanations and step-by-step tutorial lessons, you will understand the concept of calculus, how it is relates to machine learning, what it can help us on, and much more. |
| calculus for data science: Deep Learning for Coders with fastai and PyTorch Jeremy Howard, Sylvain Gugger, 2020-06-29 Deep learning is often viewed as the exclusive domain of math PhDs and big tech companies. But as this hands-on guide demonstrates, programmers comfortable with Python can achieve impressive results in deep learning with little math background, small amounts of data, and minimal code. How? With fastai, the first library to provide a consistent interface to the most frequently used deep learning applications. Authors Jeremy Howard and Sylvain Gugger, the creators of fastai, show you how to train a model on a wide range of tasks using fastai and PyTorch. You’ll also dive progressively further into deep learning theory to gain a complete understanding of the algorithms behind the scenes. Train models in computer vision, natural language processing, tabular data, and collaborative filtering Learn the latest deep learning techniques that matter most in practice Improve accuracy, speed, and reliability by understanding how deep learning models work Discover how to turn your models into web applications Implement deep learning algorithms from scratch Consider the ethical implications of your work Gain insight from the foreword by PyTorch cofounder, Soumith Chintala |
| calculus for data science: Hands-On Mathematics for Deep Learning Jay Dawani, 2020-06-12 A comprehensive guide to getting well-versed with the mathematical techniques for building modern deep learning architectures Key FeaturesUnderstand linear algebra, calculus, gradient algorithms, and other concepts essential for training deep neural networksLearn the mathematical concepts needed to understand how deep learning models functionUse deep learning for solving problems related to vision, image, text, and sequence applicationsBook Description Most programmers and data scientists struggle with mathematics, having either overlooked or forgotten core mathematical concepts. This book uses Python libraries to help you understand the math required to build deep learning (DL) models. You'll begin by learning about core mathematical and modern computational techniques used to design and implement DL algorithms. This book will cover essential topics, such as linear algebra, eigenvalues and eigenvectors, the singular value decomposition concept, and gradient algorithms, to help you understand how to train deep neural networks. Later chapters focus on important neural networks, such as the linear neural network and multilayer perceptrons, with a primary focus on helping you learn how each model works. As you advance, you will delve into the math used for regularization, multi-layered DL, forward propagation, optimization, and backpropagation techniques to understand what it takes to build full-fledged DL models. Finally, you’ll explore CNN, recurrent neural network (RNN), and GAN models and their application. By the end of this book, you'll have built a strong foundation in neural networks and DL mathematical concepts, which will help you to confidently research and build custom models in DL. What you will learnUnderstand the key mathematical concepts for building neural network modelsDiscover core multivariable calculus conceptsImprove the performance of deep learning models using optimization techniquesCover optimization algorithms, from basic stochastic gradient descent (SGD) to the advanced Adam optimizerUnderstand computational graphs and their importance in DLExplore the backpropagation algorithm to reduce output errorCover DL algorithms such as convolutional neural networks (CNNs), sequence models, and generative adversarial networks (GANs)Who this book is for This book is for data scientists, machine learning developers, aspiring deep learning developers, or anyone who wants to understand the foundation of deep learning by learning the math behind it. Working knowledge of the Python programming language and machine learning basics is required. |
| calculus for data science: A Modern Introduction to Probability and Statistics F.M. Dekking, C. Kraaikamp, H.P. Lopuhaä, L.E. Meester, 2006-03-30 Suitable for self study Use real examples and real data sets that will be familiar to the audience Introduction to the bootstrap is included – this is a modern method missing in many other books |
| calculus for data science: Doing Math with Python Amit Saha, 2015-08-01 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 |
| calculus for data science: Advanced Calculus (Revised Edition) Lynn Harold Loomis, Shlomo Zvi Sternberg, 2014-02-26 An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds. |
| calculus for data science: Deep Learning Illustrated Jon Krohn, Grant Beyleveld, Aglaé Bassens, 2019-08-05 The authors’ clear visual style provides a comprehensive look at what’s currently possible with artificial neural networks as well as a glimpse of the magic that’s to come. – Tim Urban, author of Wait But Why Fully Practical, Insightful Guide to Modern Deep Learning Deep learning is transforming software, facilitating powerful new artificial intelligence capabilities, and driving unprecedented algorithm performance. Deep Learning Illustrated is uniquely intuitive and offers a complete introduction to the discipline’s techniques. Packed with full-color figures and easy-to-follow code, it sweeps away the complexity of building deep learning models, making the subject approachable and fun to learn. World-class instructor and practitioner Jon Krohn–with visionary content from Grant Beyleveld and beautiful illustrations by Aglaé Bassens–presents straightforward analogies to explain what deep learning is, why it has become so popular, and how it relates to other machine learning approaches. Krohn has created a practical reference and tutorial for developers, data scientists, researchers, analysts, and students who want to start applying it. He illuminates theory with hands-on Python code in accompanying Jupyter notebooks. To help you progress quickly, he focuses on the versatile deep learning library Keras to nimbly construct efficient TensorFlow models; PyTorch, the leading alternative library, is also covered. You’ll gain a pragmatic understanding of all major deep learning approaches and their uses in applications ranging from machine vision and natural language processing to image generation and game-playing algorithms. Discover what makes deep learning systems unique, and the implications for practitioners Explore new tools that make deep learning models easier to build, use, and improve Master essential theory: artificial neurons, training, optimization, convolutional nets, recurrent nets, generative adversarial networks (GANs), deep reinforcement learning, and more Walk through building interactive deep learning applications, and move forward with your own artificial intelligence projects Register your book for convenient access to downloads, updates, and/or corrections as they become available. See inside book for details. |
| calculus for data science: Data Science For Dummies Lillian Pierson, 2021-08-20 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. |
| calculus for data science: The Mathematics of Data Michael W. Mahoney, John C. Duchi, Anna C. Gilbert, 2018-11-15 Nothing provided |
| calculus for data science: Machine Learning Kevin P. Murphy, 2012-08-24 A comprehensive introduction to machine learning that uses probabilistic models and inference as a unifying approach. Today's Web-enabled deluge of electronic data calls for automated methods of data analysis. Machine learning provides these, developing methods that can automatically detect patterns in data and then use the uncovered patterns to predict future data. This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach. The coverage combines breadth and depth, offering necessary background material on such topics as probability, optimization, and linear algebra as well as discussion of recent developments in the field, including conditional random fields, L1 regularization, and deep learning. The book is written in an informal, accessible style, complete with pseudo-code for the most important algorithms. All topics are copiously illustrated with color images and worked examples drawn from such application domains as biology, text processing, computer vision, and robotics. Rather than providing a cookbook of different heuristic methods, the book stresses a principled model-based approach, often using the language of graphical models to specify models in a concise and intuitive way. Almost all the models described have been implemented in a MATLAB software package—PMTK (probabilistic modeling toolkit)—that is freely available online. The book is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students. |
| calculus for data science: Data Science and Predictive Analytics Ivo D. Dinov, 2023-02-16 This textbook integrates important mathematical foundations, efficient computational algorithms, applied statistical inference techniques, and cutting-edge machine learning approaches to address a wide range of crucial biomedical informatics, health analytics applications, and decision science challenges. Each concept in the book includes a rigorous symbolic formulation coupled with computational algorithms and complete end-to-end pipeline protocols implemented as functional R electronic markdown notebooks. These workflows support active learning and demonstrate comprehensive data manipulations, interactive visualizations, and sophisticated analytics. The content includes open problems, state-of-the-art scientific knowledge, ethical integration of heterogeneous scientific tools, and procedures for systematic validation and dissemination of reproducible research findings. Complementary to the enormous challenges related to handling, interrogating, and understanding massive amounts of complex structured and unstructured data, there are unique opportunities that come with access to a wealth of feature-rich, high-dimensional, and time-varying information. The topics covered in Data Science and Predictive Analytics address specific knowledge gaps, resolve educational barriers, and mitigate workforce information-readiness and data science deficiencies. Specifically, it provides a transdisciplinary curriculum integrating core mathematical principles, modern computational methods, advanced data science techniques, model-based machine learning, model-free artificial intelligence, and innovative biomedical applications. The book’s fourteen chapters start with an introduction and progressively build foundational skills from visualization to linear modeling, dimensionality reduction, supervised classification, black-box machine learning techniques, qualitative learning methods, unsupervised clustering, model performance assessment, feature selection strategies, longitudinal data analytics, optimization, neural networks, and deep learning. The second edition of the book includes additional learning-based strategies utilizing generative adversarial networks, transfer learning, and synthetic data generation, as well as eight complementary electronic appendices. This textbook is suitable for formal didactic instructor-guided course education, as well as for individual or team-supported self-learning. The material is presented at the upper-division and graduate-level college courses and covers applied and interdisciplinary mathematics, contemporary learning-based data science techniques, computational algorithm development, optimization theory, statistical computing, and biomedical sciences. The analytical techniques and predictive scientific methods described in the book may be useful to a wide range of readers, formal and informal learners, college instructors, researchers, and engineers throughout the academy, industry, government, regulatory, funding, and policy agencies. The supporting book website provides many examples, datasets, functional scripts, complete electronic notebooks, extensive appendices, and additional materials. |
| calculus for data science: Introduction to Applied Linear Algebra Stephen Boyd, Lieven Vandenberghe, 2018-06-07 A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples. |
| calculus for data science: An Introduction to Causal Inference Judea Pearl, 2015 This paper summarizes recent advances in causal inference and underscores the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivariate data. Special emphasis is placed on the assumptions that underly all causal inferences, the languages used in formulating those assumptions, the conditional nature of all causal and counterfactual claims, and the methods that have been developed for the assessment of such claims. These advances are illustrated using a general theory of causation based on the Structural Causal Model (SCM) described in Pearl (2000a), which subsumes and unifies other approaches to causation, and provides a coherent mathematical foundation for the analysis of causes and counterfactuals. In particular, the paper surveys the development of mathematical tools for inferring (from a combination of data and assumptions) answers to three types of causal queries: (1) queries about the effects of potential interventions, (also called causal effects or policy evaluation) (2) queries about probabilities of counterfactuals, (including assessment of regret, attribution or causes of effects) and (3) queries about direct and indirect effects (also known as mediation). Finally, the paper defines the formal and conceptual relationships between the structural and potential-outcome frameworks and presents tools for a symbiotic analysis that uses the strong features of both. The tools are demonstrated in the analyses of mediation, causes of effects, and probabilities of causation. -- p. 1. |
| calculus for data science: Mathematics and Programming for Machine Learning with R William Claster, 2020-10-26 Based on the author’s experience in teaching data science for more than 10 years, Mathematics and Programming for Machine Learning with R: From the Ground Up reveals how machine learning algorithms do their magic and explains how these algorithms can be implemented in code. It is designed to provide readers with an understanding of the reasoning behind machine learning algorithms as well as how to program them. Written for novice programmers, the book progresses step-by-step, providing the coding skills needed to implement machine learning algorithms in R. The book begins with simple implementations and fundamental concepts of logic, sets, and probability before moving to the coverage of powerful deep learning algorithms. The first eight chapters deal with probability-based machine learning algorithms, and the last eight chapters deal with machine learning based on artificial neural networks. The first half of the book does not require mathematical sophistication, although familiarity with probability and statistics would be helpful. The second half assumes the reader is familiar with at least one semester of calculus. The text guides novice R programmers through algorithms and their application and along the way; the reader gains programming confidence in tackling advanced R programming challenges. Highlights of the book include: More than 400 exercises A strong emphasis on improving programming skills and guiding beginners to the implementation of full-fledged algorithms Coverage of fundamental computer and mathematical concepts including logic, sets, and probability In-depth explanations of machine learning algorithms |
| calculus for data science: Foundations of Machine Learning, second edition Mehryar Mohri, Afshin Rostamizadeh, Ameet Talwalkar, 2018-12-25 A new edition of a graduate-level machine learning textbook that focuses on the analysis and theory of algorithms. This book is a general introduction to machine learning that can serve as a textbook for graduate students and a reference for researchers. It covers fundamental modern topics in machine learning while providing the theoretical basis and conceptual tools needed for the discussion and justification of algorithms. It also describes several key aspects of the application of these algorithms. The authors aim to present novel theoretical tools and concepts while giving concise proofs even for relatively advanced topics. Foundations of Machine Learning is unique in its focus on the analysis and theory of algorithms. The first four chapters lay the theoretical foundation for what follows; subsequent chapters are mostly self-contained. Topics covered include the Probably Approximately Correct (PAC) learning framework; generalization bounds based on Rademacher complexity and VC-dimension; Support Vector Machines (SVMs); kernel methods; boosting; on-line learning; multi-class classification; ranking; regression; algorithmic stability; dimensionality reduction; learning automata and languages; and reinforcement learning. Each chapter ends with a set of exercises. Appendixes provide additional material including concise probability review. This second edition offers three new chapters, on model selection, maximum entropy models, and conditional entropy models. New material in the appendixes includes a major section on Fenchel duality, expanded coverage of concentration inequalities, and an entirely new entry on information theory. More than half of the exercises are new to this edition. |
| calculus for data science: Essential Math for Data Science Thomas Nield, 2022-05-26 Master the math needed to excel in data science, machine learning, and statistics. In this book author Thomas Nield guides you through areas like calculus, probability, linear algebra, and statistics and how they apply to techniques like linear regression, logistic regression, and neural networks. Along the way you'll also gain practical insights into the state of data science and how to use those insights to maximize your career. Learn how to: Use Python code and libraries like SymPy, NumPy, and scikit-learn to explore essential mathematical concepts like calculus, linear algebra, statistics, and machine learning Understand techniques like linear regression, logistic regression, and neural networks in plain English, with minimal mathematical notation and jargon Perform descriptive statistics and hypothesis testing on a dataset to interpret p-values and statistical significance Manipulate vectors and matrices and perform matrix decomposition Integrate and build upon incremental knowledge of calculus, probability, statistics, and linear algebra, and apply it to regression models including neural networks Navigate practically through a data science career and avoid common pitfalls, assumptions, and biases while tuning your skill set to stand out in the job market |
| calculus for data science: Methods of Mathematics Applied to Calculus, Probability, and Statistics Richard W. Hamming, 2012-06-28 This 4-part treatment begins with algebra and analytic geometry and proceeds to an exploration of the calculus of algebraic functions and transcendental functions and applications. 1985 edition. Includes 310 figures and 18 tables. |
| calculus for data science: Data Science in Practice Alan Said, Vicenç Torra, 2018-09-19 This book approaches big data, artificial intelligence, machine learning, and business intelligence through the lens of Data Science. We have grown accustomed to seeing these terms mentioned time and time again in the mainstream media. However, our understanding of what they actually mean often remains limited. This book provides a general overview of the terms and approaches used broadly in data science, and provides detailed information on the underlying theories, models, and application scenarios. Divided into three main parts, it addresses what data science is; how and where it is used; and how it can be implemented using modern open source software. The book offers an essential guide to modern data science for all students, practitioners, developers and managers seeking a deeper understanding of how various aspects of data science work, and of how they can be employed to gain a competitive advantage. |
| calculus for data science: Mindset Mathematics Jo Boaler, Jen Munson, Cathy Williams, 2017-08-28 Engage students in mathematics using growth mindset techniques The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the first-grade level through visualization, play, and investigation. During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message—that they want to incorporate more brain science into their math instruction, but they need guidance in the techniques that work best to get across the concepts they needed to teach. So the authors designed Mindset Mathematics around the principle of active student engagement, with tasks that reflect the latest brain science on learning. Open, creative, and visual math tasks have been shown to improve student test scores, and more importantly change their relationship with mathematics and start believing in their own potential. The tasks in Mindset Mathematics reflect the lessons from brain science that: There is no such thing as a math person - anyone can learn mathematics to high levels. Mistakes, struggle and challenge are the most important times for brain growth. Speed is unimportant in mathematics. Mathematics is a visual and beautiful subject, and our brains want to think visually about mathematics. With engaging questions, open-ended tasks, and four-color visuals that will help kids get excited about mathematics, Mindset Mathematics is organized around nine big ideas which emphasize the connections within the Common Core State Standards (CCSS) and can be used with any current curriculum. |
| calculus for data science: Calculus Morris Kline, 2013-05-09 Application-oriented introduction relates the subject as closely as possible to science with explorations of the derivative; differentiation and integration of the powers of x; theorems on differentiation, antidifferentiation; the chain rule; trigonometric functions; more. Examples. 1967 edition. |
| calculus for data science: Math and Architectures of Deep Learning Krishnendu Chaudhury, 2024-03-26 Math and Architectures of Deep Learning bridges the gap between theory and practice, laying out the math of deep learning side by side with practical implementations in Python and PyTorch. You'll peer inside the black box to understand how your code is working, and learn to comprehend cutting-edge research you can turn into practical applications. Math and Architectures of Deep Learning sets out the foundations of DL usefully and accessibly to working practitioners. Each chapter explores a new fundamental DL concept or architectural pattern, explaining the underpinning mathematics and demonstrating how they work in practice with well-annotated Python code. You'll start with a primer of basic algebra, calculus, and statistics, working your way up to state-of-the-art DL paradigms taken from the latest research. Learning mathematical foundations and neural network architecture can be challenging, but the payoff is big. You'll be free from blind reliance on pre-packaged DL models and able to build, customize, and re-architect for your specific needs. And when things go wrong, you'll be glad you can quickly identify and fix problems. |
| calculus for data science: Linear Algebra and Learning from Data Gilbert Strang, 2019-01-31 Linear algebra and the foundations of deep learning, together at last! From Professor Gilbert Strang, acclaimed author of Introduction to Linear Algebra, comes Linear Algebra and Learning from Data, the first textbook that teaches linear algebra together with deep learning and neural nets. This readable yet rigorous textbook contains a complete course in the linear algebra and related mathematics that students need to know to get to grips with learning from data. Included are: the four fundamental subspaces, singular value decompositions, special matrices, large matrix computation techniques, compressed sensing, probability and statistics, optimization, the architecture of neural nets, stochastic gradient descent and backpropagation. |
| calculus for data science: The Data Science Design Manual Steven S. Skiena, 2017-07-01 This engaging and clearly written textbook/reference provides a must-have introduction to the rapidly emerging interdisciplinary field of data science. It focuses on the principles fundamental to becoming a good data scientist and the key skills needed to build systems for collecting, analyzing, and interpreting data. The Data Science Design Manual is a source of practical insights that highlights what really matters in analyzing data, and provides an intuitive understanding of how these core concepts can be used. The book does not emphasize any particular programming language or suite of data-analysis tools, focusing instead on high-level discussion of important design principles. This easy-to-read text ideally serves the needs of undergraduate and early graduate students embarking on an “Introduction to Data Science” course. It reveals how this discipline sits at the intersection of statistics, computer science, and machine learning, with a distinct heft and character of its own. Practitioners in these and related fields will find this book perfect for self-study as well. Additional learning tools: Contains “War Stories,” offering perspectives on how data science applies in the real world Includes “Homework Problems,” providing a wide range of exercises and projects for self-study Provides a complete set of lecture slides and online video lectures at www.data-manual.com Provides “Take-Home Lessons,” emphasizing the big-picture concepts to learn from each chapter Recommends exciting “Kaggle Challenges” from the online platform Kaggle Highlights “False Starts,” revealing the subtle reasons why certain approaches fail Offers examples taken from the data science television show “The Quant Shop” (www.quant-shop.com) |
| calculus for data science: Calculus on Manifolds Michael Spivak, 1965 This book uses elementary versions of modern methods found in sophisticated mathematics to discuss portions of advanced calculus in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level. |
| calculus for data science: Understanding Machine Learning Shai Shalev-Shwartz, Shai Ben-David, 2014-05-19 Introduces machine learning and its algorithmic paradigms, explaining the principles behind automated learning approaches and the considerations underlying their usage. |
| calculus for data science: Model-Based Clustering and Classification for Data Science Charles Bouveyron, Gilles Celeux, T. Brendan Murphy, Adrian E. Raftery, 2019-07-25 Cluster analysis finds groups in data automatically. Most methods have been heuristic and leave open such central questions as: how many clusters are there? Which method should I use? How should I handle outliers? Classification assigns new observations to groups given previously classified observations, and also has open questions about parameter tuning, robustness and uncertainty assessment. This book frames cluster analysis and classification in terms of statistical models, thus yielding principled estimation, testing and prediction methods, and sound answers to the central questions. It builds the basic ideas in an accessible but rigorous way, with extensive data examples and R code; describes modern approaches to high-dimensional data and networks; and explains such recent advances as Bayesian regularization, non-Gaussian model-based clustering, cluster merging, variable selection, semi-supervised and robust classification, clustering of functional data, text and images, and co-clustering. Written for advanced undergraduates in data science, as well as researchers and practitioners, it assumes basic knowledge of multivariate calculus, linear algebra, probability and statistics. |
| calculus for data science: Deep Learning Ian Goodfellow, Yoshua Bengio, Aaron Courville, 2016-11-10 An introduction to a broad range of topics in deep learning, covering mathematical and conceptual background, deep learning techniques used in industry, and research perspectives. “Written by three experts in the field, Deep Learning is the only comprehensive book on the subject.” —Elon Musk, cochair of OpenAI; cofounder and CEO of Tesla and SpaceX Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts. Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors. |
To my daughter, may she know anything is possible.
Van Der Post's 'Foundations of Calculus for Data Science' shines as a pivotal guide, illuminating the deep synergy between abstract mathematical theories and practical analytical applications.
Vector Calculus - Marc Deisenroth
It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For …
Mathematical Methods in Data Science - GitHub Pages
Many mathematical methods in data analysis rely on linear algebra and probability. In the first two lectures we will recall basic concepts from these fields. 1.1 Linear Algebra This lecture is …
Course Reader for, MATH7501 Mathematics for Data Science 1
the mathematics involved in data science and practice in calculating associated quanti-ties. Through studying the material in this course, you will have a better understanding of …
Discrete Calculus - download.e-bookshelf.de
The goal of this book is to present the topic of discrete calculus to scientists and en-gineers and to show how the theory can be applied to solving a wide variety of real-world problems.
A-Z Linear Algebra & Calculus for AI & Data Science
A-Z Linear Algebra & Calculus for AI & Data Science Module 01: Vectors, Matrices & Linear Transformations Basic Properties: Notation, Terminologies, Sets, Subsets, Scalars, Vectors, …
KING FAHD UNIVERSITY OF PETROLEUM & MINERALS …
Oct 8, 2023 · Selected topics from linear algebra, multivariate calculus, and optimization for Data Science with an emphasis on the implementation using numerical and symbolic software, …
Linear algebra for data science - University of North Carolina …
To more faithfully portray the way linear algebra actually gets used in data science, this textbook is packaged with a so ware environment that contains extensive data sets, code snippets to …
Essential Math for Data Science - api.pageplace.de
Master the math needed to excel in data science, machine learning, and statistics. In this book, author Thomas Nield guides you through areas like calculus, probability, linear algebra, and …
DA Data Science and Artificial Intelligence - IIT Roorkee
Calculus and Optimization: Functions of a single variable, limit, continuity and differentiability, Taylor series, maxima and minima, optimization involving a single variable.
Calculus For Data Science Book - archive.ncarb.org
Calculus For Data Science Book: Essential Math for Data Science Thomas Nield,2022-05-26 Master the math needed to excel in data science machine learning and statistics In this book …
Mathematical Foundations of Data Sciences - GitHub Pages
In this chapter, we study the simplest example of non-linear parametric models, namely Multi-Layers Perceptron (MLP) with a single hidden layer (so they have in total 2 layers). Perceptron …
Data Science Summer School – Introduction to Calculus
• Calculus in R: limits, continuity, differentiation (definition and basic rules, deriva-tives of elementary functions, monotonicity, higher-order derivatives), and integra-tion (indefinite …
Building a Calculus of Data Structures - New York University
In this paper we give an overview of some recent decision procedures for reasoning about data structures, including sets and multisets with cardinality bounds, algebraic data types with …
Data Science Major - Columbia University
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Calculus for Machine Learning
Calculus is going to be an integral part of our next few lectures regarding neural networks. As a result, this is going to be a crash course into derivatives and partials|if you'd like to get into …
Mathematics in Data Science and Artificial Intelligence - IJARSCT
Calculus: Calculus is the area of mathematics that studies the accumulation of quantities (integration) and the instantaneous rates of change of quantities (differentiation). It began as a …
COURSE SYLLABUS Course Title: Honors Calculus I+II for Data …
An honors-level single course introduction to differential and integral calculus for data science students, with emphasis on a modern, empirical exposition of the classical subject, condensing …
DATA SCIENCE AND ARTIFICIAL INTELLIGENCE - MADE EASY
Database Management and Warehouse-2: Normal form, file organization, Discretization, sampling, compression; data warehouse modelling: schema for multi-dimensional data models, …
Jean Hadrien Essential Math For Data Science Take Control Of …
Jean Hadrien's "Essential Math for Data Science" rightly emphasizes the pivotal function of calculus in the data scientist's toolkit. This post unpacks the profound implications of differential …
To my daughter, may she know anything is possible.
Van Der Post's 'Foundations of Calculus for Data Science' shines as a pivotal guide, illuminating the deep synergy between abstract mathematical theories and practical analytical applications.
Vector Calculus - Marc Deisenroth
It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For …
Mathematical Methods in Data Science - GitHub Pages
Many mathematical methods in data analysis rely on linear algebra and probability. In the first two lectures we will recall basic concepts from these fields. 1.1 Linear Algebra This lecture is …
Course Reader for, MATH7501 Mathematics for Data Science 1
the mathematics involved in data science and practice in calculating associated quanti-ties. Through studying the material in this course, you will have a better understanding of …
Discrete Calculus - download.e-bookshelf.de
The goal of this book is to present the topic of discrete calculus to scientists and en-gineers and to show how the theory can be applied to solving a wide variety of real-world problems.
A-Z Linear Algebra & Calculus for AI & Data Science
A-Z Linear Algebra & Calculus for AI & Data Science Module 01: Vectors, Matrices & Linear Transformations Basic Properties: Notation, Terminologies, Sets, Subsets, Scalars, Vectors, …
KING FAHD UNIVERSITY OF PETROLEUM & MINERALS …
Oct 8, 2023 · Selected topics from linear algebra, multivariate calculus, and optimization for Data Science with an emphasis on the implementation using numerical and symbolic software, …
Linear algebra for data science - University of North Carolina …
To more faithfully portray the way linear algebra actually gets used in data science, this textbook is packaged with a so ware environment that contains extensive data sets, code snippets to …
Essential Math for Data Science - api.pageplace.de
Master the math needed to excel in data science, machine learning, and statistics. In this book, author Thomas Nield guides you through areas like calculus, probability, linear algebra, and …
DA Data Science and Artificial Intelligence - IIT Roorkee
Calculus and Optimization: Functions of a single variable, limit, continuity and differentiability, Taylor series, maxima and minima, optimization involving a single variable.
Calculus For Data Science Book - archive.ncarb.org
Calculus For Data Science Book: Essential Math for Data Science Thomas Nield,2022-05-26 Master the math needed to excel in data science machine learning and statistics In this book …
Mathematical Foundations of Data Sciences - GitHub Pages
In this chapter, we study the simplest example of non-linear parametric models, namely Multi-Layers Perceptron (MLP) with a single hidden layer (so they have in total 2 layers). Perceptron …
Data Science Summer School – Introduction to Calculus
• Calculus in R: limits, continuity, differentiation (definition and basic rules, deriva-tives of elementary functions, monotonicity, higher-order derivatives), and integra-tion (indefinite …
Building a Calculus of Data Structures - New York University
In this paper we give an overview of some recent decision procedures for reasoning about data structures, including sets and multisets with cardinality bounds, algebraic data types with …
Data Science Major - Columbia University
%PDF-1.3 %Äåòåë§ó ÐÄÆ 4 0 obj /Length 5 0 R /Filter /FlateDecode >> stream x Åœ[“ݶ‘Çßù)([ ™±(‚w&¶åK4cËq"'ãÍîFyrÅ ©ÊVeýý«òktã ‚‡ yf´µ–kH‚`ãÒÿ¾ 8ÿÊ Ìÿ•»®èr7 í8ŽCÞöC1ä}Ûð÷ …
Calculus for Machine Learning
Calculus is going to be an integral part of our next few lectures regarding neural networks. As a result, this is going to be a crash course into derivatives and partials|if you'd like to get into …
Mathematics in Data Science and Artificial Intelligence
Calculus: Calculus is the area of mathematics that studies the accumulation of quantities (integration) and the instantaneous rates of change of quantities (differentiation). It began as a …
COURSE SYLLABUS Course Title: Honors Calculus I+II for …
An honors-level single course introduction to differential and integral calculus for data science students, with emphasis on a modern, empirical exposition of the classical subject, condensing …
DATA SCIENCE AND ARTIFICIAL INTELLIGENCE - MADE …
Database Management and Warehouse-2: Normal form, file organization, Discretization, sampling, compression; data warehouse modelling: schema for multi-dimensional data …
Jean Hadrien Essential Math For Data Science Take Control …
Jean Hadrien's "Essential Math for Data Science" rightly emphasizes the pivotal function of calculus in the data scientist's toolkit. This post unpacks the profound implications of …
