A Mathematical Introduction To Data Science

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A Mathematical Introduction To Data Science
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Author : Yi Sun
language : en
Publisher: Springer Nature
Release Date : 2025-07-09
A Mathematical Introduction To Data Science written by Yi Sun and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-09 with Computers categories.
This textbook provides a comprehensive foundation in the mathematics needed for data science for students and self-learners with a basic mathematical background who are interested in the principles behind computational algorithms in data science. It covers sets, functions, linear algebra, and calculus, and delves deeply into probability and statistics, which are key areas for understanding the algorithms driving modern data science applications. Readers are guided toward unlocking the secrets of algorithms like Principal Component Analysis, Singular Value Decomposition, Linear Regression in two and more dimensions, Simple Neural Networks, Maximum Likelihood Estimation, Logistic Regression and Ridge Regression, illuminating the path from mathematical principles to algorithmic mastery. It is designed to make the material accessible and engaging, guiding readers through a step-by-step progression from basic mathematical concepts to complex data science algorithms. It stands out for its emphasis on worked examples and exercises that encourage active participation, making it particularly beneficial for those with limited mathematical backgrounds but a strong desire to learn. This approach facilitates a smoother transition into more advanced topics. The authors expect readers to be proficient in handling numbers in various formats, including fractions, decimals, percentages, and surds. They should also have a knowledge of introductory algebra, such as manipulating simple algebraic expressions, solving simple equations, and graphing elementary functions, along with a basic understanding of geometry including angles, trigonometry and Pythagoras’ theorem.
Data Science For Mathematicians
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Author : Nathan Carter
language : en
Publisher: CRC Press
Release Date : 2020-09-15
Data Science For Mathematicians written by Nathan Carter and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-15 with Mathematics categories.
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.
Mathematical Problems In Data Science
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Author : Li M. Chen
language : en
Publisher: Springer
Release Date : 2015-12-15
Mathematical Problems In Data Science written by Li M. Chen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-15 with Computers categories.
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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Author : Avrim Blum
language : en
Publisher: Cambridge University Press
Release Date : 2020-01-23
Foundations Of Data Science written by Avrim Blum and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-23 with Computers categories.
Covers mathematical and algorithmic foundations of data science: machine learning, high-dimensional geometry, and analysis of large networks.
Data Assimilation
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Author : Kody Law
language : en
Publisher: Springer
Release Date : 2015-09-05
Data Assimilation written by Kody Law and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-05 with Mathematics categories.
This book provides a systematic treatment of the mathematical underpinnings of work in data assimilation, covering both theoretical and computational approaches. Specifically the authors develop a unified mathematical framework in which a Bayesian formulation of the problem provides the bedrock for the derivation, development and analysis of algorithms; the many examples used in the text, together with the algorithms which are introduced and discussed, are all illustrated by the MATLAB software detailed in the book and made freely available online. The book is organized into nine chapters: the first contains a brief introduction to the mathematical tools around which the material is organized; the next four are concerned with discrete time dynamical systems and discrete time data; the last four are concerned with continuous time dynamical systems and continuous time data and are organized analogously to the corresponding discrete time chapters. This book is aimed at mathematical researchers interested in a systematic development of this interdisciplinary field, and at researchers from the geosciences, and a variety of other scientific fields, who use tools from data assimilation to combine data with time-dependent models. The numerous examples and illustrations make understanding of the theoretical underpinnings of data assimilation accessible. Furthermore, the examples, exercises and MATLAB software, make the book suitable for students in applied mathematics, either through a lecture course, or through self-study.
Mathematical Introduction To Data Science
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Author : Sven A. Wegner
language : en
Publisher: Springer Nature
Release Date : 2024-08-30
Mathematical Introduction To Data Science written by Sven A. Wegner and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-30 with Computers categories.
This textbook is intended for students of mathematics who have completed the foundational courses of their undergraduate studies and now want to specialize in Data Science and Machine Learning. It introduces the reader to the most important topics in the latter areas focusing on rigorous proofs and a systematic understanding of the underlying ideas. The textbook comes with 121 classroom-tested exercises. Topics covered include k-nearest neighbors, linear and logistic regression, clustering, best-fit subspaces, principal component analysis, dimensionality reduction, collaborative filtering, perceptron, support vector machines, the kernel method, gradient descent and neural networks.
Choosing Chinese Universities
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Author : Alice Y.C. Te
language : en
Publisher: Routledge
Release Date : 2022-10-07
Choosing Chinese Universities written by Alice Y.C. Te and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-07 with Education categories.
This book unpacks the complex dynamics of Hong Kong students’ choice in pursuing undergraduate education at the universities of Mainland China. Drawing on an empirical study based on interviews with 51 students, this book investigates how macro political/economic factors, institutional influences, parental influence, and students’ personal motivations have shaped students’ eventual choice of university. Building on Perna’s integrated model of college choice and Lee’s push-pull mobility model, this book conceptualizes that students’ border crossing from Hong Kong to Mainland China for higher education is a trans-contextualized negotiated choice under the "One Country, Two Systems" principle. The findings reveal that during the decision-making process, influencing factors have conditioned four archetypes of student choice: Pragmatists, Achievers, Averages, and Underachievers. The book closes by proposing an enhanced integrated model of college choice that encompasses both rational motives and sociological factors, and examines the theoretical significance and practical implications of the qualitative study. With its focus on student choice and experiences of studying in China, this book’s research and policy findings will interest researchers, university administrators, school principals, and teachers.
Mathematics For Machine Learning
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Author : Marc Peter Deisenroth
language : en
Publisher: Cambridge University Press
Release Date : 2020-04-23
Mathematics For Machine Learning written by Marc Peter Deisenroth and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-23 with Computers categories.
Distills key concepts from linear algebra, geometry, matrices, calculus, optimization, probability and statistics that are used in machine learning.
Introduction To Data Science
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Author : Rafael A. Irizarry
language : en
Publisher: CRC Press
Release Date : 2019-11-12
Introduction To Data Science written by Rafael A. Irizarry and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-12 with Mathematics categories.
Introduction to Data Science: Data Analysis and Prediction Algorithms with R introduces concepts and skills that can help you tackle real-world data analysis challenges. It covers concepts from probability, statistical inference, linear regression, and machine learning. It also helps you develop skills such as R programming, data wrangling, data visualization, predictive algorithm building, file organization with UNIX/Linux shell, version control with Git and GitHub, and reproducible document preparation. This book is a textbook for a first course in data science. No previous knowledge of R is necessary, although some experience with programming may be helpful. The book is divided into six parts: R, data visualization, statistics with R, data wrangling, machine learning, and productivity tools. Each part has several chapters meant to be presented as one lecture. The author uses motivating case studies that realistically mimic a data scientist’s experience. He starts by asking specific questions and answers these through data analysis so concepts are learned as a means to answering the questions. Examples of the case studies included are: US murder rates by state, self-reported student heights, trends in world health and economics, the impact of vaccines on infectious disease rates, the financial crisis of 2007-2008, election forecasting, building a baseball team, image processing of hand-written digits, and movie recommendation systems. The statistical concepts used to answer the case study questions are only briefly introduced, so complementing with a probability and statistics textbook is highly recommended for in-depth understanding of these concepts. If you read and understand the chapters and complete the exercises, you will be prepared to learn the more advanced concepts and skills needed to become an expert. A complete solutions manual is available to registered instructors who require the text for a course.
R For Data Science
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Author : Hadley Wickham
language : en
Publisher: "O'Reilly Media, Inc."
Release Date : 2016-12-12
R For Data Science written by Hadley Wickham and has been published by "O'Reilly Media, Inc." this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-12 with Computers categories.
Learn how to use R to turn raw data into insight, knowledge, and understanding. This book introduces you to R, RStudio, and the tidyverse, a collection of R packages designed to work together to make data science fast, fluent, and fun. Suitable for readers with no previous programming experience, R for Data Science is designed to get you doing data science as quickly as possible. Authors Hadley Wickham and Garrett Grolemund guide you through the steps of importing, wrangling, exploring, and modeling your data and communicating the results. You'll get a complete, big-picture understanding of the data science cycle, along with basic tools you need to manage the details. Each section of the book is paired with exercises to help you practice what you've learned along the way. You'll learn how to: Wrangle—transform your datasets into a form convenient for analysis Program—learn powerful R tools for solving data problems with greater clarity and ease Explore—examine your data, generate hypotheses, and quickly test them Model—provide a low-dimensional summary that captures true "signals" in your dataset Communicate—learn R Markdown for integrating prose, code, and results