Linear Algebra, Data Science, and Machine Learning
暫譯: 線性代數、資料科學與機器學習

Calder, Jeff, Olver, Peter J.

Linear Algebra, Data Science, and Machine Learning
  • 出版商: Springer
  • 出版日期: 2025-08-26
  • 售價: $3,320
  • 貴賓價: 9.5 折 $3,154
  • 語言: 英文
  • 頁數: 629
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031937635
  • ISBN-13: 9783031937637
  • 相關分類: Machine Learning、線性代數 Linear-algebra

    • 海外代購書籍(需單獨結帳)

商品描述

This text provides a mathematically rigorous introduction to modern methods of machine learning and data analysis at the advanced undergraduate/beginning graduate level. The book is self-contained and requires minimal mathematical prerequisites. There is a strong focus on learning how and why algorithms work, as well as developing facility with their practical applications. Apart from basic calculus, the underlying mathematics -- linear algebra, optimization, elementary probability, graph theory, and statistics -- is developed from scratch in a form best suited to the overall goals. In particular, the wide-ranging linear algebra components are unique in their ordering and choice of topics, emphasizing those parts of the theory and techniques that are used in contemporary machine learning and data analysis. The book will provide a firm foundation to the reader whose goal is to work on applications of machine learning and/or research into the further development of this highly active field of contemporary applied mathematics.

To introduce the reader to a broad range of machine learning algorithms and how they are used in real world applications, the programming language Python is employed and offers a platform for many of the computational exercises. Python notebooks complementing various topics in the book are available on a companion GitHub site specified in the Preface, and can be easily accessed by scanning the QR codes or clicking on the links provided within the text. Exercises appear at the end of each section, including basic ones designed to test comprehension and computational skills, while others range over proofs not supplied in the text, practical computations, additional theoretical results, and further developments in the subject. The Students' Solutions Manual may be accessed from GitHub. Instructors may apply for access to the Instructors' Solutions Manual from the link supplied on the text's Springer website.

The book can be used in a junior or senior level course for students majoring in mathematics with a focus on applications as well as students from other disciplines who desire to learn the tools of modern applied linear algebra and optimization. It may also be used as an introduction to fundamental techniques in data science and machine learning for advanced undergraduate and graduate students or researchers from other areas, including statistics, computer science, engineering, biology, economics and finance, and so on.

商品描述(中文翻譯)

這段文字提供了一個數學上嚴謹的介紹，針對現代機器學習和數據分析的方法，適合高年級本科生及初級研究生的水平。這本書是自成一體的，對數學的前置知識要求極少。書中強調學習算法的運作原理及其實際應用的能力。除了基本的微積分外，書中所需的數學基礎——線性代數、優化、基礎概率、圖論和統計——都是從零開始發展，並以最適合整體目標的形式呈現。特別是，廣泛的線性代數內容在主題的排序和選擇上是獨特的，強調當代機器學習和數據分析中所使用的理論和技術的部分。這本書將為那些希望從事機器學習應用和/或進一步研究這個當代應用數學活躍領域的讀者提供堅實的基礎。

為了讓讀者了解廣泛的機器學習算法及其在現實世界應用中的使用，這本書採用了程式語言 Python，並提供了許多計算練習的平台。與書中各主題相輔相成的 Python 筆記本可在前言中指定的伴隨 GitHub 網站上獲得，讀者可以通過掃描 QR 碼或點擊文本中提供的鏈接輕鬆訪問。每個部分的末尾都有練習題，包括設計用來測試理解和計算技能的基本題目，還有其他涉及文本中未提供的證明、實際計算、額外的理論結果和該主題的進一步發展。學生解答手冊可從 GitHub 獲得。教師可以通過文本的 Springer 網站上提供的鏈接申請訪問教師解答手冊。

這本書可用於數學專業的高年級或大四課程，重點在於應用，亦適合其他學科的學生學習現代應用線性代數和優化的工具。它也可以作為高年級本科生和研究生或來自其他領域的研究人員（包括統計學、計算機科學、工程學、生物學、經濟學和金融等）學習數據科學和機器學習基本技術的入門書籍。

作者簡介

Jeff Calder received his Ph.D. degree in applied and interdisciplinary mathematics from the University of Michigan under the guidance of Prof. Selim Esedoglu and Prof. Alfred Hero in 2014. Between 2014 and 2016 he was a Morrey Assistant Professor at the University of California, Berkeley, under the mentorship of Lawrence C. Evans and James Sethian. He has been on the faculty of the School of Mathematics at the University of Minnesota since 2016, full professor since 2025, where he has supervised 5 PhD students, 4 postdoctoral scholars, and a number of undergraduate and high school students on research projects.


Calder's research interests lie in applied probability, numerical analysis, and partial differential equations, with a specific interest in applications to machine learning and data analysis. Calder has published over 50 articles in journals and conferences spanning pure and applied mathematics and related areas, and holds several patents. His research has been recognized with an NSF Career Award and Alfred P. Sloan Research Fellowship in 2020, a University of Minnesota McKnight Presidential Fellowship and Guillermo E. Borja Award in 2021, and he currently holds the Albert and Dorothy Marden Professorship in Mathematics (2023-2028).

Peter J. Olver received his Ph.D. from Harvard University in 1976 under the guidance of Prof. Garrett Birkhoff. After being a Dickson Instructor at the University of Chicago and a postdoc at the University of Oxford, he has been on the faculty of the School of Mathematics at the University of Minnesota since 1980, and a full professor since 1985. He served as the Head of the Department from 2008 to 2020. He has supervised 23 Ph.D. students, and mentored over 30 postdocs, visiting students and scholars from around the world, as well as supervising numerous undergraduate research projects. He is a Fellow of the American Mathematical Society, the Society for Industrial and Applied Mathematics (SIAM), the Institute of Physics, UK, and the Asia-Pacific Artificial Intelligence Association (AAIA).


Over the years, he has contributed to a wide range of fields, including symmetry and Lie theory, partial differential equations, the calculus of variations, mathematical physics, fluid mechanics, elasticity, quantum mechanics, Hamiltonian mechanics, geometric numerical methods, differential geometry, classical invariant theory, algebra, computer vision and image processing, anthropology, and beyond. He is the author of over 160 papers in refereed journals, and has given more than 500 invited lectures on his research at conferences, universities, colleges, and institutes throughout the world. He was named a "Highly Cited Researcher" by Thomson-ISI in 2003, and an inaugural "Highly Ranked Scholar" by ScholarGPS in 2024.. He has written 6 books, including the definitive text on Applications of Lie Groups to Differential Equations, and two additional undergraduate texts: Partial Differential Equations and Applied Linear Algebra, the latter coauthored with his wife, Chehrzad Shakiban.

作者簡介(中文翻譯)

Jeff Calder 於2014年在密西根大學獲得應用與跨學科數學的博士學位，指導教授為 Selim Esedoglu 教授和 Alfred Hero 教授。2014年至2016年間，他在加州大學伯克利分校擔任 Morrey 助理教授，導師為 Lawrence C. Evans 和 James Sethian。自2016年以來，他一直在明尼蘇達大學數學系任教，自2025年起為正教授，並指導了5位博士生、4位博士後研究員以及多位本科生和高中生進行研究項目。

Calder 的研究興趣包括應用概率、數值分析和偏微分方程，特別關注機器學習和數據分析的應用。Calder 在純數學和應用數學及相關領域的期刊和會議上發表了超過50篇文章，並擁有多項專利。他的研究曾獲得2020年國家科學基金會（NSF）職業獎和 Alfred P. Sloan 研究獎學金，2021年獲得明尼蘇達大學 McKnight 總統獎學金和 Guillermo E. Borja 獎，並於2023年至2028年擔任 Albert 和 Dorothy Marden 數學教授。

Peter J. Olver 於1976年在哈佛大學獲得博士學位，指導教授為 Garrett Birkhoff 教授。在擔任芝加哥大學的 Dickson 講師和牛津大學的博士後研究員後，他自1980年以來一直在明尼蘇達大學數學系任教，自1985年起為正教授。他於2008年至2020年擔任系主任。他指導了23位博士生，並指導了來自世界各地的30多位博士後、訪問學生和學者，以及多個本科生研究項目。他是美國數學學會、工業與應用數學學會（SIAM）、英國物理學會和亞太人工智慧協會（AAIA）的會士。

多年來，他在對稱性和李群理論、偏微分方程、變分法、數學物理、流體力學、彈性、量子力學、哈密頓力學、幾何數值方法、微分幾何、經典不變理論、代數、計算機視覺和圖像處理、人類學等廣泛領域做出了貢獻。他在經過審核的期刊上發表了超過160篇論文，並在全球的會議、大學、學院和研究所上發表了超過500場邀請講座。他於2003年被 Thomson-ISI 評選為「高被引研究者」，並於2024年被 ScholarGPS 評選為首屆「高排名學者」。他撰寫了6本書籍，包括《李群在偏微分方程中的應用》的權威文本，以及兩本本科教材：《偏微分方程》和《應用線性代數》，後者與他的妻子 Chehrzad Shakiban 共同撰寫。

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