LEADER 05141nam 22006855 450 001 9911021962903321 005 20250825130208.0 010 $a9783031937644$b(electronic bk.) 010 $z9783031937637 024 7 $a10.1007/978-3-031-93764-4 035 $a(MiAaPQ)EBC32271006 035 $a(Au-PeEL)EBL32271006 035 $a(CKB)40416498400041 035 $a(DE-He213)978-3-031-93764-4 035 $a(OCoLC)1534435187 035 $a(EXLCZ)9940416498400041 100 $a20250825d2025 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLinear Algebra, Data Science, and Machine Learning /$fby Jeff Calder, Peter J. Olver 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (645 pages) 225 1 $aSpringer Undergraduate Texts in Mathematics and Technology,$x1867-5514 311 08$aPrint version: Calder, Jeff Linear Algebra, Data Science, and Machine Learning Cham : Springer,c2025 9783031937637 327 $aPreface -- 1 Vectors -- 2 Inner Product, Orthogonality, Norm -- 3 Matrices -- 4. How Matrices Interact with Inner Products and Norms -- 5 Eigenvalues and Singular Values -- 6 Basics of Optimization -- 7 Introduction to Machine Learning and Data -- 8 Principal Component Analysis -- 9 Graph Theory and Graph-based Learning -- 10 Neural Networks and Deep Learning -- 11 Advanced Optimization -- Bibliography -- Index. 330 $aThis 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. 410 0$aSpringer Undergraduate Texts in Mathematics and Technology,$x1867-5514 606 $aAlgebras, Linear 606 $aArtificial intelligence$xData processing 606 $aMachine learning 606 $aMathematical optimization 606 $aProbabilities 606 $aLinear Algebra 606 $aData Science 606 $aMachine Learning 606 $aOptimization 606 $aApplied Probability 615 0$aAlgebras, Linear. 615 0$aArtificial intelligence$xData processing. 615 0$aMachine learning. 615 0$aMathematical optimization. 615 0$aProbabilities. 615 14$aLinear Algebra. 615 24$aData Science. 615 24$aMachine Learning. 615 24$aOptimization. 615 24$aApplied Probability. 676 $a512.5 700 $aCalder$b Jeff$01845711 701 $aOlver$b Peter J$040590 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9911021962903321 996 $aLinear Algebra, Data Science, and Machine Learning$94429510 997 $aUNINA