Algebraic Foundations for Applied Topology and Data Analysis

Schenck, Hal

Algebraic Foundations for Applied Topology and Data Analysis
  • 出版商: Springer
  • 出版日期: 2023-11-22
  • 售價: $2,460
  • 貴賓價: 9.5 折 $2,337
  • 語言: 英文
  • 頁數: 224
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3031066669
  • ISBN-13: 9783031066665
  • 相關分類: Data Science

    • 海外代購書籍(需單獨結帳)

商品描述

This book gives an intuitive and hands-on introduction to Topological Data Analysis (TDA). Covering a wide range of topics at levels of sophistication varying from elementary (matrix algebra) to esoteric (Grothendieck spectral sequence), it offers a mirror of data science aimed at a general mathematical audience.

The required algebraic background is developed in detail. The first third of the book reviews several core areas of mathematics, beginning with basic linear algebra and applications to data fitting and web search algorithms, followed by quick primers on algebra and topology. The middle third introduces algebraic topology, along with applications to sensor networks and voter ranking. The last third covers key contemporary tools in TDA: persistent and multiparameter persistent homology. Also included is a user's guide to derived functors and spectral sequences (useful but somewhat technical tools which have recently found applications in TDA), and an appendix illustrating a number of software packages used in the field.

Based on a course given as part of a masters degree in statistics, the book is appropriate for graduate students.

商品描述(中文翻譯)

這本書提供了對拓撲數據分析（Topological Data Analysis, TDA）的直觀且實用的介紹。涵蓋了從基礎（矩陣代數）到深奧（Grothendieck 光譜序列）等多種主題，為一般數學讀者提供了一面數據科學的鏡子。

所需的代數背景詳細闡述。書的前三分之一回顧了幾個數學的核心領域，從基本的線性代數及其在數據擬合和網頁搜尋算法中的應用開始，接著是代數和拓撲的快速入門。中間的三分之一介紹了代數拓撲及其在感測器網絡和選民排名中的應用。最後的三分之一涵蓋了TDA中的關鍵當代工具：持久性和多參數持久性同調。此外，還包括了導出函子和光譜序列的使用者指南（這些工具雖然有些技術性，但最近在TDA中找到了應用），以及附錄中展示了該領域中使用的多個軟體包。

這本書基於一門作為統計碩士學位課程的一部分所開設的課程，適合研究生閱讀。

作者簡介

Hal Schenck received a BS in Applied Math and Computer Science from Carnegie-Mellon University in 1986. From 1986 to 1990 he served as an Army officer in Georgia and Germany, then returned to graduate school at Cornell, earning his Ph.D. in 1997. After an NSF postdoc at Harvard and Northeastern, he was a professor at Texas A&M (2001-2007), at the University of Illinois (2007-2017), and Chair at Iowa State (2017-2019). Since 2019 he has been the Rosemary Kopel Brown Eminent Scholars Chair at Auburn University.

He has earned teaching awards from Cornell and Illinois, and awards for departmental leadership and outreach to student veterans from Iowa State. He was elected as a fellow of the AMS in 2020, and as a fellow of the AAAS in 2023; recent academic visits include a Leverhulme Professorship at Oxford, and a Clare Hall Fellowship at Cambridge. His research is at the interface of algebra, geometry, and computation.

作者簡介(中文翻譯)

Hal Schenck於1986年獲得卡內基梅隆大學的應用數學與計算機科學學士學位。從1986年到1990年，他在喬治亞州和德國擔任陸軍軍官，隨後回到康奈爾大學攻讀研究生，並於1997年獲得博士學位。在哈佛大學和東北大學完成國家科學基金會的博士後研究後，他曾擔任德州農工大學的教授（2001-2007）、伊利諾伊大學的教授（2007-2017），以及愛荷華州立大學的系主任（2017-2019）。自2019年以來，他擔任奧本大學的羅絲瑪莉·科佩爾·布朗傑出學者講座。

他曾獲得康奈爾大學和伊利諾伊大學的教學獎，以及愛荷華州立大學的系部領導和對學生退伍軍人服務的獎項。他於2020年被選為美國數學學會的會士，並於2023年被選為美國科學促進會的會士；最近的學術訪問包括牛津大學的Leverhulme教授職位和劍橋大學的Clare Hall研究員。他的研究位於代數、幾何和計算的交界處。

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