Mathematical Foundations of Deep Learning: Theory and Algorithms
暫譯: 深度學習的數學基礎：理論與演算法
Ye, Xiaojing
- 出版商: CRC
- 出版日期: 2026-08-25
- 售價: $3,240
- 貴賓價: 9.5 折 $3,078
- 語言: 英文
- 頁數: 268
- 裝訂: Quality Paper - also called trade paper
- ISBN: 1032877081
- ISBN-13: 9781032877082
-
相關分類:
DeepLearning
尚未上市，無法訂購
商品描述
Mathematical Foundations of Deep Learning offers a comprehensive and rigorous treatment of the mathematical principles underlying modern deep learning. The book spans core theoretical topics, from the approximation capabilities of deep neural networks and the theory and algorithms of optimal control and reinforcement learning integrated with deep learning techniques to contemporary generative models that drive today's advances in artificial intelligence.
Designed as both a textbook for graduate and advanced undergraduate students as well as a long-term reference, this volume aims to equip students with a solid mathematical understanding of deep learning while serving researchers, scientists, and engineers seeking a principled framework for developing and analyzing modern artificial intelligence systems.
Features
- Comprehensive and rigorous, featuring detailed theoretical developments, mathematical proofs, and algorithmic frameworks throughout.
- Materials thoughtfully selected from this book support a full one-semester course for graduate students and advanced undergraduates.
- Concise yet precise exposition of core deep learning concepts and techniques, presented using exact and rigorous mathematical language.
商品描述(中文翻譯)
《深度學習的數學基礎》提供了對現代深度學習背後數學原則的全面且嚴謹的探討。本書涵蓋了核心理論主題，包括深度神經網絡的近似能力、最佳控制理論及算法，以及與深度學習技術整合的強化學習，還有當前推動人工智慧進步的生成模型。
本書旨在作為研究生和高年級本科生的教科書，同時也作為長期參考資料，旨在為學生提供深度學習的堅實數學理解，並為尋求建立和分析現代人工智慧系統的研究人員、科學家和工程師提供一個原則性框架。
**特色**
- 全面且嚴謹，整體包含詳細的理論發展、數學證明和算法框架。
- 本書中精心挑選的材料支持為研究生和高年級本科生提供完整的一學期課程。
- 對核心深度學習概念和技術的簡潔而精確的闡述，使用精確且嚴謹的數學語言呈現。
作者簡介
Dr. Xiaojing Ye is a Professor of Mathematics at Georgia State University in Atlanta, USA. His research interests lie in applied and computational mathematics, with a particular focus on numerical methods that integrate deep learning techniques for scientific computing. His work also spans network science, numerical optimization, image processing, and related interdisciplinary areas.
Dr. Ye began his undergraduate studies at Peking University in China in 2001, initially majoring in chemistry. Motivated by a growing interest in mathematics and physics, he transferred to the mathematics major in 2002 while pursuing physics as a minor. He received his Bachelor's degree in Mathematics major in July 2005. After one year of professional experience, he returned to academia to pursue graduate studies at the University of Florida in the USA, supported by a prestigious four-year university alumni fellowship. Dr. Ye earned a Master's degree in Statistics in 2009 and completed his Ph.D. in Mathematics in May 2011. He subsequently served as a Visiting Assistant Professor in the School of Mathematics at the Georgia Institute of Technology for two years. In 2013, he joined the Department of Mathematics and Statistics at Georgia State University as a tenure-track Assistant Professor, where he was awarded tenure and later promoted to Full Professor.
作者簡介(中文翻譯)
葉小京博士是美國亞特蘭大的喬治亞州立大學數學教授。他的研究興趣在於應用數學和計算數學，特別專注於將深度學習技術整合進科學計算的數值方法。他的工作還涵蓋了網絡科學、數值優化、圖像處理及相關的跨學科領域。
葉博士於2001年在中國北京大學開始他的本科學習，最初主修化學。隨著對數學和物理的興趣日益增長，他於2002年轉入數學專業，同時輔修物理。他於2005年7月獲得數學學士學位。在獲得一年的專業經驗後，他回到學術界，前往美國佛羅里達大學攻讀研究生學位，並獲得了一項享有盛譽的四年大學校友獎學金支持。葉博士於2009年獲得統計學碩士學位，並於2011年5月完成數學博士學位。隨後，他在喬治亞理工學院數學學院擔任訪問助理教授兩年。2013年，他加入喬治亞州立大學數學與統計系，擔任終身教職的助理教授，並獲得終身教職，後來晉升為正教授。
