Applied Mathematics Toolkit: Modeling, Data, and Algorithms for Scientists and Engineers
暫譯: 應用數學工具包：科學家與工程師的建模、數據與演算法

現代科學與工程系統越來越多地受到非線性、高維度、部分可觀察性和不確定性的定義。應對這種複雜性需要的不僅僅是孤立的技術，而是需要一種整合的應用數學視角，將建模、數據分析和計算連接在一個一致的框架內。本書開發了這樣一個統一的工具包。它不僅將數學方法視為獨立的學科，而是強調它們在理解、分析和預測複雜系統中的互補角色，並專注於直覺、實用性和在科學與工程領域之間的可轉移性。

- 提供一系列基本的應用數學工具，組織方式強調它們之間的相互作用，而不是將它們視為孤立的主題。
- 每種方法都通過簡單而啟發性的例子介紹，使高級概念在不犧牲嚴謹性的情況下變得易於理解。
- 對於每種技術，展示中突出了其背後的動機、關鍵假設、優勢、限制以及最有效的應用情境。
- 理論、數據和算法始終整合在一起，以展示它們在實際應用中的協同作用。
- 附有短小的「一個概念-一個例子」視頻，每個視頻長度為5-10分鐘，專注於單一想法，並使用故意簡單的例子來支持初步接觸、直覺建立和高效回顧。
- 包含示例代碼以加強概念並促進實踐學習。

本書旨在為尋求現代數學工具實用掌握的高年級本科生、研究生和應用數學、科學及工程領域的研究人員提供指導。特別適合於主題課程和自學，尤其是對於在建模、數據和計算交叉領域工作的讀者。通過將概念清晰性與實踐示例和整合方法論相結合，本書為解決各種跨學科環境中的現實問題提供了基礎。

Nan Chen is Associate Professor in the Department of Mathematics at the University of Wisconsin-Madison and is affiliated with the Institute for Foundations of Data Science. He received his PhD from the Courant Institute of Mathematical Sciences at New York University in Applied Mathematics and Atmospheric and Ocean Sciences, followed by two years as a Postdoctoral Research Associate at Courant. Dr. Chen's research spans applied mathematics, atmospheric and ocean sciences, materials science, and data science. He has received several major honors, including the Kurt O. Friedrichs Prize, the Silver Medal of the New World Mathematics Awards, the Office of Naval Research Young Investigator Award, and multiple teaching awards. He has published over 100 papers in leading journals, including Proceedings of the National Academy of Sciences, Nature Geoscience, Nature Communications, and Notices of the American Mathematical Society. Dr. Chen has delivered more than 100 invited presentations worldwide, and his work has been featured in SIAM News, SIAM DSWeb, Eos, and many other media outlets. He has organized nearly 30 workshops and mini-symposia at major conferences. Dr. Chen has mentored postdoctoral researchers, PhD students, and undergraduates, many of whom have received major research and presentation awards. He is committed to supporting early-career scientists and promoting interdisciplinary and international collaboration at the interface of applied mathematics, engineering, and geoscience. He currently serves as Secretary of SIAM Mathematics of Planet Earth and Chair of the AGU session ``Applied Math Perspectives on Modeling, Analyzing, and Predicting Complex Geophysical Systems'', playing an active role in shaping interdisciplinary efforts at the interface of applied mathematics and other disciplines.

Charlotte Moser is a PhD researcher in Mathematics at the University of Wisconsin-Madison, where she works as a research assistant at the interface of applied mathematics and environmental science. Her research focuses on mathematical modeling, uncertainty quantification, data assimilation, machine learning, Bayesian inference, and the analysis of complex dynamical systems, with applications to atmospheric and oceanic phenomena. She received her B.S. in Applied Mathematics, with minors in Environmental Science and Psychology. Ms. Moser has received multiple honors, including the DANOC Best Student Presentation Award, the Henry Schaerf Mathematics Graduate Award, and the AGU Outstanding Student Presentation Award, as well as the Dean's Distinguished Fellowship, the Mathematics Honors Program distinction, the IBA Biomathematics Education with Applications and Methods Grant, and the JD and Marcia Wine Mathematics Award. She has presented her research at leading national and international conferences and is emerging as a young researcher at the intersection of applied mathematics and environmental science. In addition to her research, she is actively engaged in scientific communication and education. She develops accessible content on applied mathematics and Earth science through online platforms, aiming to broaden participation and foster interdisciplinary learning. She is also committed to broadening participation in STEM and fostering collaborative scientific communities. Her work is driven by a strong interest in connecting mathematical theory with real-world environmental challenges.

陳楠是威斯康辛大學麥迪遜分校數學系的副教授，並隸屬於數據科學基礎研究所。他在紐約大學的Courant數學科學研究所獲得應用數學及大氣與海洋科學的博士學位，隨後在Courant擔任了兩年的博士後研究助理。陳博士的研究涵蓋應用數學、大氣與海洋科學、材料科學及數據科學。他獲得了多項重要榮譽，包括Kurt O. Friedrichs獎、世界數學獎銀獎、海軍研究辦公室青年研究者獎及多項教學獎項。他在領先的期刊上發表了超過100篇論文，包括美國國家科學院院刊、自然地球科學、自然通訊及美國數學學會通訊。陳博士在全球發表了超過100場受邀演講，他的研究成果曾在SIAM News、SIAM DSWeb、Eos及其他多個媒體上報導。他在主要會議上組織了近30場工作坊和迷你研討會。陳博士指導過博士後研究人員、博士生及本科生，其中許多人獲得了重要的研究和演講獎項。他致力於支持早期職業科學家，並促進應用數學、工程學和地球科學之間的跨學科和國際合作。他目前擔任SIAM地球數學的秘書及AGU會議“應用數學在建模、分析和預測複雜地球物理系統中的視角”的主席，積極參與塑造應用數學與其他學科之間的跨學科努力。

夏洛特·莫澤是威斯康辛大學麥迪遜分校的數學博士研究生，擔任應用數學與環境科學交界處的研究助理。她的研究專注於數學建模、不確定性量化、數據同化、機器學習、貝葉斯推斷及複雜動態系統的分析，並應用於大氣和海洋現象。她獲得了應用數學學士學位，並輔修環境科學和心理學。莫澤女士獲得了多項榮譽，包括DANOC最佳學生演講獎、亨利·沙爾夫數學研究生獎及AGU傑出學生演講獎，以及院長傑出獎學金、數學榮譽計劃的榮譽、IBA生物數學教育應用與方法獎助金及JD和Marcia Wine數學獎。她在國內外主要會議上展示了她的研究，並在應用數學與環境科學的交叉領域中崭露頭角。除了研究外，她還積極參與科學傳播和教育。她通過在線平台開發可接觸的應用數學和地球科學內容，旨在擴大參與並促進跨學科學習。她也致力於擴大STEM領域的參與，並促進合作的科學社群。她的工作受到強烈興趣驅動，旨在將數學理論與現實世界的環境挑戰相連接。