SIAM Review, Volume 66, Issue 1, Page 193-201, February 2024.
If you are keen to understand the world around us by developing mathematical or data-driven models, or if you are interested in the methodologies that can be used to analyze those models, this collection of reviews may help you identify a useful book or two. Our featured review was written by Tim Hoheisel, on the book Convex Optimization: Introductory Course, written by Mikhail Moklyachuk. Hoheisel argues that convex optimization is not “solved” and certainly not “dead,” as had been deemed by some academics. Indeed, he believes that the explosive growth of machine learning problems, which often rely on convexity, has posed new challenges and renders convex optimization all the more relevant. Hoheisel notes pros and cons of the book, and concluded that it “can serve as an introductory text for students who want to learn the fundamentals of convex analysis and some theoretical aspects of convex optimization,” even though it may not be necessarily useful for researchers. After making a brief appearance in the first review, machine learning is featured in the second review, written by Diyora Salimova, on the volume, Mathematical Aspects of Deep Learning, edited by Philipp Grohs and Gitta Kutyniok. The edited volume encompasses a collection of topics concerning the mathematics of deep learning. After describing each of the eleven chapters, Salimova concludes that “it is nice to have this book in one's library,” given the increasing popularity and applications of deep learning everywhere. While some edited volumes lack cohesiveness, Salimonva notes that a strength of the book is that “it approaches modern deep learning from many different perspectives and provides various theoretical insights.” Continuing on the theme of data science, the next book is Optimization for Data Analysis, by Stephen J. Wright and Benjamin Recht. The review was written by our former section editor Volker Schulz, who commends the authors for providing “a very good basis for a course on optimization algorithms in data science.” Outside of the classroom, the book is also suitable for self-learning, as helpful exercises are provided to deepen the context. I reviewed the next book, Foundations of Computational Imaging: A Model-Based Approach, written by Charles A. Bouman. The author first started writing the book 20 years ago for a course that he was teaching---at a time when “Computational Imaging” did not exist as a field. What I like most about this book is that Bouman has succeeded in his stated goal of providing “a foundation for a collection of theoretical material that can serve as a common language for both researchers and practitioners of Computational Imaging.” The next review was written by Shaun Hendy, on the book Climate, Chaos and COVID: How Mathematical Models Describe the Universe, by Chris Budd. The book describes recent examples of how mathematical modeling has helped us navigate the world and formulate critical policies, such as climate change and COVID. While the book is engaging, Hendy notes the limited representation of women and mathematicians from minority groups. We conclude with a review on the book An Introduction to the Numerical Simulation of Stochastic Differential Equations, authored by Desmond J. Higham and Peter E. Kloeden. Minh-Binh Tran calls the book “a marvelous introduction into the theory of numerical SDEs for undergraduate students and young researchers.” Tran also notes that the book also gives excellent instructions on how to efficiently implement SDE-based models and simulations.

中文翻译：

---

书评

《SIAM 评论》，第 66 卷，第 1 期，第 193-201 页，2024 年 2 月。
如果您热衷于通过开发数学或数据驱动模型来了解我们周围的世界，或者如果您对可用于分析这些模型的方法感兴趣，那么这组评论可能会帮助您找到一两本有用的书。我们的专题评论是由 Tim Hoheisel 在 Mikhail Moklyachuk 撰写的《凸优化：入门课程》一书中撰写的。 Hoheisel 认为，凸优化并没有“解决”，当然也没有像一些学者认为的那样“死亡”。事实上，他认为，通常依赖于凸性的机器学习问题的爆炸性增长带来了新的挑战，并使凸优化变得更加重要。 Hoheisel 指出了这本书的优点和缺点，并得出结论，它“可以作为想要学习凸分析基础知识和凸优化的一些理论方面的学生的入门教材”，尽管它可能对研究人员不一定有用。在第一篇评论中简短介绍之后，机器学习在第二篇评论中得到了重点介绍，该评论由 Diyora Salimova 撰写，收录于 Philipp Grohs 和 Gitta Kutyniok 编辑的《深度学习的数学方面》卷中。编辑后的卷包含一系列有关深度学习数学的主题。在描述了十一章的每一章后，萨利莫娃得出结论：“鉴于深度学习在各地的日益普及和应用，“很高兴能在自己的图书馆里拥有这本书”。虽然一些编辑的书籍缺乏凝聚力，但萨利蒙瓦指出，这本书的优势在于“它从许多不同的角度探讨现代深度学习，并提供了各种理论见解。”继续以数据科学为主题，下一本书是 Stephen J. Wright 和 Benjamin Recht 所著的《数据分析优化》。这篇评论是由我们的前任编辑 Volker Schulz 撰写的，他赞扬作者“为数据科学优化算法课程提供了非常好的基础”。在课堂之外，本书也适合自学，因为提供了有用的练习来加深背景知识。我回顾了下一本书，《计算成像的基础：基于模型的方法》，作者是 Charles A. Bouman。作者于 20 年前首次为他所教授的课程撰写这本书，当时“计算成像”这个领域还不存在。我最喜欢这本书的地方是，布曼成功地实现了他既定的目标，即“为理论材料集合奠定了基础，可以作为计算成像研究人员和实践者的共同语言”。下一篇评论是由肖恩·亨迪 (Shaun Hendy) 撰写的，内容涉及克里斯·巴德 (Chris Budd) 所著的《气候、混沌和新冠病毒：数学模型如何描述宇宙》一书。这本书描述了数学模型如何帮助我们驾驭世界和制定关键政策（例如气候变化和新冠疫情）的最新例子。虽然这本书很吸引人，但亨迪指出，来自少数群体的女性和数学家的代表性有限。最后，我们对 Desmond J. Higham 和 Peter E. Kloeden 所著的《随机微分方程数值模拟简介》一书进行了评论。 Minh-Binh Tran 称这本书是“为本科生和年轻研究人员提供的数值 SDE 理论的精彩介绍”。 Tran 还指出，本书还就如何有效实现基于 SDE 的模型和模拟提供了出色的指导。