AMS Book Reviews

March 2023

Algebraic Geometry: Notes on a Course

Piotr Pokora's zbMathOpen review of Algebraic Geometry: Notes on a Course, by Michael Artin

"The present book under review entitled Algebraic Geometry – Notes on a Course by Michael Artin is, according to my very subjective viewpoint, one of the best textbooks devoted to basics on algebraic geometry. I am aware of the fact that this is a rather bold statement, but I will try to justify my claim here. There are many textbooks devoted to the foundations of algebraic geometry, and it seems that there is no room for new ideas or strategies in writing such books. Everything has been tried. This was also my first prediction before receiving this book, and I can honestly say that I am very happy to have been wrong.

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Living Proof: Stories of Resilience Along the Mathematical Journey

Keri Sather-Wagstaff's MathSciNet review of Living Proof: Stories of Resilience Along the Mathematical Journey, edited by Allison K. Henrich, Emille D. Lawrence, Matthew A. Pons, and David G. Taylor

"...With this in mind, I tell you that this is a book filled with stories of love. It is, of course, more than that. It is a book about resilience, struggle, persistence, obstacles, grit, barriers, determination, failure, success, and so many other things. But at its core, I see the common theme of love. I read these as stories of people who love mathematics so much that they have endured heartbreaking struggle within systems that are built to keep them out. They have overcome obstacles that many of us can only imagine, just for the privilege to do math. These are also stories of people who helped them to succeed, through large and small acts of kindness, generosity, and thoughtfulness; in other words: love. And this is why I think you should read this book."

Read the full review at MathScinet

Combinatorial Convexity

Jeno Lehel's MathSciNet review of Combinatorial Convexityby Imre Bárány

"It is a real gift for students and the much larger readership if they can learn firsthand from an active researcher in a subject. Imre Bárány is one of them; in particular his work has been a driving force behind the recent progress of combinatorial convexity. His book of the highest standard can be used as a textbook for graduate or undergraduate courses. The short chapters are suitable for one- or two-hour lectures. At the end of each chapter various exercises complete the material and help deepen understanding. Basic linear algebra, linear programming, and some experience in graph and hypergraph theory, that is, certain mathematical maturity, are expected from the reader."

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The Calculus of Complex Functions

Jay M. Jahangiri's MathSciNet review of The Calculus of Complex Functionsby William Johnston

“This is an excellent self-explanatory and self-contained textbook for senior undergraduate or freshman graduate complex analysis and number theory students. It clearly explains how theoretical complex analysis can help mathematicians answer difficult questions about real numbers, in particular, questions about integers. Each of the six chapters starts with an easy explanation of the topic and then brilliantly moves to more involved problems and discoveries. Each section comes with both helpful solved examples as well as a comprehensive set of exercises with answers to most problems. These topics and their related exercises are beautifully illustrated using Mathematica graphing technology. What is special about this textbook is that at the end of each chapter, a history of the leading mathematicians and their discoveries is nicely narrated, which can be good motivation for curious young mathematicians to further explore and investigate these topics. These short, but informative, biographies explain how our current understanding of complex analysis evolves from three distinct lines of development, arising from the work of Riemann, Cauchy, and Weierstrass.”

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February 2023

Finite Fields, with Applications to Combinatorics

Allen Stenger's MAA review of Finite Fields, with Applications to Combinatorics, by Kannan Soundararajan  

“The writing is very clear, and there are abundant cross-references and a good index in case you want to start in the middle of things rather than reading straight through. In particular the book is valuable if you already know about finite fields but would like to see some interesting applications. As abstract algebra texts go, this treatment is very concrete with lots of specific examples. The book has a strong number theory flavor and brings out how these abstract structures generalize the integers.”

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Mathematics via Problems: Part 2: Geometry

Jasmine Sourwine's MAA review of: Mathematics via Problems: Part 2: Geometryby Alexey A. Zaslavsky and Mikhail B. Skopenkov

“Zaslavsky and Skopenkov’s Mathematics via Problems Part 2: Geometry is not your average textbook. Though it touches upon most high school geometry topics, it does go beyond the level required by the standards. In fact, it is not an instructive book for students’ first time engaging with relevant geometry content; rather, it is a collection of relevant problems meant to be pondered and discussed. The book serves as a problem-solving agenda for mathematics clubs and communities of practice called “math circles.” Math circles are vertical clubs of mathematicians, from elementary-aged students to professionals and researchers, that support engagement with mathematics via problems.” 

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Primes of the Form x^2 + ny^2: Fermat, Class Field Theory, and Complex Multiplication

Fernando Guovea's MAA review of: Primes of the Form x^2 + ny^2: Fermat, Class Field Theory, and Complex Multiplicationby David A. Cox

"There are exercises throughout, including many cases of “we leave the proof as an exercise.” The major change in this third edition is that full solutions are now included. Many of these were written by Roger Lipsett and then completed and revised by Cox. Inevitably, small errors and unclear spots were found in the course of preparing solutions, so one of the advantages of the new edition is that “small errors have been fixed and many hints have been clarified and/or expanded.” The solutions to the exercises fill 219 pages of the book, almost doubling its size." 

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The History of Mathematics: A Source-Based Approach, Volume 2

Thomas Sonar's zbMathOpen review of: The History of Mathematics: A Source-Based Approach, Volume 2, by June Barrow-Green, Jeremy Gray and Robin Wilson

"... As with the first volume, this one is a very readable introduction into the history of mathematics starting from the 16th century. Appealing are the boxes summarizing important results. The volume is full of graphs, figures, and depiction and photos of mathematicians. It is obvious that the choice of topics concerning the sheer mass of material may be criticized in some cases but all in all the choices have been made wisely. According to its subtitle ‘A source-based approach’ there are very many excerpts of important sources so that the reader can ‘listen’ directly to the creators of the theories described."  

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An Invitation to Pursuit-Evasion Games and Graph Theory

Thomas Wiseman's zbMathOpen review of: An Invitation to Pursuit-Evasion Games and Graph Theory, by Anthony Bonato 

"In this textbook, the author provides a thorough introduction to pursuit-evasion games, a class of dynamic interactions that take place on a graph. In a pursuit-evasion game, there is a set of vertices and a set of edges linking them. Time is discrete and measured in rounds. One player, the evader, can move across vertices of the graph according to fixed rules. One or more other players, the pursuers, can move according to their own rules. The goal of the pursuers is to reach the same location as the evader, or to surround or locate the evader. A classic example is Cops and Robbers, where the evader and pursuers move in alternating rounds, and each may move along a single edge to a neighboring vertex."  

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January 2023

A Festival of Mathematics: A Source Book

Steve Benson's MAA review of: A Festival of Mathematics: A Source Book, by Alice Peters and Mark Saul 

"There are a number of books available with intriguing problems for students (and others) to puzzle over, but you will want to make room in your bookshelf for one more. This collection, the 28th volume from MSRI’s Mathematical Circles Library, provides a unique set of resources for use in mathematical circles and similar formal and informal settings. The activities, chosen from those used in Julia Robinson Mathematics Festivals (founded in 2007 by Nancy Blackman and inspired by the Saint Mary’s College contests of the 1970s) have been carefully curated to optimize involvement (low threshold/high ceiling with ample opportunities for “tweaks” motivating new investigations)..."  

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Partial Differential Equations: A First Course

Jürgen Appell's zbMathOpen review of: Partial Differential Equations: A First Course, by Rustum Choksi

"This is really an excellent textbook. It covers a wealth of interesting material, it is written in a very clear and convincing style, and it explains ideas, rather than drowning the reader in technicalities, as many other books do. The author takes his task serious, by not restricting himself to just the presentation of definitions, theorems, and proofs, which makes reading often pretty dry, but also by giving some hints which should prevent unexperienced readers from walking into certain traps. (Such sections are called “Examples where this is illegal” and refer, for example, to differentiating under the integral sign.)" 

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