New Books in Mathematics

Peter Winkler has been collecting mathematical puzzles since childhood. He has had published two previous collections, and recently he compiled his largest curated collection to date. Mathematical Puzzles (A K Peters, 2021) also takes an alluring new approach to the genre: In the Roman-numbered front matter, 300+ puzzles are presented, roughly in order of increasing difficulty. Fuller discussions of the puzzles are then organized into 24 chapters according to the key insight that leads to their solutions. Each insight gets a brief mathematical treatment, and by the end of each chapter the reader is primed to appreciate an important and kindred mathematical result.In our interview, Dr. Winkler walked me through a handful of puzzles from two chapters. The first, "The Law of Small Numbers", gives a tongue-in-cheek name to the strategy of gaining insight from a smaller version of a larger problem. The puzzles lead up to a discussion of perfect matchings, whose small-number analogues reveal an elegant geometric solution. The second, "Infinite Choice", begins with some variations on hat-guessing puzzles, which turn out to admit surprisingly powerful strategies even among infinitudes of players! The chapter closes with an accessible peek at graph coloring problems.The book is delightfully designed with playful header fonts and illustrations by cartoonist Jess Johnson, through an equally delightful collaboration we took a moment to discuss. As Dr. Winkler aimed, i believe the book will appeal both to the puzzle enthusiast with a limited background in mathematics and to the mathematics enthusiast who, like myself, never really took to puzzles—as well, of course, to those dual enthusiasts whom the author epitomizes.Suggested companion works: How to Solve It: A New Aspect of Mathematical Method by Georg Pólya Martin Gardner’s Mathematical Games: The Entire Collection of his Scientific American Columns Peter Winkler is the William Morrill Professor of Mathematics and Computer Science at Dartmouth College and, for 2019–2020, the Distinguished Visiting Professor for the Public Dissemination of Mathematics at the National Museum of Mathematics. He is the author of 160 research papers, a dozen patents, two previous puzzle books, a book on cryptographic techniques in the game of bridge, and a portfolio of compositions for ragtime piano. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

In Community College Mathematics: Past, Present, and Future (CRC Press, 2022), Brian Cafarella addresses the key questions: How can we build a future model for community college gatekeeper math classes that is both successful and sustainable? Additionally, how can we learn from the past and the present to build such a model? From the 1970’s to the pandemic in the early 2020’s, the book uses interviews with 30 community college faculty members from seven community colleges to explore math curricula as well as trends, initiatives, teaching practices, and mandates that have impacted community college mathematics.Brian Cafarella is a professor in mathematics at Sinclair Community College in Dayton, Ohio. He has taught a variety of courses ranging from developmental math through pre-calculus. Brian is a past recipient of the Roeche Award for teaching excellence and a past recipient of the Ohio Magazine Award for excellence in education.Marc Goulet is Professor in mathematics and Associate Dean in the College of Arts and Sciences at the University of Wisconsin-Eau Claire. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Today I had the pleasure of talking to Joe Mileti, associate professor of mathematics at Grinnell College. Even if you are not "into" math, you will enjoy this conversation. We talked about how math is not what you think it is. It's not just memorizing formulas and grinding. It's about thinking and, like all thinking, it involves abstraction, logic, using analogies and metaphors, and a bunch of imagination. We also talked about how math is about talking to other mathematicians and doing a kind of "brainstorming." Joes's new book is Modern Mathematical Logic (Cambridge UP, 2022).Marshall Poe is the founder and editor of the New Books Network. He can be reached at marshallpoe@newbooksnetwork.com. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

In Probability and Forensic Evidence: Theory, Philosophy, and Applications (Cambridge UP, 2021), Ronald Meester and Klaas Slooten address the role of statistics and probability in the evaluation of forensic evidence, including both theoretical issues and applications in legal contexts. It discusses what evidence is and how it can be quantified, how it should be understood, and how it is applied (and, sometimes misapplied).Ronald Meester is Professor in probability theory at the Vrije Universiteit Amsterdam. He is co-author of the books Continuum Percolation (1996), A Natural Introduction to Probability Theory (2003), Random Networks for Communication (2008), and has written around 120 research papers on topics including percolation theory, ergodic theory, philosophy of science, and forensic probability.Klaas Slooten works as Statistician at the Netherlands Forensic Institute and at the Vrije Universiteit Amsterdam where he is Professor by special appointment. He as published around 30 articles on forensic probability and statistics. He is interested in the mathematical, legal, and philosophical evaluation of evidence.Marc Goulet is Professor in mathematics and Associate Dean in the College of Arts and Sciences at the University of Wisconsin-Eau Claire. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

In Formulations: Architecture, Mathematics, Culture (MIT Press, 2022), Andrew Witt examines the visual, methodological, and cultural intersections between architecture and mathematics. The linkages Witt explores involve not the mystic transcendence of numbers invoked throughout architectural history, but rather architecture’s encounters with a range of calculational systems—techniques that architects inventively retooled for design. Witt offers a catalog of mid-twentieth-century practices of mathematical drawing and calculation in design that preceded and anticipated digitization as well as an account of the formal compendia that became a cultural currency shared between modern mathematicians and modern architects.Witt presents a series of extensively illustrated “biographies of method”—episodes that chart the myriad ways in which mathematics, particularly the mathematical notion of modeling and drawing, was spliced into the creative practice of design. These include early drawing machines that mechanized curvature; the incorporation of geometric maquettes—“theorems made flesh”—into the toolbox of design; the virtualization of buildings and landscapes through surveyed triangulation and photogrammetry; formal and functional topology; stereoscopic drawing; the economic implications of cubic matrices; and a strange synthesis of the technological, mineral, and biological: crystallographic design.Trained in both architecture and mathematics, Witt uses mathematics as a lens through which to understand the relationship between architecture and a much broader set of sciences and visual techniques. Through an intercultural exchange with other disciplines, he argues, architecture adapted not only the shapes and surfaces of mathematics but also its values and epistemic ideals.Bryan Toepfer, AIA, NCARB, CAPM is the Principal Architect for TOEPFER Architecture, PLLC, an Architecture firm specializing in Residential Architecture and Virtual Reality. He has authored two books, “Contractors CANNOT Build Your House,” and “Six Months Now, ARCHITECT for Life.” He is an Assistant Professor at Alfred State College and has served as the Director of Government Affairs and as the Director of Education for the AIA Rochester Board of Directors. Always eager to help anyone understand the world of Architecture, he hosts the New Books Network – Architecture podcast, is an NCARB Licensing Advisor and helps coach candidates taking the Architectural Registration Exam. btoepfer@toepferarchitecture Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Formal mathematical models have provided tremendous insights into politics in recent decades. Formal Models of Domestic Politics (Cambridge UP, 2021) is the leading graduate textbook covering the crucial models that underpin current theoretical and empirical research on politics by both economists and political scientists. This textbook was recently updated to reflect the wealth of new theory-building around the functioning of authoritarian regimes, as well as to include recent developments in the theory of electoral competition, delegation, legislative bargaining, and collective action.Author Scott Gehlbach is a professor at the University of Chicago, where he is the director of their new PhD program in Political Economy. He is a widely published political economist, with influential articles published in both economics and political science journal as well as two other books. Scott also has a regional specialty in the politics of Russia, Ukraine, and other postcommunist countries.In our interview, we discuss what formal models are, how they work, and illustrates their usefulness with several examples. We also speak briefly at the end about current Russian politics and the ideas he outlined in his February Washington Post Monkey Cage blog piece on the implications of the invasion of Ukraine.Host Peter Lorentzen is an Associate Professor in the Department of Economics at the University of San Francisco, where he leads a new Master's program in Applied Economics focused on the digital economy. His own research focus is the political economy of governance in China. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Today I talked to Seth Stephens-Davidowitz about his new book Don't Trust Your Gut: Using Data to Get What You Really Want in LIfe (Dey Street Books, 2022)Looking for advice on how to get a date, how to have a successful marriage, or just how to have a happier life? Don’t trust your gut, don’t trust conventional wisdom, and put down that self-help book full of plausible arguments and compelling anecdotes that just happens to contradict the advice you got from the self-help book you. Instead, let Seth Stephens-Davidowitz guide you, using data!Seth Stephens-Davidowitz is a data scientist, author, keynote speaker, and recovering economist. His first book Everybody Lies, was a New York Times bestseller that showed how social scientists have used new data about our online behavior to gain new insights about who we really are and what we really think. His latest book, Don’t Trust Your Gut, is about how we can use data not just to understand other people but also how to get what we want in life, whether it’s health, wealth, attractiveness, or inner peace.Host Peter Lorentzen is an Associate Professor in the Department of Economics at the University of San Francisco, where he leads a new Master's program in Applied Economics focused on the digital economy. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Plan S: the open access initiative that changed the face of global research. Robert-Jan Smits and Rachael Pells's book Plan S for Shock: Science. Shock. Solution. Speed. (Ubiquity Press, 2022) tells the story of open access publishing - why it matters now, and for the future. In a world where information has never been so accessible, and answers are available at the touch of a fingertip, we are hungrier for the facts than ever before - something the Covid-19 crisis has brought to light. And yet, paywalls put in place by multi-billion dollar publishing houses are still preventing millions from accessing quality, scientific knowledge - and public trust in science is under threat. On 4 September 2018, a bold new initiative known as 'Plan S' was unveiled, kickstarting a world-wide shift in attitudes towards open access research. For the first time, funding agencies across continents joined forces to impose new rules on the publication of research, with the aim of one day making all research free and available to all. What followed was a debate of global proportions, as stakeholders asked: Who has the right to access publicly-funded research? Will it ever be possible to enforce change on a multi-billion dollar market dominated by five major players? Here, the scheme's founder, Robert-Jan Smits, makes a compelling case for Open Access, and reveals for the first time how he set about turning his controversial plan into reality - as well as some of the challenges faced along the way. In telling his story, Smits argues that the Covid-19 crisis has exposed the traditional academic publishing system as unsustainable.Galina Limorenko is a doctoral candidate in Neuroscience with a focus on biochemistry and molecular biology of neurodegenerative diseases at EPFL in Switzerland. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

What is mathematical music? In Mathematical Music from Antiquity to AI (Routledge, 2022), musicologist Nikita Braguinski discusses how mathematics has historically been used to make music, how it continues to influence musical composition, and the ways in which it may influence music in the future, including through artificial intelligence (AI). From pre-historic sounds to Gregorian chant to jazz to rock and beyond, from Mozart to M.C. Hammer, from the definition of an interval to time signatures to what gives human music its “soul,” Braguinski, a 2019-2020 Harvard University Music Department fellow, takes us on a fascinating journey.David Hamilton Golland is professor of history and immediate past president of the faculty senate at Governors State University in Chicago's southland. @DHGolland. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Games are an established aide in pre-college mathematics education. Meanwhile, innumerable popular books have investigated the mathematics of games. In a new edited volume for the AMS/MAA Classroom Resource Materials Series, topologist and NSF educational program director Mindy Capaldi and contributors join advanced topics with innovative lesson designs in possibly the first book of game-based mathematics education for college curricula. Teaching Mathematics Through Games (MAA Press, 2020) comprises lesson material for the full breadth of coursework taken by math students involving just as diverse and often surprising a breadth of games.I've become interested in how edited collections come about, especially in mathematics, so i took some time at the start to ask Dr. Capaldi about the conception and production of this project. We then discussed a selection of six of the book's seventeen chapters that offer a sense of its scope and a taste of its value. To touch briefly on some chapters we did not discuss: Christine Latulippe use the combinatorial format of Sudoku and dates in the history of mathematics to practice converting between numeration systems; and Jacob Heidenreich adapts the game play of Battleship to hone students' understanding of properties of functions.In addition to a detailed description of game play and how it ties in to the topic, each chapter contains exercises, problems, or activities that build upon the core lesson, and an online supplement provides material to support the lessons in practice. The book is designed specifically for instructors and provides rich material for an active learning curriculum, but avid and curious gamers and math geeks will also find much to enjoy.Suggested companion works: MAA Instructional Practices Guide Gathering 4 Gardner Mindy Capaldi is an Associate Professor of Mathematics and Statistics at Valparaiso University in Indiana. She completed her Ph.D. at North Carolina State University in 2010 and is currently on a leave of absence as a Program Director at the National Science Foundation.Cory Brunson is an Assistant Professor at the Laboratory for Systems Medicine at the University of Florida. His research focuses on geometric and topological approaches to the analysis of medical and healthcare data. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics