New Books in Mathematics

The Price is Right is television's longest-running game show. Since its inception in 1956, contestants have won cars, tropical vacations, diamond jewelry, even a live horse, and the hosts' excited catchphrase "come on down!" has become part of our everyday vernacular. Part of the program's enduring appeal is the apparent ease of the game, guessing the cash value of certain prizes. But, if that's the case, then why do so many contestants come away from the show empty-handed? Solving The Price is Right (Prometheus Books, 2023) is an in-depth exploration of the underlying probability theory of the popular television program that explores how biases and behavioral pitfalls limit our ability to successfully apply logic and math both on and off the show. With rigorous data and analysis compiled from Seasons 47 and 48 (356 total episodes), investor and math practitioner Justin L. Bergner draws strategic and mathematical insights from all facets of the show, from Contestant's Row bidding to the Showcase Showdown, and all 77 Pricing Games, using a combination of game theory, probability theory, statistics, and pattern recognition. In each section, Bergner summarizes contestant performance, highlights the biases leading to sub-par outcomes, and shows how outcomes can be improved by executing the right strategies while avoiding cognitive biases. Throughout, Bergner applies the lessons learned to the fields of business, finance, and our real lives, shedding light on themes of reverse psychology, strategic patience, and the importance of establishing what is sufficient for success in our pursuits. The result is a truly unique and meticulously researched book that uses Solving The Price is Right as a lens to examine our own choices - and how to make better ones. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

African-Americans and women are increasingly visible in professional mathematical institutions, organizations, and literature, expanding our mental models of the mathematics community. Yet early representation also matters: We begin building these models as soon as we begin seeing and doing mathematics, and they can be slow to adapt. In her wonderful activity book Women Who Count: Honoring African American Women Mathematicians (MAA Press, 2019), Dr. Shelly Jones invites children, and their parents and educators, to immerse themselves in the lives and deeds of Black women mathematicians.The 29 profiles trace back to "the Firsts" in their fields, such as early PhD awardee Evelyn Boyd Granville; the "Pioneers" of emerging fields and programs, including ethnomathematics co-founder Gloria Gilmer; through "Unhidden Figures" like Dorothy Johnson Vaughan of recent biopic fame; and to "Contemporary Firsts" who are living, working, and opening new doors today. Along with their mathematical contributions, Dr. Jones shares details of these mathematicians' early lives, their hobbies and interests, and how they have been shaped by and in turn shaped their communities. Each mini-biography introduces a whole person whom readers new to mathematics can relate to and be inspired by.Each profile is accompanied by a pencil-and-paper activity that brings to life the some part of their story. Some are classics, including word searches and I-Spy, while others introduce readers to mathematical and educational concepts explored by their subjects—coloring tessellations, for example, or solving equations to decode messages. The text and activities are targeted to grades 3–8, and are ideal for elementary and middle school classrooms.In our conversation, Dr. Jones described how she conceived the book, assembled the stories and activities, and connected with illustrator Veronica Martins. I came away with a richer perspective on the state of the field for aspiring mathematicians—in addition to a perfect gift for my second-grade nephew.Suggested companion works: Mathematicians of the African Diaspora Mathematically Gifted and Black Mathematician Project Lathisms We are Indigenous Mathematicians Black Girl MATHgic Talitha Washington Dr. Shelly M. Jones is a Professor of Mathematics Education at Central Connecticut State University. She has been an educator for 30 years and currently teaches undergraduate mathematics content and methods courses for pre-service teachers as well as graduate level mathematics content, curriculum and STEM courses for in-service teachers. Dr. Jones serves her community by working with various professional and community organizations. You can see her CCSU TEDx talk on YouTube where she talks about culturally relevant mathematics. She is also a contributing author to The Brilliance of Black Children in Mathematics: Beyond the Numbers and Toward a New Discourse and co-author of Engaging in Culturally Relevant Math Tasks: Fostering Hope. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

On this episode of the MIT Press podcast, Thomas Lin, Editor-in-Chief of Quanta Magazine, discusses the research and current climate behind the science and math in Alice and Bob Meet the Wall of Fire: The Biggest Ideas in Science from Quanta and The Prime Number Conspiracy: The Biggest Ideas in Math from Quanta.  Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Jeffrey Carpenter and Andrea Robbett's book Game Theory and Behavior (MIT Press, 2022) is an introduction to game theory that offers not only theoretical tools but also the intuition and behavioral insights to apply these tools to real-world situations. This introductory text on game theory provides students with both the theoretical tools to analyze situations through the logic of game theory and the intuition and behavioral insights to apply these tools to real-world situations. It is unique among game theory texts in offering a clear, formal introduction to standard game theory while incorporating evidence from experimental data and introducing recent behavioral models. Students will not only learn about incentives, how to represent situations as games, and what agents “should” do in these situations, but they will also be presented with evidence that either confirms the theoretical assumptions or suggests a way in which the theory might be updated.Jeffrey Carpenter is the James Jermain Professor of Political Economy at Middlebury College. His research interests include Experimental and Behavioral Economics with applications to Labor, Public and Development Economics. While pursuing these interests he has conducted lab and field experiments in North America, South America, Europe and Asia.Andrea Robbett is an Associate Professor of Economics at Middlebury College. Her research uses laboratory experiments to test canonical theoretical models, new ideas, and conventional wisdom. Her work has addressed topics in public economics, labor, voting, information avoidance, financial decision-making and "attribute overload," trust and cooperation, and auctions.Peter Lorentzen is economics professor at the University of San Francisco. He heads USF's Applied Economics Master's program, which focuses on the digital economy. His research is mainly on China's political economy. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Seduction is not just an end result, but a process -- and in mathematics, both the end results and the process by which those end results are achieved are often charming and elegant.This helps to explain why so many people -- not just those for whom math plays a key role in their day-to-day lives -- have found mathematics so seductive. Math is unique among all subjects in that it contains end results of amazing insight and power, and lines of reasoning that are clever, charming, and elegant. James D. Stein's Seduced by Mathematics: The Enduring Fascination of Mathematics (World Scientific, 2022) is a collection of those results and lines of reasoning that make us say, 'OMG, that's just amazing, ' -- because that's what mathematics is to those who love it. In addition, some of the stories about mathematical discoveries and the people who discovered them are every bit as fascinating as the discoveries themselves.Seduced by Mathematics contains material capable of being appreciated by students in elementary school -- as well as some material that will probably be new to even the more mathematically sophisticated. Most of the book can be easily understood by those whose only math courses are algebra and geometry, and who may have missed the magic, enchantment, and wonder that is the special province of mathematics.James D. Stein is a professor emeritus of mathematics at Cal State Long Beach.Caleb Zakarin is the Assistant Editor of the New Books Network (Twitter: @caleb_zakarin). Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Innumeracy, by John Allen Paulos, was first published in 1988. In it the author brilliantly highlighted many of the sorry truths those of us who teach math and science know – not only can’t most people do algebra or geometry, they can’t estimate size, they don’t understand simple probability and statistics, and they believe in things that make no sense. In Who’s Counting? (Prometheus, 2022), Paulos investigates topics which – like Innumeracy – connect with the age in which we live.Who's Counting? features dozens of his insightful essays-original writings on contemporary issues like the COVID-19 pandemic, online conspiracy theories, "fake news," and climate change, as well as a selection of enduring columns from his popular ABC News column of the same name. With an abiding respect for reason, a penchant for puzzles with societal implications, and a disarming sense of humor, Paulos does in this collection what he's famous for: clarifies mathematical ideas for everyone and shows how they play a role in government, media, popular culture, and life. He argues that if we can't critically interpret numbers and statistics, we lose one of our most basic and reliable guides to reality. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Alfred S. Posamentier's The Secret Lives of Numbers: Numerals and Their Peculiarities in Mathematics and Beyond (Prometheus Books, 2022) is the first book I’ve ever seen written by a mathematician that will absolutely, definitely, certainly appeal to people who love numbers and who don’t love mathematics. I would urge all listeners to tell everyone they know who has a fascination with numbers to listen to this podcast, especially if they don’t love mathematics because they will definitely love this book. Hopefully the love of numbers will translate into an appreciation of mathematics -- if not for them, then for their children. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

In this episode of High Theory, Justin Joque talks with Júlia Irion Martins about Probability. This conversation is part of our High Theory in STEM series, which tackles topics in science, technology, engineering, and medicine from a highly theoretical perspective. If you want to learn more about the philosophical, technical, and economic implications of probability, check out Justin’s new book, Revolutionary Mathematics: Artificial Intelligence, Statistics, and the Logic of Capitalism (Verso, 2022).Justin Joque is a visualization librarian at the University of Michigan, Ann Arbor. Justin’s research focuses on philosophy, media, and technology and he is also the author of Deconstruction Machines: Writing in the Age of Cyberwar (University of Minnesota Press, 2018).Image: © 2022 Saronik Bosu Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

I’ve never read a book like Mathematical Tools for Real-World Applications: A Gentle Introduction for Students and Practitioners (MIT Press, 2022) – it’s a book about how engineers and scientists see math, and I found it fascinating. What intrigued me about this book was not that it just presents and solves a bunch of interesting problems, it shows how scientists and engineers differ in their approach to problem solving from mathematicians. Shame on me, but as a mathematician, I’ve always been a little uncomfortable with the way engineers and scientists use mathematics. I wish I’d seen this book when I was in college, I’d have done a lot better in my physics courses. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Performing Math: A History of Communication and Anxiety in the American Mathematics Classroom (Rutgers University Press, 2020) by Dr. Andrew Fiss tells the history of expectations for math communication—and the conversations about math hatred and math anxiety that occurred in response.Focusing on nineteenth-century American colleges, this book analyzes foundational tools and techniques of math communication: the textbooks that supported reading aloud, the burnings that mimicked pedagogical speech, the blackboards that accompanied oral presentations, the plays that proclaimed performers’ identities as math students, and the written tests that redefined “student performance.” Math communication and math anxiety went hand in hand as new rules for oral communication at the blackboard inspired student revolt and as frameworks for testing student performance inspired performance anxiety.With unusual primary sources from over a dozen educational archives, Performing Math argues for a new, performance-oriented history of American math education, one that can explain contemporary math attitudes and provide a way forward to reframing the problem of math anxiety.This interview was conducted by Dr. Miranda Melcher whose doctoral work focused on post-conflict military integration, understanding treaty negotiation and implementation in civil war contexts, with qualitative analysis of the Angolan and Mozambican civil wars. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics