New Books in 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

Freeman Dyson (1923–2020)—renowned scientist, visionary, and iconoclast—helped invent modern physics. Not bound by disciplinary divisions, he went on to explore foundational topics in mathematics, astrophysics, and the origin of life. General readers were introduced to Dyson’s roving mind and heterodox approach in his 1979 book Disturbing the Universe, a poignant autobiographical reflection on life and science. "Well, Doc, You're In": Freeman Dyson’s Journey through the Universe (MIT Press, 2022) (the title quotes Richard Feynman’s remark to Dyson at a physics conference) offers a fresh examination of Dyson’s life and work, exploring his particular way of thinking about deep questions that range from the nature of matter to the ultimate fate of the universe. The chapters—written by leading scientists, historians, and science journalists, including some of Dyson’s colleagues—trace Dyson’s formative years, his budding interests and curiosities, and his wide-ranging work across the natural sciences, technology, and public policy. They describe Dyson’s innovations at the intersection of quantum theory and relativity, his novel nuclear reactor design (and his never-realized idea of a spacecraft powered by nuclear weapons), his years at the Institute for Advanced Study, and his foray into cosmology. In the coda, Dyson’s daughter Esther reflects on growing up in the Dyson household. “Well, Doc, You’re In” assesses Dyson’s successes, blind spots, and influence, assembling a portrait of a scientist’s outsized legacy. Contributors: Jeremy Bernstein, Robbert Dijkgraaf, Esther Dyson, George Dyson, Ann Finkbeiner, Amanda Gefter, Ashutosh Jogalekar, David Kaiser, Caleb Scharf, William Thomas.Matthew Jordan is a university instructor, funk musician, and clear writing enthusiast. He studies the history of science and technology, driven by the belief that we must understand the past in order to improve the future. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

The Story of Proof: Logic and the History of Mathematics (Princeton UP, 2022) investigates the evolution of the concept of proof--one of the most significant and defining features of mathematical thought--through critical episodes in its history. From the Pythagorean theorem to modern times, and across all major mathematical disciplines, John Stillwell demonstrates that proof is a mathematically vital concept, inspiring innovation and playing a critical role in generating knowledge.Stillwell begins with Euclid and his influence on the development of geometry and its methods of proof, followed by algebra, which began as a self-contained discipline but later came to rival geometry in its mathematical impact. In particular, the infinite processes of calculus were at first viewed as "infinitesimal algebra," and calculus became an arena for algebraic, computational proofs rather than axiomatic proofs in the style of Euclid. Stillwell proceeds to the areas of number theory, non-Euclidean geometry, topology, and logic, and peers into the deep chasm between natural number arithmetic and the real numbers. In its depths, Cantor, Gödel, Turing, and others found that the concept of proof is ultimately part of arithmetic. This startling fact imposes fundamental limits on what theorems can be proved and what problems can be solved.This book could well serve as a history of mathematics, because in developing the evolution of the concept of proof and how it has arisen in the various different mathematical fields. The author essentially traces the important milestones in the development of mathematics. It's an amazing job of collecting and categorizing many of the most important ideas in this area. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

We’ve all heard that a picture is worth a thousand words, but what if we don’t understand what we’re looking at? Social media has made charts, infographics, and diagrams ubiquitous―and easier to share than ever. We associate charts with science and reason; the flashy visuals are both appealing and persuasive. Pie charts, maps, bar and line graphs, and scatter plots (to name a few) can better inform us, revealing patterns and trends hidden behind the numbers we encounter in our lives. In short, good charts make us smarter―if we know how to read them.However, they can also lead us astray. Charts lie in a variety of ways―displaying incomplete or inaccurate data, suggesting misleading patterns, and concealing uncertainty―or are frequently misunderstood, such as the confusing cone of uncertainty maps shown on TV every hurricane season. To make matters worse, many of us are ill-equipped to interpret the visuals that politicians, journalists, advertisers, and even our employers present each day, enabling bad actors to easily manipulate them to promote their own agendas.In How Charts Lie: Getting Smarter about Visual Information (W. W. Norton, 2019), data visualization expert Alberto Cairo teaches us to not only spot the lies in deceptive visuals, but also to take advantage of good ones to understand complex stories. Public conversations are increasingly propelled by numbers, and to make sense of them we must be able to decode and use visual information. By examining contemporary examples ranging from election-result infographics to global GDP maps and box-office record charts, How Charts Lie demystifies an essential new literacy, one that will make us better equipped to navigate our data-driven world. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

In The New Era in American Mathematics, 1920-1950 (Princeton University Press, 2022) Karen Parshall explores the institutional, financial, social, and political forces that shaped and supported the American Mathematics community in the first half of the twentieth century. Drawing from extensive archival and primary-source research, Professor Parshall uncovers the key players in American mathematics who worked together to effect change. She highlights the educational, professional, philanthropic, and governmental entities that bolstered progress and uncovers the strategies implemented by American mathematicians in their quest for the advancement of knowledge. Through an examination of how the American Mathematical community asserted itself on the international state, The New Era in Mathematics, 1920-1950 shows the way one nation became the focal point for the field.Karen Hunger Parshall is the Commonwealth Professor of History and Mathematics at the University of Virginia. She is the author of James Joseph Sylvester: Jewish Mathematician in a Victorian World and the coauthor of Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century.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

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