New Books in Mathematics

Doing mathematics can be stimulating, deep, and sometimes fantastic. It can also be frustrating, impenetrable, and at times dispiriting. In her new collection of essays, writer and mathematician Susan D'Agostino shows how math itself can be a useful guide through these experiences. How to Free Your Inner Mathematician: Notes on Mathematics and Life (Oxford University Press) draws upon the theorems, applications, and history of mathematics to inspire lessons and advice for us along our mathematical (and other) pursuits.While the math, some familiar and some less so, has clear scientific significance, the lessons help us also appreciate its humanistic value. Delightful illustrations and an (honestly) enjoyable exercise accompany each essay, and readers can jump around the text however they please.This book will appeal to aspiring mathematicians at any career stage, but its most important audience may be the latent mathematicians who have been discouraged from the discipline but are open to a fresh invitation.Susan D'Agostino is a mathematician and writer whose essays have been published in Quanta Magazine, Scientific American, Financial Times, Nature, Undark, Times Higher Education, Chronicle of Higher Education, Math Horizons, Mathematics Teacher, and others.Cory Brunson (he/him) is a Research Assistant Professor at the Laboratory for Systems Medicine at the University of Florida. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

The book being discussed is Mathematics Entertainment for the Millions (World Scientific Publishing Co.), by Alfred Posamentier. In reading this book, it occurred to me that it might equally well have been entitled Millions of Mathematical Entertainments.There may not be millions of entertainments, but there’s an incredible amount – most of it easily accessible to a middle-school or high-school student, and that’s exactly the audience that we want to show how enticing mathematics can be.  Anyone who loves mathematics will find a number of old favorites in this book, but almost certainly there’s a lot of cool stuff you’ve never seen before.  I’ve been looking at math for more than seven decades, and there’s a lot of cool stuff I’d never seen.Alfred S Posamentier is currently Distinguished Lecturer at New York City College of Technology of the City University of New York. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Calculus Reordered: A History of the Big Ideas (Princeton UP, 2019) takes readers on a remarkable journey through hundreds of years to tell the story of how calculus evolved into the subject we know today. David Bressoud explains why calculus is credited to seventeenth-century figures Isaac Newton and Gottfried Leibniz, and how its current structure is based on developments that arose in the nineteenth century. Bressoud argues that a pedagogy informed by the historical development of calculus represents a sounder way for students to learn this fascinating area of mathematics.Delving into calculus’s birth in the Hellenistic Eastern Mediterranean—particularly in Syracuse, Sicily and Alexandria, Egypt—as well as India and the Islamic Middle East, Bressoud considers how calculus developed in response to essential questions emerging from engineering and astronomy. He looks at how Newton and Leibniz built their work on a flurry of activity that occurred throughout Europe, and how Italian philosophers such as Galileo Galilei played a particularly important role. In describing calculus’s evolution, Bressoud reveals problems with the standard ordering of its curriculum: limits, differentiation, integration, and series. He contends that the historical order—integration as accumulation, then differentiation as ratios of change, series as sequences of partial sums, and finally limits as they arise from the algebra of inequalities—makes more sense in the classroom environment.Exploring the motivations behind calculus’s discovery, Calculus Reordered highlights how this essential tool of mathematics came to be.David M. Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College and Director of the Conference Board of the Mathematical Sciences. His many books include Second Year Calculus and A Radical Approach to Lebesgue’s Theory of Integration. He lives in St. Paul, Minnesota.Mark Molloy is the reviews editor at MAKE: A Literary Magazine. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

There are very few math books that merit the adjective ‘charming’ but Mage Merlin's Unsolved Mathematical Mysteries (MIT Press, 2020) is one of them. Satyan Devadoss and Matt Harvey have chosen a truly unique, creative and charming way to acquaint readers with some of the unsolved problems of mathematics. Some are classic, such as the Goldbach Conjecture, some are fairly well known, such as the Collatz Conjecture. Others are less well known but no less fascinating – and all are intriguing and both enjoyable and tantalizing to contemplate. The authors have woven the problems into a coherent story, and I think you’ll enjoy hearing – and reading – both the story and the associated problems. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

The branch of mathematics called game theory – the Prisoners Dilemma is a particularly well-known example of a game – is used by philosophers, social scientists, and others to explore many types of social relations between humans and between nonhuman creatures.In Games in the Philosophy of Biology (Cambridge University Press, 2020), Cailin O’Connor introduces the basics of game theory and its particular branch, evolutionary game theory, and discusses how game theoretic models have helped explain the genesis of the meanings of linguistic and nonlinguistic signals, altruistic behavior, the spread of misinformation, and the origins of fair and unfair distributions of benefits in society.O’Connor, who is associate professor of logic and philosophy of science at the University of California–Irvine, also considers some of the drawbacks of game theoretic models. Her short introduction makes a major area of social scientific investigation accessible to readers without mathematical background.  Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Category theory is well-known for abstraction—concepts and tools from diverse fields being recognized as specific cases of more foundational structures—though the field has always been driven and shaped by the needs of applications. Moreover, category theory is rarely introduced even to undergraduate math majors, despite its unifying role in theory and its flexibility in application.Postdoctoral Associate Brendan Fong and Research Scientist David I. Spivak, both at MIT, have written a marvelous and timely new textbook that, as its title suggests, invites readers of all backgrounds to explore what it means to take a compositional approach and how it might serve their needs.An Invitation to Applied Category Theory: Seven Sketches in Compositionality (Cambridge University Press, 2019) has few mathematical prerequisites and is designed in part as a gateway to a wide range of more specialized fields. It also centers its treatment on applications, motivating several key developments in terms of real-world use cases.In this interview we discussed their views on the promise of category theory inside and outside mathematics, their motivations for writing this book, several of the accessible examples and remarkable payoffs included in its chapters, and their aspirations for the future of the field.Suggested companion works:--Tai-Danae Bradley, Math3ma--Eugenia Cheng, The Catsters--Saunders Mac Lane, Mathematics Form and Function--F. William Lawvere & Stephen H. Schanuel, Conceptual Mathematics: A First Introduction to Categories--Eugenia Cheng, x + y: A Mathematician's Manifesto for Rethinking GenderCory Brunson (he/him) is a Research Assistant Professor in the Laboratory for Systems Medicine at the University of Florida. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

For decades, statisticians, social scientists, psychologists, and economists (among them Nobel Prize winners) have spent massive amounts of precious time thinking about whether streaks actually exist.After all, a substantial number of decisions that we make in our everyday lives are quietly rooted in this one question: If something happened before, will it happen again? Is there such a thing as being in the zone? Can someone have a “hot hand”? Or is it simply a case of seeing patterns in randomness? Or, if streaks are possible, where can they be found?In The Hot Hand: The Mystery and Science of Streaks (Custom House, 2020), Wall Street Journal reporter Ben Cohen offers an unfailingly entertaining and provocative investigation into these questions.He begins with how a $35,000 fine and a wild night in New York revived a debate about the existence of streaks that was several generations in the making. We learn how the ability to recognize and then bet against streaks turned a business school dropout named David Booth into a billionaire, and how the subconscious nature of streak-related bias can make the difference between life and death for asylum seekers. We see how previously unrecognized streaks hidden amidst archival data helped solve one of the most haunting mysteries of the twentieth century, the disappearance of Raoul Wallenberg.Cohen also exposes how streak-related incentives can be manipulated, from the five-syllable word that helped break arcade profit records to an arc of black paint that allowed Stephen Curry to transform from future junior high coach into the greatest three-point shooter in NBA history.Crucially, Cohen also explores why false recognition of nonexistent streaks can have cataclysmic results, particularly if you are a sugar beet farmer or the sort of gambler who likes to switch to black on the ninth spin of the roulette wheel.Paul Knepper was born and raised in New York and currently resides in Austin. He used to cover basketball for Bleacher Report and his first book titled Knicks of the Nineties: Ewing, Oakley, Starks and the Brawlers Who Almost Won It All is due out this year. You can reach Paul at paulknepper@gmail.com and follow him on Twitter @paulieknep. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Brian Greene is a Professor of Mathematics and Physics at Columbia University in the City of New York, where he is the Director of the Institute for Strings, Cosmology, and Astroparticle Physics, and co-founder and chair of the World Science Festival. He is well known for his TV mini-series about string theory and the nature of reality, including the Elegant Universe, which tied in with his best-selling 2000 book of the same name. In this episode, we talk about his latest popular book Until the End of Time: Mind, Matter, and Our Search for Meaning in an Evolving Universe (Random House, 2020)Until the End of Time gives the reader a theory of everything, both in the sense of a “state of the academic union”, covering cosmology and evolution, consciousness and computation, and art and religion, and in the sense of showing us a way to apprehend the often existentially challenging subject matter. Greene uses evocative autobiographical vignettes in the book to personalize his famously lucid and accessible explanations, and we discuss these episodes further in the interview. Greene also reiterates his arguments for embedding a form of spiritual reverie within the multiple naturalistic descriptions of reality that different areas of human knowledge have so far produced.John Weston is a University Teacher of English in the Language Centre at Aalto University, Finland. His research focuses on academic communication. He can be reached at john.weston@aalto.fi and @johnwphd. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Introductory courses in discrete mathematics cover a variety of distinctive but interconnected topics, from the underpinnings of logic and set theory through overviews of combinatorics and graph theory, which lend themselves to equally diverse presentation styles. In Discrete Mathematics with Ducks (Second Edition; CRC Press, 2018), dr. sarah-marie belcastro has reimagined both course and text. The book is written in an accessible and lighthearted style yet covers the full breadth of conventional topics and several more besides: Early chapters include much valuable advice on how to read, do, and write mathematics—essential points of reference for the mathematically inexperienced or disinclined. Meanwhile, the book includes an introductory chapter on algorithms and several bonus chapters, for example on number theory and on complexity, which instructors and interested students can subset as they please. Each chapter is arranged to support a week of gentle prep reading and discovery-based classroom activity. This makes the book a solid resource for active learning in the mathematics curriculum as well as for independent and group study.Suggested companion work: Daniel Pinkwater, Ducks!Cory Brunson (he/him) is a Postdoctoral Fellow at the Center for Quantitative Medicine at UConn Health. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Slavery and the University: Histories and Legacies (University of Georgia Press, 2019), edited by Leslie M. Harris, James T. Campbell, and Alfred L. Brophy, is the first edited collection of scholarly essays devoted solely to the histories and legacies of this subject on North American campuses and in their Atlantic contexts. Gathering together contributions from scholars, activists, and administrators, the volume combines two broad bodies of work: (1) historically based interdisciplinary research on the presence of slavery at higher education institutions in terms of the development of proslavery and antislavery thought and the use of slave labor; and (2) analysis on the ways in which the legacies of slavery in institutions of higher education continued in the post–Civil War era to the present day.The collection features broadly themed essays on issues of religion, economy, and the regional slave trade of the Caribbean. It also includes case studies of slavery’s influence on specific institutions, such as Princeton University, Harvard University, Oberlin College, Emory University, and the University of Alabama. Though the roots of Slavery and the University stem from a 2011 conference at Emory University, the collection extends outward to incorporate recent findings. As such, it offers a roadmap to one of the most exciting developments in the field of U.S. slavery studies and to ways of thinking about racial diversity in the history and current practices of higher education.Today I spoke with Leslie Harris about the book. Dr. Harris is a professor of history at Northwestern University. She is the coeditor, with Ira Berlin, of Slavery in New York and the coeditor, with Daina Ramey Berry, of Slavery and Freedom in Savannah (Georgia).Adam McNeil is a History PhD student at Rutgers University-New Brunswick. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics