New Books in Mathematics

Christopher J. Phillips‘ new book is a political history of the “New Math,” a collection of curriculum reform projects in the 1950s & 1960s that were partially sponsored by the NSF and involved hundreds of mathematicians, teachers, professors, administrators, parents, and students. The New Math: A Political History (University of Chicago Press, 2015) explores the formation of an idea of the “American subject” in an environment where math was considered to be a component of intelligent citizenship. As classrooms became sites shaped by Cold War politics, efforts to reform mathematics curricula were bound up in ideas of subjectivity and discipline. Phillips pays special attention to the work of the School Mathematics Study Group (SMSG) in this context, looking closely at the textbooks that the SMSG produced for children studying at a range of levels. Importantly, The New Math explores not just the production of these textbooks but also what happened when they were actually brought into American classrooms and engaged by teachers, students, and parents. As a result, in addition to being a fascinating political history it’s also a model of how we can treat the archaeology of the classroom as a way to approach the history of science. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

The book discussed in this interview is Zombies and Calculus (Princeton University Press, 2014) by Colin Adams.   This is a truly unique book; a novel written in the first-person by the survivor of a zombie apocalypse who has managed to make it that far thanks to his knowledge of calculus.  The author starts his narrative by warning the reader that the book is not for the squeamish, but you shouldn’t be deterred by that, as I found the zombies to be more comical than horrific.  The book is especially worthwhile for the way it introduces some of the really intriguing applications of calculus that are not typically found in the standard three-semester calculus sequence, and the author has done a good job of making those applications relevant to his tale.  In an era when education competes with entertainment for attention – and generally fights a losing battle – books such as Zombies and Calculus are to be applauded.  They may prevent some of those taking math courses from becoming classroom zombies. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

The book discussed in this interview is How Not To Be Wrong: The Power of Mathematical Thinking (Penguin Press, 2014), by Jordan Ellenberg.  This is one of those rare books that belong on the reading list of every educated person, especially those who love mathematics, but more importantly, those who hate it.  Ellenberg succeeds in explaining the value of mathematical reasoning without ever needing to go into technical detail, which makes the book ideal for those who want to learn why mathematics is so important.  What makes the book doubly delightful is Ellenberg’s writing style; he intersperses the math with amusing anecdotes, dispensed with a sense of humor rarely found in books such as this.  The book is chock-full of OMG moments; the introductory anecdote about Abraham Wald and the missing bullet holes absolutely whets the appetite for more and Ellenberg never fails to deliver. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

[Re-published with permission from Inspired by Math] Sue VanHattum is a math professor, blogger, mother, author/editor, and fundraiser. She’s a real powerhouse of motivation for making math fun and accessible to more of our young folks. Sue has teamed up with a number of writers to compile a book, Playing With Math, which she is producing in partnership withMaria Droujkova in a community sponsored publication model. Sue and I shared a delightful chat about what math is, what the book is about, and how we can all get more inspired to engage in math with our kids. And, Sue sprinkles the conversation with some interesting open-ended math problems. Think part coffee table conversation part math circle. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

[Re-published with permission from Inspired by Math] The MAA (Mathematical Association of America) sent me a review copy of their new book Learning Modern Algebra: From Early Attempts to Prove Fermat’s Last Theorem. I don’t typically review textbooks but the title and then the contents of the book convinced me that I needed to interview the authors. Joe Rotman wasn’t available but I was able to chat with the other co-author, Al Cuoco. I was really struck with Al’s passion about teaching the teachers as well as the students. Al shared some great insights about the ingredients that I think should go into every math textbook to help teachers and students to develop the right habits of mind to succeed. Here are some of the questions we discussed. 1. What is your background and your experience teaching high school math to students and to teachers? 2. I attended the Ross program and you have a key role in a program that has its roots in the Ross program. Tell me about this program and your involvement with it. 3. There’s something special about number theory and algebra that makes it accessible to bright students without a deep background in math. What do you think of that thought? 4. What is “Learning Modern Algebra” about and who is the audience? 5. How does Fermat’s Last Theorem unite the book’s chapters? 6. What are the challenges with how Modern Algebra is taught? 7. Why is exploration so important and how do you promote it? 8. Rigorous thinking about open-ended problems runs through the book. PODASIP (prove or disprove and salvage if possible) problems contribute to this. Can you speak to that? 9. Why is historical setting important in learning math and how do you weave history into the book? 10. Tell us about the importance of the “Connections” sections in the book. 11. Is there a next book or project? 12. The question I ask everyone: “What advice would you give to a parent whose child was struggling with math?” Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

[Re-posted with permission from Sol Lederman’s Wild About Math] I love novel ways of looking at arithmetic. I’m fascinated with how computers compute in binary, with tricks for simplifying calculations and with how Vedic mathematicians handle difficult arithmetic efficiently. So, when Princeton University Press sent me a review copy of their new book Count Like an Egyptian: A Hands-on Introduction to Ancient Mathematics (Princeton University Press, 2014), I immediately fell in love with it. I was delighted to learn even more techniques and the ideas behind them to deepen my appreciation of the beauty of what most consider to be mundane arithmetic. Count Like an Egyptian is a delightful book, full of color illustrations, fun stories, lots of hands-on exercises, and an appreciation for the power of simple but deep ideas. David Reimer was a pleasure to interview. He is a brilliant mathematician who hasn’t lost sight of the power and beauty of mathematics. He taught me and modeled that, despite the stereotype, the more advanced mathematicians are the ones who are more likely to communicate ideas well. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

A conceptual space sounds like a rather nebulous thing, and basing a semantics on conceptual spaces sounds similarly nebulous. In The Geometry of Meaning: Semantics Based on Conceptual Spaces (MIT Press, 2014), Peter Gardenfors demonstrates that this need not be the case. Indeed, his research is directed towards establishing a formal, mathematically-grounded account of semantics, an account which – as expounded here – is nevertheless accessible. In this interview we discuss the essence of this proposal, focusing in particular on its implications for linguistic analysis, but also touching upon its relation to cognitive science and other related fields. The proposal makes testable predictions about the organization of individual linguistic systems, as well as their acquisition (and potentially their evolution over time). Notably, the “single domain constraint” posits that individual lexical items refer to convex regions of single domains. We discuss the significance of this idea as a bridge between linguistics and cognitive science, what would constitute its falsification, and how it can usefully be investigated from a linguistic standpoint. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

The book discussed in this interview is Everyday Calculus: Discovering the Hidden Math All around Us (Princeton University Press, 2014) by Oscar E. Fernandez, who teaches mathematics – and calculus in particular – at Wellesley College.  While it can be read by someone who wants to obtain a sense of what calculus is and how it’s used, it is even more enjoyable and enlightening if the reader has taken the first semester of a calculus course.  The author takes the reader through a day in the author’s life, during which things one typically encounters – stock price quotations, cooling cups of coffee, getting good seats at a movie – afford an opportunity to investigate how calculus explains these everyday occurrences.  Fernandez also introduces some instances where calculus has totally unexpected applications to our lives – why our GPS system relies upon Einstein’s Theory of Relativity, and why we obtain electricity via alternating current rather than direct current.  Everyday Calculus should not only add to the appreciation of calculus by those who have studied the subject, the book will hopefully persuade readers unfamiliar with calculus to take a course in it. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

When we’re faced with a choice between Door #1, Door #2, and Door #3, how do we infer correctly that there’s an equal chance of the prize being behind any of the doors? How is it that we are generally correct to choose the shorter of two checkout lines in the supermarket when we’re in a hurry? In his new book, Tychomancy: Inferring Probability from Causal Structure (Harvard University Press, 2013), Michael Strevens – professor of philosophy at New York University, argues that we are all equipped with a reliable, probable innate, and not fully conscious skill at probabilistic reasoning—a “physical intuition” that enables us to infer physical probabilities from perceived symmetries. This skill is found in six-month-old infants watching as red and white balls are removed in different proportions from an urn. But it also underlies important advances in the sciences, such as James Clerk Maxwell’s reasoning when he hit upon the correct distribution of velocities of a moving particle in a gas. In this intriguing essay on a very special type of cognitive capacity, Strevens’ defends controversial claims about the rules guiding our reasoning about physical probability, its probable innateness, and its role in science as well as in everyday judgment. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

[Re-posted with permission from Wild About Math] My favorite kind of math challenges are those that children can understand and professional mathematicians can’t solve easily (or at all.) Math Bytes: Google Bombs, Chocolate-Covered Pi, and Other Cool Bits in Computing (Princeton University Press, 2014) is a brand new book from Princeton University Press that has a great collection of fun problems that kids (middle school and above) and their parents can work on together. Author Tim Chartier does a fantastic job of weaving some wonderful stories into his sharing of a number of challenges that are either original or new spins on old problems. And, many (all?) of the puzzles in the book are classroom tested. Tim is a mathematician and a professional mime. He’s got a neat relationship with the Mathematical Association of America, and with the Museum of Mathematics in New York City. He’s got a DVD course coming out, and a second book. Tim is quite the math celebrity and a really great guy. I think you’ll all enjoy the many topics we manage to touch on in just over an hour. Oh, and if you didn’t win a billion dollars in Warren Buffett’s March Madness challenge then you might want to listen to the podcast and read the book. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics