New Books in Mathematics

By Marshall PoeScience Natural Sciences

New Books in Mathematics episodes

June 20, 2014 Al Cuoco and Joe Rotman, “Learning Modern Algebra: From Early Attempts to Prove Fermat’s Last Theorem” (MAA, 2013)
[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?”
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1 hr 14 min
June 09, 2014 David Reimer, “Count Like an Egyptian: A Hands-on Introduction to Ancient Mathematics” (Princeton UP, 2014)
[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.
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1 hr 17 min
June 09, 2014 Peter Gardenfors, “The Geometry of Meaning: Semantics Based on Conceptual Spaces” (MIT Press, 2014)
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.
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43 min
April 17, 2014 Oscar E. Fernandez, “Everyday Calculus: Discovering the Hidden Math All around Us (Princeton UP, 2014)
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.
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52 min
April 15, 2014 Michael Strevens, “Tychomancy: Inferring Probability from Causal Structure” (Harvard UP, 2013)
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.
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1 hr
April 08, 2014 Tim Chartier, “Math Bytes: Google Bombs, Chocolate-Covered Pi, and Other Cool Bits in Computing” (Princeton UP, 2014)
[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.
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1 hr 12 min
February 14, 2014 Chuck Adler, “Wizards, Aliens, and Starships: Physics and Math in Fantasy and Science Fiction” (Princeton UP, 2014)
[Re-posted with permission from Wild About Math]
I’ve admitted before that Physics and I have never gotten along. But, science fiction is something I enjoy. So, when Princeton University Press sent me a copy of Physics Professor Chuck Adler‘s new book Wizards, Aliens, and Starships: Physics and Math in Fantasy and Science Fiction (Princeton University Press, 2014), I was intrigued enough that I wanted to interview the author. This interview rambled, but in a good way. Chuck is a great guest, he’s passionate about physics and math as well as fantasy and science fiction. We flowed through a number of subjects and had a grand time.
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1 hr 35 min
February 11, 2014 Eli Maor and Eugen Jost, “Beautiful Geometry” (Princeton UP, 2014)
Beautiful Geometry (Princeton UP, 2014), by the mathematician prof. Eli Maor and the noted artist Eugen Jost. It’s a fascinating collaboration which helps to bridge the gap deplored by C. P. Snow in his classic The Two Cultures. If you’re a lover of geometry, you’ll find some of your favorites depicted here – as well as a number of theorems that will undoubtedly be new to many readers (including the interviewer). Each result is accompanied by an original work of art by Eugen Jost. It’s fascinating not only to read about some of the more piquant results in a field (geometry) that is more than 2,500 years old, but just as delightful to see how these results inspire the creativity of an artist. If you come for the geometry, you’ll certainly stay for the artwork – and if your interest is in art, you’ll be intrigued by how a presumably dry subject such as geometrical theorems can give birth to works of exquisite beauty.
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50 min
November 08, 2013 Edward Frenkel, “Love and Math: The Heart of Hidden Reality” (Basic Books, 2013)
The book discussed in this interview is Love and Math: The Heart of Hidden Reality Basic Books, 2013) by Edward Frenkel of the University of California at Berkeley.It’s a toss-up which is more interesting – the description of Frenkel’s life or his description of his interest in – and love for – mathematics and physics. Before he was twenty years old, Frenkel had written a paper that a visiting Swedish physicist thought so intriguing that he smuggled it out of Russia.That paper started Frenkel on a career which resulted in his collaborating with some of the world’s foremost mathematicians and physicists – and to his writing Love and Math. It’s a fascinating read.
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56 min
September 26, 2013 Colm Mulcahy, “Mathematical Card Magic: Fifty-Two New Effects” (A K Peters, 2013)
[Re-posted with permission from Wild About Math] I had the pleasure of interviewing mathematician and mathematical card magic innovator Colm Mulcahy. Dr. Mulcahy just published a book, Mathematical Card Magic: Fifty-Two New Effects (A K Peters, 2013)
We spent a delightful hour discussing his book, his love of math and magic, and the inspiration behind writing the book. Plus, Dr. Mulcahy shares a few challenges listeners might enjoy chewing on, sprinkled throughout the interview. And, we discuss Martin Gardner, who Colm Mulcahy knew for the last decade of his life and met with several times.
You may also enjoy Shecky’s text interview with Colm Mulcahy at Math Tango.

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1 hr 15 min

About New Books in Mathematics

From the publisher's feed

This podcast is a channel on the New Books Network. The New Books Network is an academic audio library dedicated to public education. In each episode you will hear scholars discuss their recently published research with another expert in their field.