New Books in Mathematics

The book discussed here is the The Joy of Mathematics (Prometheus Books, 2017), whose lead author, Alfred Posamentier, is our guest today. The subtitle Marvels, Novelties, and Neglected Gems That Are Rarely Taught in Math Classdescribes the book nicely. Much of the book can be read by someone with only a couple of years of high school math, and the book does a terrific job of showing the reader why those of us who love math do so. We like arithmetic, algebra, geometry, infinity, and the counterintuitively surprising, and the book contains lovely examples of all of these. Enjoy! Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Big Data: How the Information Revolution Is Transforming Our Lives (Icon Books, 2017), by Brian Clegg, is a relatively short book about a subject that has emerged only recently, but is rapidly becoming a significant force in the evolution of society. Most of us have heard the term “big data,” but many of us erroneously assume that its just a lot of little data. It’s considerably more than that, and Big Data, which is an easy and fun read, serves as a terrific introduction to a topic which has an ever-increasing impact on many aspects of our lives. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Brian Clegg is one of England’s most prolific and popular writers on science. His latest work, The Reality Frame: Relativity and Our Place in the Universe (Icon Books, 2017), covers Einstein’s Theories of Relativity and a whole lot more. Simply as an exposition of Einstein’s theories, the book is excellent its beautifully organized and delivered, with Clegg’s usual clarity and insight. But what makes the book transcend the usual work on this subject is that Clegg looks at relativity as a concept that can help us understand what distinguishes humanity as a species, and where our species fits into the Universe. Einstein himself would have enjoyed participating in a discussion of this fascinating topic, and may well have shared some of Clegg’s points of view. 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 here is entitled The Calculus of Happiness: How a Mathematical Approach to Life Adds Up to Health, Wealth, and Love (Princeton University Press, 2017) by Oscar Fernandez. If the thought of calculus makes you nervous, don’t worry, you won’t need calculus to enjoy and appreciate this book. Its actually an intriguing way to introduce some of the precalculus topics that will later be needed in a calculus class, through the examination of some of the basic mathematical ideas that can be used to analyze the problems of how to attain relationship bliss, live long, and prosper and all without being a Vulcan. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

For many cognitive scientists, psychologists, and philosophers of mind, the best current theory of cognition holds that thinking is in some sense computation “in some sense,” because that core idea can and has been elaborated in a number of different ways that are or at least seem to be incompatible in at least some respects. In Unifying the Mind: Cognitive Representations as Graphical Models (MIT Press, 2014), David Danks proposes a version of this basic theory that links the mind closely with the computational framework used in machine learning: the idea that thinking involves manipulation of symbols encoded as graphical models. Danks, who is Professor of Philosophy and Psychology at Carnegie Mellon University, argues that graphical models provide a unifying explanation of why we are able to move smoothly between different cognitive processes and why we are able to focus on features of situations that are relevant to our goals. While the book includes the mathematics behind graphical models, Danks explains his proposal in accessible yet precise terms for the non-mathematically trained reader. He discusses how graphical models work in causal reasoning, categorization, and other processes, how his view is related to more familiar cognitive frameworks, and some implications of his view for modularity and other traditional debates. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

If ever there were a course that needs a book like Raffi Grinberg’s The Real Analysis Lifesaver: All the Tools You Need to Understand Proofs (Princeton University Press, 20170, analysis is unquestionably it, and I only wish that Raffi had gotten into the wayback machine and delivered me a copy when I was taking this course more than half a century ago. I got a C+, and almost certainly would have done a lot better if I’d had this book, and so will present and future students who struggle with this course. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Matthew L. Jones’s wonderful new book traces a history of failed efforts to make calculating machines, from Blaise Pascal’s work in the 1640s through the efforts of Charles Babbage in the nineteenth century, incorporating an account of both the work and relationships of scholars and artisans, and their reflections on the nature of invention. Innovative in its approach and its form, Reckoning with Matter: Calculating Machines, Innovation, and Thinking about Thinking from Pascal to Babbage (University of Chicago Press, 2016) offers a thoughtful and beautifully-written history of technology that offers an important perspective on a division between two poles of writing the history of technology: “the collective, deterministic account of inventive activity and the individualistic, heroic, creative account (7).” In Jones’s hands, we are offered a third way of understanding cultural production in early modernity, one that did not bifurcate between imitation and originality, social and individual making, or design and production. Central to the story is the history of efforts to mechanize the process of carrying ones in addition, and this fascinating problem persists as a thread through many of the projects discussed in the book. On the pages of Reckoning with Matter, readers will not only enjoy a compelling account of machine calculation through the nineteenth century, but will also find the story of a frog that tears out the eyes of a fish, a man who designed machines for making breakfast, and discussions of the significance of credit and intellectual property, modern programming, sketching, imitation, and debates over the nature of thinking. Highly recommended!   Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Brian Clegg’s Are Numbers Real? The Uncanny Relationship of Mathematics and the Physical World (St. Martin’s Press, 2016) is a compact, very readable, and highly entertaining history of the development and use of mathematics to answer the important practical questions involved in advancing civilization. The question “Are Numbers Real?” is a terrific way to attack the problem so compellingly stated by the physicist Eugene Wigner what accounts for the unreasonable effectiveness of mathematics in describing the natural and the man-made Universe? Some of Clegg’s journey from the basics of counting through the intricate mathematical structures currently being used to explore reality will be familiar to the experienced reader. But even such a reader will find new insights and pleasures in the book and for those just starting out on their intellectual journey, Are Numbers Real? Is a superb introduction to mathematics, science, and that branch of philosophy devoted to exploring the nature of reality. 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 here is Ian Stewart’s Calculating the Cosmos: How Mathematics Unveils the Universe (Basic Books, 2016). If you would like to read a book that in my opinion represents the nicest job of presenting astronomy and cosmology in one volume since Isaac Asimov wrote The Universe half a century ago, this is absolutely the one to get. In addition, for those of us who are lovers of math, this book does a far better job than Asimov of presenting the close relationship between mathematics, astronomy, and cosmology. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

From the title, you might guess that Alfred Posamentier and Stephen Krulik’s Effective Techniques to Motivate Mathematics Instruction (Routledge, 2016) is aimed at mathematics teachers which it is. However, the techniques and strategies discussed in the book can be effectively employed by a much larger group of people, and one who hasconsiderably more influence with students. Those people are parents, who play as large or larger a role in their children’s education than do teachers. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics