Reviews of “Proofiness,” by Charles Seife

I recently finished reading Proofiness, written by Charles Seife, science writer and journalism professor at the Arthur L. Carter Journalism Institute at New York University, and it’s excellent. There are a number of glowing reviews out there (see Stephen Strogatz in the New York Times, John Allen Paulos in the Washington Post, Alexandra Witze in … Read more

A Question From The USSR Olympiad Problem Book; Updated With Solution

A few days ago I posted on a problem (Problem 4(a) on Page 7) from the very nice The USSR Olympiad Problem Book, by D.O. Shklarsky, N.N. Chentzov, and I.M. Yaglom: We are given 80 coins of the same denomination; we know that one of them is counterfeit and that it is lighter than the … Read more

A Question From The USSR Olympiad Problem Book

I just picked up a copy of The USSR Olympiad Problem Book, by D.O. Shklarsky, N.N. Chentzov, and I.M. Yaglom, and it looks delightful. The book’s foreword states that it is intended for high-school students, although outstanding middle-school students might also give it a go. Complete solutions are given, which are particularly detailed for the … Read more

An Amusing (And Instructive) Error I Made While Solving A Recurrence Relation

One way to specify a sequence of numbers is recursively; that is, the first one or more terms in the sequence are stated, and then a formula for the general term of the sequence is given in terms of one or more previous terms. For example, in the famous Fibonacci sequence, the first two terms … Read more

Journal of Humanistic Mathematics

The Journal of Humanistic Mathematics, a new online-only, peer-reviewed mathematics journal, is in its first issue. The Journal of Humanistic Mathematics aims to provide an open forum for both academic and informal discussions on the various threads of mathematical inquiry. The focus of submitted papers should be on the aesthetic, cultural, historical, literary, pedagogical, philosophical, … Read more

Rota On Teaching Mathematics

From Indiscrete Thoughts, by Gian-Carlo Rota: The best introduction to mathematics is not achieved by rigorous presentation. No one can learn calculus, linear algebra, or group theory by reading an axiomatic presentation. What one wishes is a feeling for a piece of mathematics. Let the student work with unrigorous concepts that lead as quickly as … Read more

How Much Mathematics Should A Student Memorize? Part 4, Geometric Series

In teaching mathematics for many years, one of the things I emphasized over and over again was that students should memorize the absolute minimum necessary, and then I did my best to make explicit what this absolute minimum is. It is better, I explained, to spend time solving problems, discussing applications, “reading around the subject,” … Read more

Words, Episode 6: “… 2000 times as small …”

I’ve been reading the very fine book Superconductivity: A Very Short Introduction, by Stephen Blundell, about which I’ll have more to say in a subsequent post. The book is very well written, with only a very few editorial infelicities in the book, the most striking of which is the following phrase, which appears on page … Read more

A Practical Use For Logarithms, Part 2: How We Multiplied Large Numbers 40 Years Ago, And How Integral Transforms Use The Same Basic Idea

(Click here for Part 1.) A common argument for the use of technology is that it frees students from doing boring, tedious calculations, and they can focus attention on more interesting and stimulating conceptual matters. This is wrong. Mastering “tedious” calculations frequently goes hand-in-hand with a deep connection with important mathematical ideas. And that is … Read more

A Practical Use For Logarithms

What can you do when you have to describe phenomena that extend over many orders of magnitude? One option is to use different units; this is what we typically do in every-day life: We use centimetres or inches to describe distances on our desks, we use feet or yards or metres to quote the dimensions … Read more