A somewhat similar issue comes up with the way Mazur uses the term "imaginary part" in his book "Imagining Numbers". The discrepancy between his use of the term and the way many high school students are taught to use the term led one reviewer to proclaim on Amazon as follows: "I regret that I cannot recommend this book for general enlightenment. Neither can I see how anyone reviewing this book can honestly call it lucid and well-written. Professor Mazur begins by saying that he will help explain the square root of minus 1, sqrt(-1) in a clear manner accessible to non-mathematicians. However, his text rambles all over the place. In 228 pages he manages to quote no less than 182 references. I suspect that he is trying to impress the world of academia as much as he is trying to explain imaginary or complex numbers to non-mathematicians. His writing style is pedantic. He manages to sprinkle Latin, German, Italian and French quotes from original sources such as Cardin, Bombelli and Ferrari like sand grains on the beach. At the end of Chapter 9, Section 52, he spends an entire page and one-half saying that a mathematician friend read the text and told him it digressed too much. Quite appropriately he entitled this section "Telling a Straight Story." So much for heeding one's friend's advice! Many things are irritating about this book. I'll mention two. First, he does not use the general form for the quadratic equation. He drops the "a" constant. This gives the non-mathematician a false impression of the actual parameters of the equation. *Second, he mistakenly states that the imaginary part of a complex number is "bi." Any mathematics text will tell you that it is only the "b" that constitutes the imaginary part of a complex number, not "b" and "i" taken together.* Enough said. Don't spend your money, either hard-earned or largesse, on this book. Many books explain both imaginary and complex numbers better than this one. Try Churchill's text, for one. I could say more, but need I? Caveat Emptor!!" I've highlighted the relevant passage from the guy's review (I say "guy" because, although the reviewer doesn't give a first name from which gender could be deduced, more men than women write this sort of bombastic prose). And, much as I resent the guy's tone and general ignorance, I have to admit that on this point, I can sort of see where he's coming from. Various books and teachers have told him that the imaginary part of a+bi is b, so when an author uses the phrase "imaginary part" in a different way, all this guy can think is that the author doesn't know what he's talking about. I don't think there's much hope for "saving" that guy's "soul", but I'm worried about the people who read his review and believe him. And this particular misunderstanding could have been avoided by a more sensitive understanding of the differences between the K-through-12 and 13-through-infinity ways of talking about math, and a little bit of outreach/translation embedded in the text. Some would say that there'll always be bozos, and that you can't anticipate every way in which you'll be misunderstood by bozos. Maybe I'll feel that way once I've actually done some writing aimed at math-interested high school students. (Though I plan to show all such writings to some high school math teachers I know; I expect they'll notice subtle ways in which I misjudge my audience.) Jim Propp On Sat, Feb 28, 2015 at 5:13 PM, Eugene Salamin via math-fun < math-fun@mailman.xmission.com> wrote:
Mazur and Stein handle this by writing "log" for natural logarithm. The number e and the exponential and logarithmic functions are defined in the text. Teachers insist on all kinds of stupid things, and there's no need to take up space dealing with them. For example, in the Santa Cruz Public Schools, 1 is prime, though one teacher did point out that mathematicians say otherwise. -- Gene
From: James Propp <jamespropp@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Sent: Saturday, February 28, 2015 1:56 PM Subject: Re: [math-fun] Fwd: New book: Prime Numbers and the Riemann Hypothesis
Given that they're writing for high school students (among others), I would hope that they mention (at least in a footnote) that they, like most researchers, write "log" where high school teachers would insist upon "ln".
Can someone who's read the book comment on how Mazur and Stein handle this?
Jim
On Friday, February 27, 2015, meekerdb <meekerdb@verizon.net> wrote:
On 2/26/2015 9:06 PM, James Buddenhagen wrote:
On p. 48, last line, first paragraph of Mazur/Stein book, shouldn't it be Li(X) = integral 2 to X of (1/log(t)) dt, rather than what is written?
I think you're right - I passed on your comment to Stein.
Brent
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