Re: The latest homework assignment

[Kenneth A. Ribet]

To Christian and Math 115,

I get your message, and I'm sorry that you're frustrated with the
Erdos book. I take responsibility for its choice. No student
lobbied for this book -- it was unavailable in the library and hard
to find in bookstores. Students did have objections to the two other
books, which were available online. Both are fine, but maybe not for
our particular course. (The Stein book relied too much on Math 113
material.) I liked the Erdos book for its novel approach to lots of
standard topics. I guessed (probably correctly) that most people in
the class had seen the standard proof of the fundamental theorem of
arithmetic, which relies on the Euclidean algorithm, and wanted to
present a slightly different proof. It's true that the authors
present their proof as based on geometry, but in class I translated
their proof into much more familiar algebraic language.

The Erdos proof of quadratic reciprocity is different from the proof
that's in most books. Both proofs are due to Gauss, who found around
five proofs during his life. The proof that I explained on Monday is
also a variant of one of Gauss's proofs.

I personally don't much like geometry either, but it's important not
to forget that geometry has its uses. I have every reason to believe
that you can translate the geometric proof of the irrationality of
the square root of m^2 +1 into a proof that uses 11th grade algebra
instead of 10th grade geometry.

The series in problem 7 converge like wildfire. In Math 1B, one
would say that they converge because of a comparison with a geometric
series.

The best way to study for the midterm is to look at what we've done
in class. Previous Math 115 midterms might not be all that relevant
to this course because our course is not identical to previous
versions of Math 115.

Students with questions and concerns show up to my office hours. We
go through some of the homework problems, and we discuss mathematical
issues from the lectures and reading. Usually around 6 to 10 people
show up. When it gets crowded, we sometimes move up to 1015, where
there's more room.

Best,
Ken R

[zenk...@gmail.com]

yeah it's a pretty frustrating book. for example, i'd venture to guess
that most people had to look up incommensurability...

BUT it's also a cool book. there have been just as many proofs that i
hated and re-read a dozen times before only half understanding them and
proofs that i just said "wow, that's damn clever."