<p>What are important criteria in judging the quality of undergraduate mathematics? I don't trust rankings much because 1) there are next to zero actual undergraduate rankings and 2) ranking methodology itself is extremely questionable. What are some things to look for (e.g. faculty, availability of undergrad research opportunities, etc.) in choosing an ideal college/university for pure mathematics?</p>
<p>Hmm interesting question.</p>
<p>Here’s a list my son came up with when emailing math departments when he was looking for colleges:</p>
<p>*MUST HAVES:</p>
<pre><code>Program available with an emphasis on pure math and proof based math over applied math
Meaningful honors math courses (proof based or more depth of subject)
Availability of graduate level courses as an undergrad
Lots of interaction with other students who love math, and interaction with faculty
Good support for applying to summer REU’s and grad schools.
Affordable
</code></pre>
<p>PREFERRED:</p>
<pre><code>TA positions available from sophomore year forward
Active math club, speaker’s series, annual math conference, etc
Active problem solving and contest math groups, teams, clubs, etc*
</code></pre>
<p>I agree with PinotNoir, but do consider departments which have also a healthy component of applied math along with the pure stuff. There are plenty of proofs to deal with on the applied side of things, and real-life problems that come with tough to crack theoretical issues. Departments that completely neglect either the pure or applied aspects of maths are missing the boat, either proving useless theorems or just crunching numbers for other people. If the pure math program has no applied requirement or vice versa, it’s not a good sign.</p>