<p>I'm also applying to some PhD math programs in December, I'm an undergrad at Georgia Tech. This is the information I've gathered from talking to people. </p>
<p>First to answer your questions...</p>
<p>1) Math grades are first and foremost important. That is what they will look at, while your other grades could play a part high grades in math classes will be key.</p>
<p>2) I doubt they'll care about their age in fact I don't think they can even use it as a factor. What a lot of schools do look for is promise that you can finish the program, but that shouldn't have anything to do with your age.</p>
<p>3) Definately try and find some research, talk to professors and advisors, they will be able to find some. In the US we have REU programs (Research Experience for Undegraduates) that are funded by the National Science Foundation that a lot of colleges offer over the summer. Just talk to profs who are doing things you like and they will be able to help. Research is not required but know that many of the students you'll be competing for space for will have done some. The schools want to know that you have an idea of what resarch is about and are capable of doing it, that in mind you dont NEED to advance mankind or anything, but it can't hurt. Math research is not particuarly easy and schools know that it takes a good deal of education to be sucessful in it.</p>
<p>As far as 'safer' schools I'd say the best place to find ideas is the American Mathematical Society website, <a href="http://www.ams.org%5B/url%5D">www.ams.org</a>, particuarly <a href="http://www.ams.org/employment/groups_des.html%5B/url%5D">http://www.ams.org/employment/groups_des.html</a></p>
<p>The AMS groups math programs (group I, II, III) rather than rank them. They are, as many ranking are not quite perfect but they will be a good guide. There are plenty of group I and II schools there which offer great programs.</p>
<p>Also apply for fellowships, you can also find information about those on the AMS website but also talk to your advisor. Often if you can show a school that you already have funding to go its a ticket in.</p>
<p>Also take the GRE and GRE Subject test for Math.</p>
<p>Good luck. What schools are you looking at?</p>