<p>thanks for the response, kryptonsa36,</p>
<p>Well, in maths, the closest thing to experimentation methods is probably conjecture & proof techniques.</p>
<p>Any way, take a look at a summer research program at: [Rose-Hulman</a> Math REU](<a href=“404 | Rose-Hulman”>404 | Rose-Hulman)
For each research topic, the institute actually requires the applicants to have the background listed in brackets (like group theory for the computational number theory research). Then, such requirement I assume, is deemed necessary by the faculty there to yield some considerable research progress.
Yes, we can argue that students can actually approach these research topics from scratch using just proof techniques and some creativity in problem solving (you can actually do this for any branch of math I assume, provided with some axioms), but that’s just reinventing the wheel. You can however, obtain similar background for the computational number theory research topic from some applied class like cryptography.</p>
<p>Maybe it’s just this school doing such background screening. I am not sure. However, what I am most curious about is, is “experimentation tool” ALL you need for performing research? OR, this is actually field dependent? In fact, every where I look online, at least for the Math REU’s, the institutes actually explicitly say the applicants should have taken some advanced maths classes in so and so.</p>
<p>Hope kryptonsa36 or any one else can comment on this.</p>
<p>thanks</p>