<p>After looking around suggestions for admission into math Ph.D programs, I noticed there was some heavy emphasis on taking the Putnam exam as a means of distinguishing yourself. Is this actually important? It seems that it would be something that could help one's prospects should one do well, but it's hardly expected or necessary.</p>
<p>For some perspective, I'm a rising senior at a decent institution, have ~3.95 GPA, A's in graduate courses, and two summers of research experience*. I'm not looking to apply to "Top 5" schools; the "most prestigious" is possibly the University of Wisconsin-Madison.</p>
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<li>On a related note, one of these summers was spent doing experimental physics, back when I still wanted to go in to the area. I did quite well there, winning a "Best Project" award. Will this be considered as a positive indication of the ability to work hard on a project, or as an irrelevant, unrelated summer job?</li>
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