<p>It sounds like you are in a perfect position to do research with a professor for a couple of years. That is a great thing because not only will you learn what it is actually like to be a mathematician but you may even get a publication or two while an undergrad which will be very helpful when applying for grad school. </p>
<p>Normally I would say research experience is the one thing you absolutely need to have to get into grad school, but I guess this thread brings up a good point. An undergrad degree is the one you absolutely need to get into grad school. </p>
<p>Don’t feel like you are going to be wasting the next three years. Even if you could get accepted into grad school now there is no way you would survive with no prior research experience, and only one year of college experience.</p>