Issue regarding Schengen visa

Yes, you should -- as a matter of principle -- be as complete as possible about your travel plans when you apply for a visa. Not doing so is strictly speaking fraud and, if found out, can have much more serious consequences than the information you're concealing would have.

There is essentially no risk that a few days of side trip on the way to or from your summer school would cause a visa application to be rejected if it would otherwise have been approved. About the only way I can see that happen is if you can't show that you can afford to support yourself for those three extra days.

Remember that what the consular officers will ask themselves is not, "does this guy deserve to visit Heidelberg?" but simply "can we risk letting him into the country at all?" And letting you into the country is what will happen no matter whether the visa covers only the summer school or the summer school plus three days of leisure travel.

What you'll be suspected of -- simply by virtue of being a young person from a visa-requiring country who wants to travel to the Schengen area -- is that you're actually going to immigrate illegally, taking jobs from the locals etc. etc. But once you provide enough documentation to convince them that this is not the case, you're actually going because of the summer school and are motivated to return home, then appending a bit of tourism to your trip is not going to sound like an increased risk of overstaying. On the contrary, it is normal and routine for visitors to spend some time playing tourist in conjunction with a more serious visit.