Go to this page and read it carefully: http://collegecatalog.uchicago.edu/thecollege/thecurriculum/
There are some pretty broad hints in there as to which courses are directed at people like you: Courses that are recommended “for students of the humanities and social sciences.” Courses that are open only to first years, second years, and entering transfer students, with preference given to first years. Courses that do not meet pre-med requirements. Courses that do not meet any pre-requisite requirements for a major in the department offering the course. A lot of these specific courses are relatively new, and I haven’t heard anything about them, but they replace courses that, um, did not receive a lot of respect from students in Chicago’s “learn 'til it hurts” culture. One of my kids met the core science requirement taking some of these courses (including Core Bio and Global Warming: Understanding The Forecast) and complained about how un-challenging they were, so that’s a pretty good sign. But during orientation week you should consult your advisor and older students about this for up-to-date assessments of which courses will try to teach you the least.
You know how Eskimos supposedly have 60 words for snow? (Yes, today it’s Inuit, but it doesn’t seem right to embed a term that is more technically and politically correct in an old cliche.) Well, the University of Chicago has almost as many options for math placement. You will take a math placement test, and that will tell you a lot about where you belong. If your math preparation is really bad, and you are not exaggerating, there is a remedial pre-calculus class offered. That doesn’t count toward the Core requirement, but it can get you up to the level where you can take a class that does.
I’m sure that well over 90% of Chicago students meet the math Core requirement by taking at least two quarters of one of the three calculus sequences (or placing out of calculus altogether and taking higher-level courses). But you really need only one quarter of a math-ish class for the Core, and you can get that with several classes that do not require any calculus, including a special “Elementary” statistics class, some equivalent computer science classes, and two non-calculus math classes directed at fundamental math concepts other than calculus. Again, the tip-off is that prospective majors can’t get credit toward the major for them, and they don’t meet pre-med requirements. (If you only take one math course, you can’t take calculus, and you will have to take an extra bio or physical science course, but those fields have richer menus of easy options. Again, talk to your advisor and current students when you get there.)
If you are really thinking about political science, you should plan on trying to take at least one introductory statistics course. It’s not required, but I can’t imagine doing political science without it.
When my kids went through, the advisors were terrible about letting students know they had the option not to take calculus. At least back then, there was a quasi-religious belief in the spiritual value of calculus, even for people who knew they were not going to be majoring or going to graduate school in a field that required it. So if you want a non-calculus math option, you may have to push back a little to keep yourself from being railroaded into a calculus sequence. (Study the page I linked above!)
One final word: I have tried to answer you question honestly, and without too much sarcasm. But you probably ought to consider at least not taking the approach your question reflects, and not looking for the least challenging math and science courses. You should look for the most challenging, best-taught course you are capable of handling, and you may be surprised at how capable you are, and how stimulating you find the “real” science and math courses.