I am a current Harris student and entered without any background math. In fact, I hadn't taken a math course since HS since my undergrad BA allowed me to take language instead.
That said, I would strongly recommend using Schaumann's calc and algebra books this summer.
If you plan to take a class, take one that will challenge you. U of C math is a breed unto itself. again, the Schaumann's books were super helpful, and I wish I'd known about them earlier.
If you go to Harris, you'll need to attend math camp - it's not a course, but a review. Mandatory math proficiency is a requirement. If you were a math major, math camp is still helpful to meet people. It's fun (sort of).
Full disclosure, I did not pass the algebra or calculus exams and took the extra math classes. It was not ideal to take the classes during the core, but I survived. In the core, you will need to know how to take a full and partial derivative. You also need to be very comfortable with slope, functions and algebra - also freshen up on working with fractions.
If you are not a math person, I recommend you practice practice practice this summer.
if you have to take the math classes, it's not the end of the world. They are genuinely helpful. I am now quite comfortable with the quant parts of the program and am proud to have moved so far.
Harris is super quant-y. There are a fair number of non-quant people. Their philosophy starts to make sense once you get used to it. Everything is analyzed from an econ point of view - even the management class. So brush up on marginal benefit, expected utility, probability, and maximization.