Is it a good choice for a high school student to take a summer class from UCB? For example, N53 Multivariable Calculus and N55 Discrete Math.
The reason to try such a class is all similar classes in nearby community colleges are full. And due to COVID-19, there isn’t much else a HS junior can do.
I’m not sure if it is risky. I guess classes from UCB might be higher quality than local CC, but is the chance of getting A much lower?
My advice as a UCB alum: Taking both M53 and M55 in a summer for HS student is quite a challenging task even for a college freshman to do so. Not to mention to get an A and therefore a good recommendation from each class. Please take a look at each course description on the website before the decision:
*Math 53: https://math.berkeley.edu/courses/choosing/lowerdivcourses/math53
*Math 55: https://math.berkeley.edu/courses/choosing/lowerdivcourses/math55
If I remember correctly, summer school session held @UCB is usually taught by visiting professors or TAs or teaching staffs from Berkeley Extension Program. You may want to check the teacher’s background profile and also compare with the regular course agenda: http://summer.berkeley.edu/courses/online/math-w53
Math 55 is crucial if you planned to be a CS/Math/Stat (L&S) or EECS (CoE) major. It’s your first course in learning proof techniques and writing which is extremely useful and important for later courses.
As for the Math 53, I remember I had difficult time learning the concepts of vector analysis in the beginning (i.e., Green, Gauss, and Stokes Theorems). The book written by Stewart is much easier to grasp than the one I used.
Again, check the links yourself and see if you’re comfortable with then decide which class to take.
Good luck! 
BTW, the grading is purely depends on the professor. And as expected, you may encounter some students retake the course.
Typically, as I have checked with my friend’s brother lately, the summer session covers fewer topics (but not necessarily in more depth) than the normal semester class does and it naturally leads to somewhat more generous grading. Again, it really depends on the professor and I’d suggest you to sit in both classes for the 1st week and see if you are comfortable with the faster-paced instructions.
Here is a reference link for talking summer classes:
https://study.com/articles/The_Pros_and_Cons_of_Taking_Summer_Classes.html
Really appreciate your help and will check out all the links. The class will start next week and let’s see how it goes.
Thanks!
8 units in an 8 week summer session is like a full time course load with similar work per week as 15 units in a 15 week semester. The summer course will cover material at nearly twice the speed that the same course in a regular semester will cover it. Note: calculus BC (including the AB material) approximates the content of 5/6 of Math 1A and 1B at UCB.
A student who is strong in math should be able to handle it. But be aware that discrete math is somewhat different from the kinds of math that you have been used to. If you want to get an idea of what you may see in Math 55, you can take a look at the course home page for CS 70, a course with substantial overlapping content intended for CS majors at https://www.eecs70.org/ (includes lecture notes that are used instead of a textbook), or an older Math 55 home page at https://math.berkeley.edu/~vivek/55.html (refers to a textbook).
Thanks for the advice. It seems safer to just focus on one course. Dropping before the deadline won’t cause any impact for college application, right?
Choose your summer session class wisely and make sure you know all the enrollment change deadlines info (e.g., w/ refund). Good luck!
http://summer.berkeley.edu/registration/schedule
http://summer.berkeley.edu/sites/default/files/BSS_Catalog2020_web.pdf