It honestly depends on the person.
If you have a solid math foundation (in both reasoning and computations), I don’t think it’s undo-doable.
In fact, I think that schedule is pretty much the norm in college for a first year.
And I don’t want to sound elitist but… scheduling is only going to get harder from there.
I know of a sophomore taking Operating Systems, Real Analysis, Computer Networking, Compilers, Music, and 1 other humanities + part time job + 1 club and they seem to be doing fine. (though at this point, I do question the sanity of the sophomore in itself. Is he planning to take graduate math and computer science from end of second year? …) {this is semester scheduling but still, very intensive}
Anyways, while Calculus and Programming is quite time intensive, it is I believe the norm for computer science majors to take in the second semester / last quarter of college.
If you google almost any college in the US the schedule of a CS major, your schedule is more or less taken by everyone else.
Personally, I don’t know you. Maybe you have a full time job outside this. Maybe your school is harder than CalTech. Who knows.
However, if your school is like most schools, I recommend registering 5~6 courses and then tuning it down to 3~4 (depending on how comfortable you are with the scheduling).
I should not be claiming this (please don’t bash me as it is my opinion and everyone has differing thoughts about this) but… I don’t honestly think advisers in most colleges want to give a frank opinion about what courses to take, etc.
The role of an adviser in my belief is to ensure students cannot graduate in 4 years and instead has to drag to 5, 6, etc. to get as much money from the students as possible. This view to me makes sense since by convincing students to take less courses early, it makes those students struggle to graduate in the 4 years with the scheduling they have.
Honestly though, outside this pessimistic view I have…
just register for at least 2 more courses. Calculus II and Programming II is nowhere as time consuming as it is made out to be. It is the norm for almost all engineering/cs majors to take those together and it is not unusual (in fact, even greatly expected) for students to take more on top of that.
** Just note you want to take around 15 units a semester/quarter to graduate on time. Personally, I never experienced 15 since from freshmen, I took ~18 with all my AP credits to allow myself to take other courses I want to take outside requirements before graduating and considering I am breathing, it is completely possible.