I wanted to see how many CS and CSrelated classes a Mathematics of Computation major ( I’ll abbreviate this as “MoC”) could take at a minimum and at a maximum, the latter with various opt outs as in the language requirement, one or two of the Calculus classes, Writing I, and Physics 1A.
There are three classifications of classes at UCLA: the GEs, the premajor courses, and the major courses; in which all these must be satisfied with at least 180 units. The unit cap at UCLA Is 216, but the administration wouldn’t like it if you were stealthily accumulating that many units, in addition to it costing the student more fees/tuition. You have to figure that neither side would be inclined to want the student to accumulate that many credits, but rather he/she would probably rather go for a masters if he/she wanted to take > 200 units in addition to obtaining his/her BS degree.
Please note corrections for CS 33L to the correct CS 35L.
Let’s estimate for all three:
I. GE courses.
Since MoC is in Letters and Science, it has the highest possible amount of GEs of all the colleges at UCLA. These units will amount to between 60 and 70 units, and comprise Writing I, Writing II, possibly the Freshman Clusters, fulfilling the Foundation classes, Language, and Diversity.
Consider that these will take 6070 units at a max.
II. MoC premajor courses.
Here are the links for the Math, Statistics, Program In Computing, and the CS classes.
Here is the link to the requirements for MoC.

Math 31A, 31B, 32A, 32B, 33A, 33B, total of 24 units for the Calculus series.

Math 61, 4 units.

Physics 1A, 1B, 10 units.

Program in Computing 10A, 10B, 10C, 15 units. Or Sub in CS 31, 32, 33 and 35L, 17 Units.

One of the following, Chem&Biochem 20A, 20B, Physics 1C, 4 or 5 units.

The total of these courses is 57 to 60 units.
III. MoC major courses.

Math 115A, 4 units

Math 131A, 4 units

Math 131B or 132, 4 units

Math 151A, 4 units

Math 151B, 4 units

Six Courses from Math 106 through 199, and Statistics 100A through 101C, 24 units

Three upperdiv CS courses, 12 units

Total of these courses is 56 units.
Both A & B of the following would apply with the student having to take all the GEs without any AP or dual enrollment credits, including taking 815 units of a language and having to take all the Calculus and Physics classes, as well as Writing I and II.
A. The addition of the three types of classes at a minimum is 60 + 57 + 56 = 173 units.
B. The addition of the three types of classes at a maximum is 70 + 60 + 56 =186 units.
Here’s a listing of CS and CS type classes for scenario B with minimal CS and CSrelated classes:

Math 61  Introduction to Discrete Structures, 4.0

Program in Computing 10A  Introduction to Programming, 5.0

Program in Computing 10B  Intermediate Programming, 5.0

Program in Computing 10C  Advanced Programming, 5.0

Math 151A  Applied Numerical Methods, 4.0

Math 151B  Applied Numerical Methods, 4.0

CS 1xx  Required Upper Division CS Class 1, 4.0

CS 1xx  Required Upper Division CS Class 2, 4.0

CS 1xx  Required Upper Division CS Class 3, 4.0
This is a total of 9 CS and CSrelated classes totaling 39 units. In addition, one can take computational classes in Math and Stats for the six electives in these two subjects, including in Data Science and Machine Learning.
But if a student can opt out of language classes, Writing I, Math 31A and possibly 31B in addition to a one of the two Physics classes then he/she can add six to seven more CS classes.
The student taking more CS upperdiv classes requires that the the CS 3135L series be taken rather than the PIC 10A, 10B, and 10C series, because upperdiv CS classes require the 3135L series. Here are the max CS classes, unless more GE units are knocked out by dual enrollment or however else:

Math 61  Introduction to Discrete Structures, 4.0

CS 31  Introduction to Computer Science I, 4.0

CS 32  Introduction to Computer Science II, 4.0

CS 33  Introduction to Computer Organization, 5.0

CS 35L  Software Construction, 4.0

Math 151A  Applied Numerical Methods, 4.0

Math 151B  Applied Numerical Methods, 4.0

CS 1xx  Required Upper Division CS Class 1, 4.0

CS 1xx  Required Upper Division CS Class 2, 4.0

CS 1xx  Required Upper Division CS Class 3, 4.0

CS 1xx  In lieu of Writing I, 4.0

CS 1xx  in lieu of Language 1, 4.0

CS 1xx  in lieu of Language 2, 4.0

CS 1xx  in lieu of Math 31A, 4.0

CS 1xx  in lieu of Math 31B, 4.0

CS 1xx  in lieu of Physics 1A, 4.0
The max CS type classes in this scenario would probably max out at 16 classes at 65 units.
All in all, beware of gpa requirements. Taking the CS 3135L series might also put the student in line with possibly applying to the CS major from the prereqs. There’s a 3.5 min in prereqs that is required.