You also have to consider how each UC admits Freshman applicants and where the majors of interest reside. In general for CS/Engineering, you want a direct admit without having to go through a secondary admission process.
For Data Science and Applied Math, you can check where these majors reside but in general, these majors can be found in the College of Letters and Sciences which normally does not admit by major.
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UC Davis - Offers a Bachelor of Science (BS) degree in Data Science (this is a new major offered at this school, starting fall 2022)
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UC Berkeley - Offers a Bachelor of Arts (BA) degree in Data Science / Ranked #1 for data science majors in the US out of 24 schools
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UC Irvine - Offers a BS degree in Data Science
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UC Los Angeles - Offers a BS degree in Data Theory / Ranked #12 for data science
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UC Riverside - Offers a BS degree in Data Science
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UC San Diego - Offers a BS degree in Data Science / Also ranked #12 for data science
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UC Santa Barbara - Offers BA and BS degrees in Statistics & Data Science
UCB:
Division (L&S, CNR, CoC, CED, CoE) matters for admission selectivity.
Within CoE (but not the other divisions), major matters for admission selectivity. Changing majors within the CoE after enrolling is not guaranteed, unless one is CoE undeclared.
Note that L&S admits students as undeclared; admission to capped majors (e.g. CS, economics, psychology, ORMS, statistics, art practice, and a few others) is by college GPA in prerequisite courses (and portfolio for art practice) after attending for a few semesters.
Note: CS in the College of L&S may be a direct admit for in-coming Freshman but specifics have not been finalized.
UCD:
College of Letters and Science admits by College but within specific academic departments: ie. (Humanities, Arts and Cultural Studies; Mathematics and Physical Sciences; Social Sciences)
UCI:
UCI admits into the University first and then into the major. In the case that UCI is unable to accommodate all qualified applicants in their first-choice major, those students who indicate a valid alternate major may be offered admission in that major or Undeclared.
UCLA:
For the College of Letters and Science, the applicant’s major is not considered during the review process.
UCSD:
The campus does not admit students on the basis of academic major or choice of UC San Diego undergraduate college. UCSD admits into the University first then into the major. Alternate majors are considered and capped majors are highly competitive. Also note: Capped majors require additional pre-req courses and specific GPA to be able to qualify if changing majors. Also if applying to a capped major, select an non-capped major as an alternate.
UCSB:
College of Letters and Sciences: Choice of major is not considered in selection to the College of Letters and Science. The exceptions to this rule are dance and music performance majors. Both majors require applicants to complete an audition in late January or early February.
In the College of Letters and Science, students are admitted to a major or a pre-major. If admitted to a pre-major, the student must meet additional requirements at UCSB prior to being in the full major.
UCSC:
Important Note for Prospective Engineering Students: Choice of major does not influence the selection of first-year students, except for those applicants interested in a major offered by the Jack Baskin School of Engineering (BSOE).
UCR:
Admission by major but alternate/2nd choice major will be considered if applicant does not meet their first choice admission standards.