Applied Math v. Engineering - Or a school where you are guaranteed opportunity to do both?

Greeting -

My daughter will be entering college as a freshmen this fall and needs to choose between universities where she is admitted to the engineering school and ones where she is admitted to the schools of science. She loves math and does not know much about engineering but is open to that discipline. We are concerned that if she pursues a pure math curriculum (even if it is applied math), she will be limited in the job market when she gets out and will be pushed towards teaching (high school or lower) or will need to go on and get an advanced degree.

Her choices are as follows: CU Boulder Engineering (where she designated applied math but can freely get any engineering major within the school); Colorado State Engineering (same); Purdue School of Science (where she designated applied math); and Cal Poly San Luis Obispo School of Science (same). My understanding is that it is very difficult at Purdue and Cal Poly to transfer into Engineering or get a dual degree if you are not already in that school.

She is a Colorado girl and the idea of going out of state (especially California) is intriguing.

If she decides to go the math route at Cal Poly or Purdue, she would want to combine with stats (Cal Poly) or computer science (Purdue). She is also open to combining with a business degree at one of these schools if that is possible.

Any thoughts greatly appreciated.

Since many college students change their minds about majors, my advise is for her to go to one of the colorado colleges, where she has an easy opportunity to study engineering, and /or math.
You are right to be concerned about her limiting her career opportunities by attending one of the 2 OOS colleges that have admitted her.

It’s super difficult to take CS courses at Purdue as a non major. I agree with @menloparkmom that her best options are schools where she can combine or change majors/minors.

Yes, if undecided, choose a school where changing majors is less difficult.

But she should make sure to take first year courses that will prepare her for all majors of interest, so that she will not be behind on whatever one she eventually chooses.

Thank you all for your comments.