If I purchased my daughter a computer to begin college. Can I claim it on taxes as equipment for education expenses?

Probably.   See IRS Pub 970, page 47.

https://www.irs.gov/pub/irs-pdf/p970.pdf

Qualified Higher Education Expenses
These are expenses related to enrollment or attendance at an eligible post secondary school. As shown in the fol-lowing list, to be qualified, some of the expenses must be required by the school and some must be incurred by students who are enrolled at least half-time.

4.
The purchase of computer or peripheral equipment, computer software, or Internet access and related services if it is to be used primarily by the beneficiary during any of the years the beneficiary is enrolled at an eligible post secondary school. (This doesn’t include expenses for computer software for sports, games, or hobbies unless the software is predominantly educational in nature.)