Simple answer: Yes. A computer, required for class work, is a qualified expense for claiming the American Opportunity Tax credit (AOTC) . To qualify for the alternative Lifetime Learning Credit (LLC), the computer must be purchased from the school. The AOTC is not available to grad students.
A computer is not a qualified expense for the alternative Tuition and Fees deduction (TFD).
The AOTC is a maximum of $2500, $1000 of which is refundable. It only takes $2000 of expenses to get the first $2000 of the credit. It only takes $4000 of total expenses to get the maximum $2500 credit. So, if you already have $4000 of expenses (tuition, fees and books), claiming the computer will not get you any more credit. Or if you already have $2000 of other expenses, the computer will only get you 25% back and only up to $500.
The LLC is 20% of expenses and a max of $2000, based on $10K of expenses.
