Some data visualization experts don't like tree maps because it's hard to make precise comparisons of area across distance, but I do like it for this purpose: You can pretty easily see the data in one view with minimal effort, and since precise comparisons aren't vital, you can get a good sense of the lay of the land.
It's also very easy to ask your questions of this chart. For instance, if you want to see how degrees shook out within a program (like engineering, or English) you can quickly make those selections and see the results by ethnicity. If you want to exclude non-resident students, for your analysis, you can. If you want to see what Hispanic students majored in, you can look at all programs but select just"Hispanic" on the ethnicity filter. Just make your selections in any combination and click "apply" on the filters. And choose which year you want to look at.