This question is not easy to answer in the form stated. This is about database design and has little to do with PHP or even SQL really. I would approach the problem by creating a scholarship table and a field table and relate them with a primary/foreign key. Thus scholarship #1 above would have two records in the field table, one for Geography, one for Architecture.
tbl_scholarship
PK: AUTONUMBER
S_NAME: VARCHAR(x) (or similar character field)
... whatever else you need here
tbl_fields
PK: AUTONUMBER
FK: INTEGER
F_NAME: VARCHAR(x)
... and maybe others
The example table would look like this:
TBL_SCHOLARSHIP
PK S_NAME
1 Scholarship1
2 Scholarship2
3 Scholarship3
TBL_FIELDS
PK FK F_NAME
1 1 Geography
2 1 Architecture
3 2 Geography
4 3 Architecture
Now to get what scholar ships are available for a field ("Geography") use a join
SELECT tbl_scholarship.s_name, tbl_fields.f_name
FROM (tbl_scholarship INNER JOIN tbl_fields ON tbl_fields.fk = tbl_scholarship.pk) WHERE f_name LIKE 'Geography'
This would return:
s_name f_name
Scholarship1 Geography
Scholarship3 Geography