The BSN is a bachelor's of science degree in nursing.
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There are a number of US schools that have a Masters program for
a Bachelor of Science in Nursing. They include the NYU College of
Nursing and the Columbia University School of Nursing.
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It appears to be the same thing.
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No. A bachelor's of science is a general degree category from
which many specific programs of study fall. The BSN, is only one of
those specific programs of study. In other words, a bachelor of
science in nursing (BSN).
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Yes - it is a proper noun. The full name of the degree is
"Bachelor of Science in Nursing," so when you refer to that
specific degree, you must capitalize "Bachelor's," as in
"Bachelor's in Nursing."