The Gregg Reference Manual suggests that in a heading or title, capitalize all the elements except articles, short prepositions, and short conjunctions.
Here, the word oriented is an adjective and thus takes capitalization.
You'd only write "Mathematics" with a capital when it's part of a title of a program, or a degree, e.g.
B.Sc. Mathematics.
You do not capitalise common nouns such as "mathematics" in all normal circumstances. You (more or less) always write "mathematics" in the running text with a lower-case "m". You would have,
Emphasis: pure mathematics
So you would have something like:
Degree: BSc Mathematics
But:
I achieved a Bachelor of Science degree in mathematics, with an emphasis on pure mathematics.
Best Answer
Since your example is a single sentence, your first example
is correct, if you reformulated your second example
Capitalisation can be a question of style, but usually capitalisation occurs at the beginning of sentences and proper names.
It can also begin in an embedded quote within a sentence (your second example)