Style Guide – Title Capitalization of Hyphenated Words

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.

No. The title of a question is not like a book title, but more like a sectional heading. It should be written as a sentence and use sentence case.

Title case is used in such thing as titles of books. For example: "Harry Potter and the Philosopher's Stone" (Note that little words like "and", "the" aren't capitalised)

Some newspapers use title case for headlines. It is more common in the USA. Here we use title case for the title of this website: "StackExchange English Language Learners" (and style StackExchange in camel case)

But the titles of questions are really "headings". They should normally be written in sentence case, and use sentence grammar. So write a question like:

Should each word in a StackExchange question title be capitalized?

and not a headline:

Words Capitalized on StackExchange