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The following just sounds odd to me. I was wondering if there were a better/more correct way of saying it:

"A major component of my courses is to teach mathematics."

The "major component" is singular, while "my courses" are plural, so you get the awkward "plural-is" thing going on.

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    In both your original and this suggestion the whole noun-phrase is still singular, obviously, but this... "One of the major components..." at least has some prosodic parallelism by sharing the final "s" with courses, and may sound less "off" to you. Without flipping it around or substantially re-writing it, I might go for "One of the major components of my courses is teaching mathematics." – MDHunter Apr 24 '17 at 16:44
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    Simply put, the to-be verb is does not correspond to "my courses" in that sentence. The thing that is "being" is the "major component". You are saying there is a major component (singular), not major components (plural) – AleksandrH Apr 24 '17 at 16:54
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    This is not at all awkward. It sounds completely natural to this native speaker. – TonyK Apr 24 '17 at 16:57
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The important thing to remember in these situations is that the subject matches the predicate. Because the subject is "component," singular, it is correct to use "is." The sentence is perfectly appropriate as it is. The prepositional phrase of my courses is merely modifying "component." So since you would say

A major component is...

You still say

A major component of my courses is...

Consider this pair of sentences:

One of my apples is red.

One of my apples is green.

In both cases, "one" is the subject, and "is" is the predicate.

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