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**undergraduate**degrees?

I am contemplating on being an Applied Mathematician. I have a natural desire to solve statistics and probability questions. If I were to come across a real life problem I would try to involve these concepts in solving them.

However, at the same time I am compelled to teach math at the high school to Grade 12 level. I'm not planning to become a full time teacher, just a part-time teacher and/or private tutor. I fear that taking an Applied Mathematics degree will limit my ability to teach Pure Mathematics at the Grade 12 level.

What are the things that an Applied Mathematician would need to be competent at? Do I really need at least a Master's degree to become qualified?