Here's my situation. I am struggling with it for weeks. I am a math major applying to Ph.D. programs (pure math). I have a 3.94 major GPA, but in my sophomore year, I got an NP (no pass) in a math course of differential geometry. This is because I didn't make the final for personal reasons. I retook the course (in my junior year, because there is only one such course a year) and got an A, and actually I got full marks in all quizzes and exams.
Here is the thing. Do I need to explain in my "NP" grade in my statement of purpose? Since I am applying to good Ph.D. programs, my statement of purpose is like a research statement, and it shows my math background, research experience, and dedication - all good things. I feel it is very weird to write anything about my "NP" in such a statement. I also feel like professors don't like such things showing up in a statement of purpose.
If I don't write any explanation, I believe that professors will know the "NP" cannot reflect my academic ability. After all, I retook it and nearly all my math courses are "A". However, I am worried that they make some guesses about the "NP" like academic dishonesty (definitely not true), or I don't have the ability to handle the crisis (which is true). Besides, I think (only my guess) professors will be curious about it, so maybe they are expecting an explanation?
All in all, should I explain my "NP" grade in my statement of purpose?