I'm about one year into a math Ph.D. program. With some scientific computing background in undergraduate and master study, my research interests are in numerical analysis/PDE or probability. All of them are analysis orientated.
Recently I took (written) qualifying exam in several subjects, and passed all of them. However, I noticed my real analysis score was bare minimum passing score (i.e. I would have failed had I lost one more point.) and my algebra score was more than 30 points (out of 100) above the require passing score.
That result makes me a little bit confuse. Should I stick to my original interest, where the exam result indicates my knowledge is mediocre at best, or should I switch to a more algebra orientated field, where I did well on the test but had almost no related research experience or elective courses in the past?
People who are not in mathematics are also welcome to answer the question in the title in the context of your department and research field.