I am currently a sophomore majoring in mathematics. I plan to pursue PhD right after my graduation. According to my current schedule, I will be able to graduate within 3 years if I only take classes to satisfy minimum graduation requirement. Alternatively, I can choose to graduate in traditional 4 years and take graduate-level classes in my senior year.
I personally want to graduate early so that I can save my family cost. However, I am not sure if graduating in 3 years will put me under some disadvantages in compare to other applicants who graduate in 4 years.
I am thinking, is it possible (and recommended) for me to try applying for PhD during my third year and see if I get accepted to schools I want to go?
If I am not accepted, I will stay in college for the fourth year and improve my portfolio by taking graduate-level classes and engaging in more mathematics-related activities. Will there be any disadvantage of reapplying to the same PhD program?
My course schedule in the third year: Fall: Algebra I, Topology, Combinatorics (as an elective) Winter: Algebra II, another Combinatorics (as an elective)