I studied statistics as my major when I was an undergraduate and struggled to obtain a BA degree of statistics. Quite the opposite of your situation, I transisted from statistics to history of education for my MA because statistics was too hard for me and I thought I need more knowledge of social science and humanities.
I don't know what courses students learn in U.S.,but in China I learned higher algebra and calculus as basic courses in statistics major, then "applied random process" ,"topology","abstract algebra" and so on, all very pure and tough theory... Some of my classmates went to universities in U.S. after graduation. As they said, the Ph.D. courses were as" easy" as what we 've learned before. ..