I am a second-year undergraduate majoring in mathematics. In my first year of studies, I didn't do really well on my exams and therefore my results were not good, with a GPA at around 2. I didn't really put time into it, but when I started learning advanced probability, I found that I am interested in it and want to study more and am even thinking of doing research. Also I think I have found my way to study math as I didn't quite do before. In that semester, I got 2 A+. In my school, I heard that people who apply for a master's degree normally have a first-class honors degree. Is there another way to get into more advanced study of math, even with a low GPA?
Admissions committees (at least in the US) are generally forgiving of low grades in your first year, especially if you (and your recommendation letters) tell a compelling story about hitting your groove/finding your passion for the material in your second year. Keep your grades up, get some undergraduate research experience, and you'll be fine.
Basically, you have to compete with people that have a "first class honors degree."
Don't worry about the fact that you started with low grades and they (mostly) didn't. What you need to show is the fact that you are just as capable as them of making high math grades going forward.
Your two A-pluses are a good start. This may be a case of "he just found himself in his sophomore yea.r" That will at least get people to "sit up and take notice" (me, for one). The question people will ask, is something like, "is this a fluke, or can he keep it up over a whole program of study in math?
What you need is "several" more courses with As over the rest of your undergraduate program. You might take an extra course or two so that you get more As to replace your bad freshman grades. If you get to the point where people are thinking, he made "mostly As in his last ten math courses," it will do a lot to dispel concerns about your early grades.