Future inspite of mediocre beginnings?

[BUConsul]

Hi, I am a sophomore math major at large state school with a decent-good reputation. Currently, as I look towards the future I see two fields/career paths that interest me: i)Getting a PhD in Math to become a professor/researcher or ii)going into finance. However, as much as I would love to go into to these fields (especially Math), my performance at school the first semester has been, while not terrible, mediocre. I am aware that I need to haul it in order to fulfill my goals, and I am willing to work extremely hard towards them. My only question is, will I still be able to enter these extremely competitive fields?

My statistics are as follows:
Overall GPA = 3.5
Math GPA = 3.2
Classes: Calc I (B)
Calc II (B+)
Calc III (B)
Differential Equations (B-)(Something I'm still mad at my self for, did great all semester yet wretched on the final)
Linear Algebra (A).
No research experience to speak of.

However I am currently taking both Complex Variables/Analysis(Said to be one the harder classes in the math dept, with one of its hardest teachers), and Proof/General Higher Math, and am quite sure that I will end up with A in both of these classes. Concerning classes, I plan on taking a topics class in set theory over the summer, and am registered for (at least) Modern Algebra and Point-Set Topology in the fall. Also, on reason why both my major and overall GPA are kind of low is because before I decided to do Math I was on A Pre-Health Chem/Bio-Chem track while taking a year of organic chemistry,Biology, and calculus based physics - and did fairly well because I devoted so much attention to them. But I have no desire to go down the natural sciences track, I I realize my reasons are not a adequate excuses. I realize to do well I need to work both much smarter and harder.

So I guess my question really distills to this: if I do significantly improve GPA(major specifically) will I indeed be able to reach my goals? Can this only accomplished by getting a 4.0 from this semester onward (which is my goal, but I realize that it is a lofty one)?

Anyhow, thank you for reading this. I would really appreciate an honest appraisal, thanks.

 

[Geezer]

Grad schools will look harder at your upper division GPA than the lower division grades, so focus on doing better STARTING NOW. Instead of B's, get A's for the next two years. Find someone to so some research with...you still have time. Apply to some REUs, too, for the summer (extra cash AND research experience). Oh, and start prepping for the Math GRE today.

 

[twofish-quant]

So I guess my question really distills to this: if I do significantly improve GPA(major specifically) will I indeed be able to reach my goals?

You numbers are on the bad side, but they aren't anywhere near hopeless.

Can this only accomplished by getting a 4.0 from this semester onward (which is my goal, but I realize that it is a lofty one)?

Do what you can.

One thing that you should be careful about is that you shouldn't obsess so much about GPA, that you forget about the other parts of the application... Specifically...

1) A lowish GPA in which you are taking hard classes is better than a perfect GPA in which you are taking easy classes.
2) REU's and recommendations will help a lot.
3) Math GRE's