Can I Pursue a Math PhD?

[Halcyon18]

I just finished my first year of college and my GPA is pretty bad for someone who wants to go to grad school (3.5). My first semester was not difficult academically, but I had some social/emotional issues that I'm not going go into detail about. My second semester wouldn't have been hard if I hadn't decided to take PDE's. This was my first "upper-level" course and the class that made me question if I'm intelligent enough to pursue a math PhD. I worked my butt off for that class and ended up with a B+. But despite all the stress, I really enjoyed the class. I love math and I feel like I would regret it if I didn't pursue a PhD in it. But at the same time, if I had to work so hard to make it through one upper-level class, how could my stupid little brain survive grad school?

[GeoDUDE!]

3.5 is not bad.

 

I had a 3.05 graduating from undergrad and got into a T20 school in the earth sciences. 

 

You are also a rising sophomore. You have so much of your college career left to worry about GPA. Try and have some fun. If you end up graduating with a 3.5, there will be a spot for you in graduate school.

[eeee1923]

3.5 at the end of your first year of college is nothing to worry about. You still have at least another year to ramp up your GPA before you start to get diminishing returns on getting A's. 

 

Just focus on passing your required courses with high grades (A/A-/B+) and taking some challenging electives. You should also start doing research during your sophomore year because your research experience will outweigh your GPA once it reaches a minimum threshold (~3.6-3.8).

[pascal_barbots_wager]

3.5 at the end of your first year is not bad, and grad schools care more about how you do in upper-level courses anyway. So that's fine. Also, I was a math major too and am very, very familiar with the feeling of being too dumb to understand something. Once the abstraction ramps up your head starts hurting, and the other kids in the class who seem to just breeze through don't help. A few things that helped me get through, eventually with honors:

 

1. Work with other people, ideally people you get along with. You'd be surprised how many other students are struggling in the same boat you are. Struggling together is less scary, and talking through concepts with other people will really help understanding stuff. Worst case scenario you all just sit around bitching about the problem set, which isn't terrible. I did OK in my first year classes but it was always stressful because I did everything alone. The classes got harder as I went along, but cultivating a small math peer group in my second year and beyond helped a ton.

 

2. Don't worry too much about the kids who seem to know everything and breeze through stuff. Some of them are faster answering in class, but math in practice isn't necessarily about speed. Some of them don't have to put in much work, but putting in work is a good habit to acquire because you'll have to do it sooner or later. Some of them seem like they know a lot more than they actually do. And some of them are just smarter than you, which isn't a huge deal either because there's plenty of math for everybody. It's fine to have a little competitive spirit but don't kill yourself by constant comparison (because you'll probably end up comparing an unrealistically negative image of yourself with an unrealistically positive image of the other person).

 

3. Try and get involved in some extra-curricular math stuff if possible. Look into REUs, cultivate relationships with professors, etc. Opportunities vary by school, but it's good to make sure your professors know you and know your plans for graduate school. Go to office hours (but make sure you have something to say). Those connections turn into opportunities and rec letters that matter when you're applying to schools in a few years. Quick note about research though, it's extremely uncommon for undergrads to do actual math research before starting a PhD, even at top 10-20 places. Unlike the situation in biology or physics or even computer science, they're isn't very much "grunt work" to do in math research (this is most true for the pure side, less true as you get more applied and computational). You have to know a lot of math before you can make original contributions. That's what a PhD is for! Even REUs don't commonly result in publishable work. But they're nonetheless great experiences as you get paid to learn math and at least get a feel for what research is like, so apply for them.

Edited May 14, 2015 by pascal_barbots_wager

[Halcyon18]

Thank you all for the replies. I guess I just feel like I'm falling behind because I checked Facebook, and my former high-school classmates are now getting 3.7-4.0 GPA's. One kid was even sad that she got a 3.9 and not a 4.0. I don't understand. I did not work very hard in high school (except junior year) and still beat those kids easily. But I did work hard in college, especially this past semester, and got a 3.5 while they all got higher GPA's. Am I getting dumber?!

 

And pascal_barbots_wager, I do work with my friends sometimes, I'm getting to know my professors, and I definitely plan on doing REU's next summer and the summer after that. Also, the class I struggled in IS an upper-level class, which is one of the reasons I'm scared.

Edited May 14, 2015 by Halcyon18

[eeee1923]

Thank you all for the replies. I guess I just feel like I'm falling behind because I checked Facebook, and my former high-school classmates are now getting 3.7-4.0 GPA's. One kid was even sad that she got a 3.9 and not a 4.0. I don't understand. I did not work very hard in high school (except junior year) and still beat those kids easily. But I did work hard in college, especially this past semester, and got a 3.5 while they all got higher GPA's. Am I getting dumber?!

 

And pascal_barbots_wager, I do work with my friends sometimes, I'm getting to know my professors, and I definitely plan on doing REU's next summer and the summer after that. Also, the class I struggled in IS an upper-level class, which is one of the reasons I'm scared.

 

Are your friends also studying math? Are your programs of comparable difficulty? Those are the only questions that would make sense to ask. College is usually the first stage where kids that blew through high school finally begin to be sufficiently challenged especially in the STEM fields. Just relax and focus and mastering your craft and like pascal_barbots_wager said get involved and enjoy the college experience a bit.

[pascal_barbots_wager]

Thank you all for the replies. I guess I just feel like I'm falling behind because I checked Facebook, and my former high-school classmates are now getting 3.7-4.0 GPA's. One kid was even sad that she got a 3.9 and not a 4.0. I don't understand. I did not work very hard in high school (except junior year) and still beat those kids easily. But I did work hard in college, especially this past semester, and got a 3.5 while they all got higher GPA's. Am I getting dumber?!

 

And pascal_barbots_wager, I do work with my friends sometimes, I'm getting to know my professors, and I definitely plan on doing REU's next summer and the summer after that. Also, the class I struggled in IS an upper-level class, which is one of the reasons I'm scared.

 

Yeah, like eteshoe says it's not like you can just compare GPAs across schools or majors (or even within majors, really, depending on what courses you take). For what it's worth I struggled hard in my first upper-level math class and got a demoralizing B-. But after that adjustment period it was mostly A/A- with some scattered B+'s, which was enough to get into a Top 20 CS PhD with a fellowship (without any CS coursework, even!). It's fine and normal to be scared or intimidated, but I wouldn't get too freaked out.

Edited May 15, 2015 by pascal_barbots_wager

[Halcyon18]

Wow, that's amazing! Congratulations on the improvement and getting into a top school.

 

I'll see how things go next semester (I'll be taking two upper-levels then) and take it from there.

[MathCat]

Also, the class I struggled in IS an upper-level class, which is one of the reasons I'm scared.

What class, if I may ask?

 

As you go through a math degree, you gain a hard-to-measure ability usually referred to as "mathematical maturity". It is not surprising to struggle with an advanced class when you are new - even if you nominally have all the prerequisites, you don't have the same experience as somebody who is taking that course in their third or fourth year. By taking a lot of math classes and being exposed to abstract ideas and new ways of approaching problems, things in another class can become easier, even if the material is not directly related. You become better at grasping abstract concepts and become more comfortable writing proofs and following the omitted steps when reading proofs.

 

You don't need to be worrying so much about whether you can do a math PhD at this point. It's possible your interests will develop differently throughout your degree anyway. A lot of people change their majors (and career goals) as they move along. It sounds like you have the right plan for figuring out if this is for you (getting to know your profs, REUs, etc.), so just do your best and try to enjoy it. Don't be afraid to try other things as well. I'm happy to talk about things if you wish to message me. I changed majors twice before settling on math, got a lot of research experience, and am heading to a top 20 PhD program in the fall.

[Halcyon18]

MathCat, first, congratulations on getting into a top program! Second, the upper-level class I took was Partial Differential Equations, so it wasn't super abstract stuff like what I'll be encountering next semester and beyond. I found the lectures to be easy to digest (I had an excellent professor), but the homework and exams were tough. I feel like they involved intellectual leaps that I usually could not make as easily as most of the other kids. Now that I think about it, I'm kind of scared that my own advisor doesn't think I'm capable of doing math. Halfway through the semester, she said I should drop the class because it's not meant for first-years. And near the end of the semester when I picked out classes, she recommended not overloading because she didn't want me to burn out, which I find a little strange because overloading is not uncommon at my school. :/

 

Maybe I'm just freaking myself out now, ha ha!

 

As for other interests, I think physics, biology, philosophy, and computer science are interesting; and I REALLY like chemistry. But math tops them all. 

[pascal_barbots_wager]

MathCat, first, congratulations on getting into a top program! Second, the upper-level class I took was Partial Differential Equations, so it wasn't super abstract stuff like what I'll be encountering next semester and beyond. I found the lectures to be easy to digest (I had an excellent professor), but the homework and exams were tough. I feel like they involved intellectual leaps that I usually could not make as easily as most of the other kids. Now that I think about it, I'm kind of scared that my own advisor doesn't think I'm capable of doing math. Halfway through the semester, she said I should drop the class because it's not meant for first-years. And near the end of the semester when I picked out classes, she recommended not overloading because she didn't want me to burn out, which I find a little strange because overloading is not uncommon at my school. :/

 

Maybe I'm just freaking myself out now, ha ha!

 

As for other interests, I think physics, biology, philosophy, and computer science are interesting; and I REALLY like chemistry. But math tops them all. 

 

I think "intellectual leaps that I usually could not make as easily" falls under the umbrella of mathematical maturity mathcat mentioned. It's a tough thing to quantify, but figuring stuff out is just something you get better at with work over time. As far as math problems to have, that's a good one.

[MathCat]

MathCat, first, congratulations on getting into a top program! Second, the upper-level class I took was Partial Differential Equations, so it wasn't super abstract stuff like what I'll be encountering next semester and beyond. I found the lectures to be easy to digest (I had an excellent professor), but the homework and exams were tough. I feel like they involved intellectual leaps that I usually could not make as easily as most of the other kids. Now that I think about it, I'm kind of scared that my own advisor doesn't think I'm capable of doing math. Halfway through the semester, she said I should drop the class because it's not meant for first-years. And near the end of the semester when I picked out classes, she recommended not overloading because she didn't want me to burn out, which I find a little strange because overloading is not uncommon at my school. :/

 

Maybe I'm just freaking myself out now, ha ha!

 

As for other interests, I think physics, biology, philosophy, and computer science are interesting; and I REALLY like chemistry. But math tops them all. 

What you described does indeed fall under "mathematical maturity". You will get better at it with time. Definitely do not overload, though. Burnout is a real risk - I had more than one extremely capable classmate fall victim to this (and the result was one dropping out of grad school after).

[velua]

MathCat, first, congratulations on getting into a top program! Second, the upper-level class I took was Partial Differential Equations, so it wasn't super abstract stuff like what I'll be encountering next semester and beyond. I found the lectures to be easy to digest (I had an excellent professor), but the homework and exams were tough. I feel like they involved intellectual leaps that I usually could not make as easily as most of the other kids. Now that I think about it, I'm kind of scared that my own advisor doesn't think I'm capable of doing math. Halfway through the semester, she said I should drop the class because it's not meant for first-years. And near the end of the semester when I picked out classes, she recommended not overloading because she didn't want me to burn out, which I find a little strange because overloading is not uncommon at my school. :/

 

Maybe I'm just freaking myself out now, ha ha!

 

As for other interests, I think physics, biology, philosophy, and computer science are interesting; and I REALLY like chemistry. But math tops them all. 

For whatever it's worth, I was never very good at PDE stuff when I encountered it. I never took PDEs, but definitely saw them in several complex variables, as well as functional analysis. But I still did very well in algebra, topology, number theory, etc.

 

Also, my first upper level math class I got a B in. That class was probably what inspired me to go into math, the professor was so great, and the material was so interesting. I actually got near 100% on the midterms, but then bombed the final because I just couldn't get a handle on one of the later topics in the course. Anyway, I basically got all As in my other math classes the rest of the way, and even took several more courses with the same professor, did very well, and got a great LOR from him.

[ginagirl]

MathCat, first, congratulations on getting into a top program! Second, the upper-level class I took was Partial Differential Equations, so it wasn't super abstract stuff like what I'll be encountering next semester and beyond. I found the lectures to be easy to digest (I had an excellent professor), but the homework and exams were tough. I feel like they involved intellectual leaps that I usually could not make as easily as most of the other kids. Now that I think about it, I'm kind of scared that my own advisor doesn't think I'm capable of doing math. Halfway through the semester, she said I should drop the class because it's not meant for first-years. And near the end of the semester when I picked out classes, she recommended not overloading because she didn't want me to burn out, which I find a little strange because overloading is not uncommon at my school. :/

 

Maybe I'm just freaking myself out now, ha ha!

 

As for other interests, I think physics, biology, philosophy, and computer science are interesting; and I REALLY like chemistry. But math tops them all. 

Just a thought, but have you considered biostatistics for graduate school? You seem to have fairly diverse interests and biostatistics would help incorporate these other areas, and might also be a good option if you're nervous about a math phd being too rigorous. It sounds like you will be fine either way, as it's still early on, but I just thought I'd throw that out there

[Halcyon18]

Actually, statistics is the one branch of mathematics I DON'T like.

 

I enjoy the intellectual challenges my math classes (mainly PDE's) have thrown at me, as painful as they may be. I feel like if I don't get a math PhD, I'll regret it; like something important would be missing in my life. Not because PhD's are respected or well-paid (from what I've heard, that's not true anyway), but because I'm passionate about math. Whether or not I can handle it is another thing. 

 

I've only recently taken a good look at myself and questioned if I'm actually capable of a math PhD, or even a math major. Up until PDE's, whenever I struggled in math, I made excuses, i.e. "I'm only a junior, it's okay if I can't quite get the hang of calculus yet!", or "I'm just a high-school senior, so the fact that I'm in multivar and LA already makes me a winner!" This past semester, I almost fell into the same trap again ("This class isn't even meant for first-years; I'm doing fine!"). I decided I need to stop making excuses and sugar-coating the truth. But, goodness gracious, the truth hurts!

Edited May 22, 2015 by Halcyon18

[MathCat]

I've only recently taken a good look at myself and questioned if I'm actually capable of a math PhD, or even a math major. Up until PDE's, whenever I struggled in math, I made excuses, i.e. "I'm only a junior, it's okay if I can't quite get the hang of calculus yet!", or "I'm just a high-school senior, so the fact that I'm in multivar and LA already makes me a winner!" This past semester, I almost fell into the same trap again ("This class isn't even meant for first-years; I'm doing fine!"). I decided I need to stop making excuses and sugar-coating the truth. But, goodness gracious, the truth hurts!

I don't think it's that you need to stop making excuses. I would suggest that you stop taking advanced classes early. It seems like you got used to always being ahead in high school, but I don't think that's a good long term strategy. Take your time. It is good to challenge yourself, but be realistic as well. Don't overburden yourself, don't take classes you're not yet prepared for, and don't take too many at once.

 

This is a pretty common transitional thing, I believe. Good students are used to being more advanced and always at the top of the class, and when they move on to the next stage, it can be a tough adjustment because of that attitude.