Needing Guidance as a Math Major

[Szichedelic]

Hi all, I'm almost positive this comes up frequently but I feel like I need some sort of confirmation from other math majors who have gone through undergraduate and then graduate programs.

First and foremost, I am having trouble confirming if I'm really cut out to be a math major. I'm currently attending a decent university in California as a math major. My first quarter there, I got a 4.0 while taking 3 math courses (Advanced calculus aka intro to real analysis, number theory, and modern linear algebra). My second quarter, my grades dropped a bit and I got a B+ in Real Analysis part 1 and an A- in combinatorics. This quarter, I'm not sure what my grades will be but it might be a bit lower. I took Real Analysis part 2 and Topology. Also, I've been partaking in an REU except that I'm the only one working on the project while my faculty mentor dictates to me what he wants me to focus on.

I know that these grades are not bad but I'm feeling like I'm slowing down in my ability to understand upper division mathematics on the level required to get competitive grades in my classes. I'm very interested in math and spend a lot of my time reading books outside of class. However, I just feel like sometimes I don't really have what it takes to go on to a good graduate school and conduct original research on my way to obtaining a Phd. I see others in my class whom seem to innately understand many problems while I struggle with my confidence on a weekly basis.

I am just wondering if any other math majors went through this but ultimately went on to higher education in spite of their confidence issues. Thank you for your time.

 

[chiro]

Hey Szichedelic and welcome to the forums.

The only suggestion I can give is to think about why you would want to go to graduate school and if other options are still worth considering. Also another thing is if you haven't strongly considered other options, you should do this immediately and start asking around/doing your own googling and research/etc to find if there are alternate career/life/whatever goals that are out there.

Be aware that there are opportunities out there for math graduates that utilize lots of different kinds of skills and these can be put to use in ways that would be beneficial for yourself, and you might find that you really enjoy the work you produce, who you work with, and what you do both individually and collectively.

In terms of grad school though, only you can really know whether deep down you want to think about going that path. You are probably aware of the kind of commitment you will need to have and this is regardless of innate talent, ability to pick things up and so on: my guess is that if you want to do it and show a lot of evidence for endurance in that environment, you will have a shot somewhere.

As an example, a poster here by the name of homeomorphic has publically on this site expressed some of his feelings for his PhD project and I recommend you PM him for some really specific information: I think this might help you a lot.

 

[micromass]

Doing great in classes and doing great in research are two quite different things. There are quite a lot of people who do wonderful in classes, but who drop out eventually because they simply don't like research. On the other hand, there are some who have much difficulty with taking tests, but who do superb in research. We can really not say which one you will be.

If you absolutely want to go to grad school (but do think it through), then you must absolutely pick a topic you are extremely interested in. Otherwise, it will not work out. What math books do you read in your free time?? Those are usually the things you are interested in.

 

[nucl34rgg]

Hi all, I'm almost positive this comes up frequently but I feel like I need some sort of confirmation from other math majors who have gone through undergraduate and then graduate programs.

First and foremost, I am having trouble confirming if I'm really cut out to be a math major. I'm currently attending a decent university in California as a math major. My first quarter there, I got a 4.0 while taking 3 math courses (Advanced calculus aka intro to real analysis, number theory, and modern linear algebra). My second quarter, my grades dropped a bit and I got a B+ in Real Analysis part 1 and an A- in combinatorics. This quarter, I'm not sure what my grades will be but it might be a bit lower. I took Real Analysis part 2 and Topology. Also, I've been partaking in an REU except that I'm the only one working on the project while my faculty mentor dictates to me what he wants me to focus on.

I know that these grades are not bad but I'm feeling like I'm slowing down in my ability to understand upper division mathematics on the level required to get competitive grades in my classes. I'm very interested in math and spend a lot of my time reading books outside of class. However, I just feel like sometimes I don't really have what it takes to go on to a good graduate school and conduct original research on my way to obtaining a Phd. I see others in my class whom seem to innately understand many problems while I struggle with my confidence on a weekly basis.

I am just wondering if any other math majors went through this but ultimately went on to higher education in spite of their confidence issues. Thank you for your time.

Most math majors run into problems when they get to Real Analysis and Topology. That's okay. These topics are notoriously difficult, and B+ isn't a terrible score at all.

 

[20Tauri]

I was not a math major as an undergrad, but I took a fair amount of coursework and will be starting a mathematics MS in the fall. You have already done much more advanced math than I ever did as an undergrad, and your grades sound fine. Just try your best and if you do apply to grad school, make sure you pick a couple safety schools (that's something one of the very best math majors I knew didn't do, and he shot too high and didn't get in anywhere). As for not understanding, I think we all go through that. In my undergrad math department, we were all convinced that we weren't as good at math as person x, who in turn was convinced she wasn't as good as person y, who in turn felt he was inadequate compared to person z, etc.

 

[Szichedelic]

Hi everyone, I felt like I should respond to your posts now that my grades have been posted for the quarter.

Firstly, I got a B+ in Topology. When the instructor released the average grades for every assignment and test in the class, I realized that I could have easily gotten an A had I not panicked on the final. Unfortunately, I had a bout of test anxiety that day and I missed a lot of questions that I should have easily gotten right. Oh well, you win some and you lose some.

On the other hand, I got an A in Real Analysis Pt. II and had the 7th highest overall grade in the class out of 54 people. That was very uplifting compared to my B+ in Topology.

@chiro: I have considered other careers but maybe I have not researched as much as I should. The main issue is that I am not very interested in applied mathematics, in spite of the fact that both of my undergraduate research projects have come in that form. The careers I have looked into include community college teaching and actuarial sciences. I did a research internship with NASA and my NASA mentor told me that he briefly was involved with the actuarial sciences and that it was the most depressing, cutthroat job he has ever had in his life. He strongly discouraged me from going into this field. I've chosen to rely on his anecdotal evidence for now.

@micromass: Most of the books I read in my free time are pretty random. Last quarter, I checked out two non-linear dynamics books and one state-space modeling book. This was more pertaining to my REU I am currently doing but I checked out these books hoping to find a more theoretical approach to the field. This quarter, I checked out one book on abstract algebra and one book on probability. I have been doing problems from both books. Keep in mind I haven't taken these classes yet.

I also just went to University of Washington to present my project at an undergraduate research conference. I had some spare time so I checked out their math library and ended up spending most of my day in there reading a book called "Counterexamples in Topology" and also a book on algebraic topology.

I also like to read research papers related to topics my mentor has worked on. most of them are above my ahead but I find it fun sometimes to try and see how far I can get before I get lost.

@20Tauri: Thanks. I really do need to pick out some fallback schools because I do not want to end up in that boat.

@Everyone: Math is a very deep passion for me but it does NOT come easily to me. I work very hard trying to understand my coursework. I find myself spending time thinking about my homework problems when I am out with friends. My mentor has told me that this is a good thing but really, for me, it is the only efficient way I can get things done. I keep telling myself that in spite of my goofs on exams (I am not a great test taker, and when I make a mistake, I usually figure it out within a couple of days after the test on my own), my drive will be what keeps me going. However, sometimes, I get discouraged and fall into thinking habits that promote the idea that the only way I'll ever achieve my goal is if I just one day viscerally understand everything mathematical thrown at me, almost immediately.

Thanks for everyone's responses and hopefully this wasn't too long of a post.

 

[chiro]

You must remember that actuarial work is not the only kind of work that utilizes statistics: there are lots of different kinds of roles that utilize statistical knowledge and experience in different ways: actuarial work is a rather specific kind of statistical work generally for use in insurance and financial applications (as well as general risk management).

 

[Szichedelic]

Yes I do know that but in responding, I merely forgot to consider it. I am interested in statistics. Ultimately, I will require a job which presents me with new challenges frequently.

 

[chiro]

Yes I do know that but in responding, I merely forgot to consider it. I am interested in statistics. Ultimately, I will require a job which presents me with new challenges frequently.

There are jobs out there involving statistics with no shortage of challenges. You might have to do some boring stuff at the start, but the one constant thing is that the world is full of problems both technical, social, economical, ethical, you name it that need to be solved and this translates into jobs of your description.