Discouraged Math Major: Am I Fit for the Field?

[koh94]

Although I am a math/stat major, I find math very challenging. It's very discouraging when chemistry or biology majors breeze through their first-year bio/chem classes and I'm struggling in first-year calculus. Although I did okay in Calc I and half of Calc II, I have to put in a significant amount of effort and time to get the same grade as someone who appears to just "get it". I don't think my test anxiety helps either...

I fear that I will be overwhelmed when I start to take two or more math/stat classes and my grades will suffer, especially when I start to take those upper division proof-based math classes that everyone talks about. Is this just what being a math major is like, or do you have any suggestions for someone like me? I love everything about math. I find it fascinating. I love problem solving, and really appreciate the beauty of math on paper. However, I find it very challenging.

Am I not fit for math? Please be brutally honest as I do not want to realize that I cannot continue with math when it's too late. Thank you.

 

[micromass]

How much do you study for calculus??

Why do you find it challenging? What is it that goes wrong? Can you give some examples?

 

[Sentin3l]

Math is hard; for everyone, not just some. Just like any other pure science, it takes hard work and discipline to do well, as well as the willingness to spend long hours to do homework and study. Everyone can tell you when the subject they study got hard, the people who make a name for themselves push through it.

That being said, if you are sincerely struggling to understand first-year calculus, you're probably going to be in for a rough ride. I would talk to your professor and try to pinpoint where your foundations are lacking, from there, it's a matter of fixing your weakness(es).

 

[koh94]

I understand calculus so far and I've been getting decent grades, but it takes me twice as long to understand a particular topic than it would for my friend. I also have a tendency to not move on to the next topic until I fully understand the current material. I hate straight up memorizing formulas, so I try my best to understand what is going on behind each formula (how everyone should learn, right?). Lectures usually do not help me because the professors move at such a fast pace for me. The way I've been teaching myself calculus so far is just thoroughly reading the textbook (Thomas' Calculus). I guess I understand calculus, but I'm just very slow...

I also have bad test anxiety, especially when it comes to math. I do not know if this happens to everyone, but I have trouble falling asleep the night before the test. Right before the test, my heart starts racing and my hands get really sweaty. Sometimes during the test, my mind goes blank and I even forget how to do a simple integral.

First-year calculus is going by pretty fast and I'm just barely managing to catch up with the pace. However, I'm wondering if I will start get behind on the material when I start to take multiple math classes at once. It takes me so long to study for one math class, I do not know if I will be able to do well when I start to take multiple math classes in one quarter.

 

[micromass]

Being a slow thinker is not necessarily bad. I have met many people who were very fast and could solve problems at a very fast pace. Not every mathematician is like that. Some of the smartest people I've met were slow thinkers, but they had a very deep understanding.

Thing is that you're still in calculus, so you haven't met real math yet. Calculus is just computational, and maybe that's not an aspect of math that you're really into. Real math involves proofs and deep understanding.

Take some proof-based mathematics courses next semester (or this summer!), and see how you do in them. That will be more decisive for your math career than whether or not you like calculus.

Also, if you stop with math, do you have a plan B?

 

[koh94]

I really do not have a Plan B yet. I am interested in physics and economics, but I understand that even those subjects are heavy on math, especially at the graduate level.

In my other post I mentioned that I will be taking Modern Linear Algebra which covers:

Rigorous treatment of linear algebra; topics include vector spaces, bases and dimensions, orthogonal projections, eigenvalues and eigenvectors, similarity transformations, singular value decomposition and positive definiteness.

or Advanced Calculus which covers:

Introduction to the rigorous treatment of abstract mathematical analysis. Proofs in mathematics, induction, sets, cardinality; real number system, theory of convergence of sequences.

I will be taking these classes sometime in my second year, so I am thinking of doing some self studying over the summer. Are there any recommended readings? I am thinking of self studying some basic introductory analysis or other proof based topics that will prepare me for Modern Linear Algebra and Advanced Calculus, which will ultimately prepare me for Real Analysis.

 

[Stephen Tashi]

What kind of things do you find easy to do?

 

[APSDesEng]

I am a double major (aerospace/mechanical engineering with an applied math minor). I have taken all 3 semesters of calculus and one semester of diff'eq. I did very well (A's) in all of them. This semester I took Linear Algebra (not the applied version). This was the first time I have had to write proofs since high school geometry. I failed my first two tests and nearly dropped the class. My professor recommended "How to Prove It: A Structured Approach" by Daniel J. Velleman. I guess it was her text when she took a class in grad school. I read it cover to cover, and while not all of it applied, most of it helped out a lot. I received A's on my last two test that were very heavy on proofs. Maybe something clicked, maybe the book helped, but I am doing much better now. Also, for what it is worth, I am like you. I put in around an hour a night and study to do well. However, two years later, I still remember everything. A lot of my fellow students memorize to get an A but cannot recall years later and are now struggling in classes where the math is being applied. Hang in there!

 

[eigenperson]

In my opinion you cannot possibly know how you will do as a math major until you have taken at least one course that involves proofs.

Don't be concerned if you seem to be slower to solve the problems than other students. It's not a race. To do well at math you have to be able to understand and work with difficult and abstract concepts. It isn't really relevant how fast you are at doing that -- the important thing is to have the ability to do it at all. Now, it's true that you will have to eventually be fast enough to pass the exam in the allotted time. That's what practice is for.

Also, at any decent school (including yours), being a math major is not supposed to be easy. Even the fast problem-solvers should expect to spend a lot of time thinking. This is, in my opinion, something that makes math different from most other majors. You will need to spend a much greater percentage of your time in a clueless state searching for a solution that you can't find.

 

[homeomorphic]

Am I not fit for math? Please be brutally honest as I do not want to realize that I cannot continue with math when it's too late. Thank you.

No one can really say that at this stage. But I can say it can be really brutal. If you just have test anxiety and are slow on tests or are prone to inadvertent calculation errors, those aren't fundamental issues.

All you really need to do is have a back-up plan. There are lots of ways to make your escape at various stages, but it really helps to plan for it in advance, just in case.

Ability is not the only thing to worry about. You should also worry whether you will actually continue to like it. It gets to be very different later on. Upper division is very different from what you are doing now and research is very different from upper division. I got a whole PhD, but it turned out I really didn't like it at all once I had been doing research for a while and only finished the PhD, just out of the stubborn pride I had in not being defeated by the stupid thing. I suppose it had its moments, but it was mostly just pure misery, despite how much I had enjoyed being a math undergrad.

So, I say don't worry about whether you're good enough for math. Worry about whether math is good enough for you.

 

[Khashishi]

Chem majors breezing through first year of chem? Must be an easy prof.

 

[verty]

I know this was a few days ago but I wanted to say that this all sounds pretty normal. Calculus is harder than any math class that comes before and it takes a while to see the whole picture. Calculus (the main part of it anyway) is about calculating rates of change or total change. Everything should tie into this central concept: what do I know, what do I need. How do I get from what I know to what I need?

As for being worried before exams, I think this is better than not being worried. Not being worried is a big issue for some people, math just doesn't excite them. Having a healthy concern to do well is a very good sign. I think the slowness is just seeing the leaves but not the tree.