I'm sure this kind of question comes up alot on this board. Nevertheless, every case is different, so I need major advice. First, let me begin by saying that I absolutely despised math from 1st grade all the way up to my sophomore year of college. Because I hated it with such a passion, I consistently did poorly in all my math classes and earned C's in every single one. Among other things, the area I struggled most in was simple arithmetic and mental math. In fact, I still struggle with this. Anyway, I started college as Biology major on the Pre-Med route. Knowing that I'd have to eventually take Calculus, I started from scratch and took Intermediate Algebra my sophomore year and surprisingly earned an A. Then Precalc...another A. Then Calc 1, another A. Now I'm in Calc 2 and loving it. Despite the fact that I'm completely dependent on my calculator for any arithmetic, I've done well so far. And unlike some students in my class, I don't get the concepts right away. I only understand them after working on homework problems. I work extremely hard to stay on top of my game and not fall behind. Plus, I love it and think about it so much. So now I'm at a crossroads. Should I stay a Biology major even though my preformance in the Bio courses is mediocre? Or should I switch to Math while continuing the Pre-med route? I'm just not sure what I'm getting into with math. I've only taken lower division courses and have no grasp of what an upper division course is like. I know for a fact that I will work my hardest, but is that enough to succeed with such a weak background? Is doing well in Calc 1 & 2 a good indicator of how I'll do in the more advanced classes? I haven't done proofs yet, but I have a feeling that it could be trouble for me. With strong motivation and hard work, do you think I have what it takes?
I'd say it depends on what you enjoy about Calculus. If you like sitting there plugging numbers into formulas that the professor hands you, you might not do so well. If you like understanding how the formulas work in general and why, you might do quite well. Speaking from personal experience in a similar situation, probably the safest thing to do is choose math as a minor for now. If you find you enjoy the more advanced classes and do well, then you'll probably be far enough along in biology and math to just swap your major and minor with relative ease. Plus a good amount of experience in another scientific field could make finding a job after school that much easier. The only big problem is that it might take you longer to graduate.
It sounds like you really are getting more into your math courses than your current major. What textbooks have you been using? I'd suggest picking up a few top-notch textbooks from the library; Say, Spivak's "Calculus," (this will cover things that you already know, but from a much more rigorous perspective), Artin's "Algebra," and anything else that looks interesting. Try to follow the first few chapters on your own, and in particular try to solve a number of problems, especially from the algebra book. The style of presentation will be something remotely similar to what you'll see in higher-level (though still introductory) mathematics courses. Also, at least at my school, there aren't any professors who will object to people sitting in on their lectures; You might want to sit in on a few for some upper-level math courses. Obviously the experience will vary depending on the instructor, and if you don't do it right at the start of a course then you will be completely lost, but it may at least give you some grasp of "what an upper division course is like"! Another potential idea to talk to one or more of your former instructors about switching majors. They'll probably be able to give you some sort of insight into the differences between the courses you've taken already and more advanced courses. I wouldn't worry at all about your "mental arithmetic," as long as you understand the fundamentals of symbolic manipulation (it's surprising how many people don't!). As I've demonstrated repeatedly in other threads, I can hardly even add integers with any reliability!
Oh, arithmetic is the first skill to go when you become a mathematician, so he's already well on his way!
Thanks for the advice. For Calc 1 & 2, I've been using Stewart's "Calculus: Early Transcendentals" text. Personally, I think the text is quite helpful in explaining the concepts. I will definitely take a look at Spivak's Calc book & Artin's Alg book. As for what I enjoy about Calc, it is fun to simply plug in the numbers into formulas, but I like to understand why they work and where they came from. My college is relatively small, so all math courses usually have at most 12 students. The professors focus alot on us understanding the material and pay special attention to every student. I forgot to mention that I am a Math minor right now. If I do change majors, I'd have an extra semester, which I'm ok with. Plus, I'd end up with a double minor in Bio and Chem. I've talked to my Calc professor on numerous occasions about switiching majors, she thinks I should. But I always wonder if she's just saying that or if she really means it. I'm glad to know my mental arithmetic problem won't be too much of an issue, since I do understand symbolic manipulation.
I say go for it. One thing to keep in mind is that proofs will probably be difficult when you first start doing them, but with practice and experience, you will get the hang of it, and hopefully start to like doing them
If you do decide to major in mathematics and proofs give you trouble, you could always take a course in logic. I'm sure most schools have math or philosophy departments which offer the subject.
If your performance in grade school level math courses is what's holding you back, you should know that I failed all of my math classes from 1st through 7th grades, and I ended up getting a degree in math. Arithmetic isn't too important. But you might want to make sure you enjoy doing proofs, because real mathematics is very different from the four-semester calculus sequence that all math and science students take. It'll seem difficult at first, but once you get the hang of it, proofs are actually pretty easy. What's important is that you enjoy doing this sort of thing, because calculus won't be representative of what mathematics is really like. If you like calculus, but not the upper level math courses, then you just might fit in with us physics people!
It shouldn't matter to much, one of the reasons I loved my higher level math classes and engineering classes is because I can make a stupid mistake like taking the integral of 5x^3 and getting 5/3(x^4) or adding 5+9 and getting 16 and not being crucified for it. Sure, take off a few points, or even half the points for the problem, but at least I'm not getting D's like I did in grade school for those kinds of mistakes. On that note though, I've found that the better you know the material, the less likely those little mental lapes are. In fact, I've found that if you do enough practice problems, and do them over and over again, you are able to spot those mistakes long before you turn the test in.
One option is to change your major to mathematics and take the required courses med schools look for like anatomy, organic chemistry, etc. This gives you the option to go to med school when you are done. Just remember good grades are vital if you plan to go to med school. Also, good grades are important if you want to go to say graduate school for mathematics. So my point is, whatever you do, do really well. I studied mathematics, but I knew what I was going to do with my degree beforehand, so try to think about what you want to do AFTER you graduate. As for whether you have what it takes, only you can answer that. The things that will help you the most IMO are 1. having confidence in your own mathematical ability 2. working hard Goodluck.