Research topics appropriate for a beginning mathematics major?

[tinylights]

Okay, so, I'm about 2 semesters from completing my AA degree and I decided a couple semesters ago that I really want to be a math major. I am not a traditional student exactly - I was homeschooled and my math education was not strong, so I ended up placing into Intermediate Algebra in my first semester of college. I've worked my way through that, College Algebra, Trig, Pre-Calc and am now in Calc 1. So even though I will have the required math prereqs when I finish my AA, I am still not as ahead in math as most math majors are at this point, since they often take a calculus class in high school.

I'm also an Honors student. In the last year of study for an Honors AA, there is a required research project of some sort. It's not a huge thing at all, only 20-30 pages. But I am really drawing a blank about what the heck to do it on. I'm worried that any subject I pick up to research will be too easy, because how many unanswered questions are there to be answered by someone who is just learning basic calculus? There's also the option of doing some sort of computer programming as an alternate research project, but I am in my first programming class ever and hence I struggle with the same problem.

Does anyone have any ideas or suggestions on the kinds of projects that would be relevant for a student who is still not well-learned in calculus or computer programming, while still having a certain degree of rigor and difficulty?

Thanks :)

 

[micromass]

Do you really have to do original research as in: answering an unanswered question? I doubt very much that this is the case. I guess that the "research" will be more something like self-studying a topic you like and writing something about it. I highly doubt that it will need to be original. I suggest you ask one of your professors to clear this up.

As for programming. It is very easy to find a project where you can do something original with. Of course, you will need to learn some more programming as your program advances: just course knowledge will not be enough. But the entire point of research is to learn something more.

 

[tinylights]

No, it doesn't need to be entirely original research. I just want to pick a topic where my questions couldn't just be answered with a Google search, if you know what I mean.

I definitely want to extend beyond the limits of my classes, and I guess what I'm suffering from is having no idea where to start.

 

[micromass]

Where to start is to ask yourself what kind of things interest you in math. I realize you don't know much math yet, but I'm sure you can identify some things you like. For example, are you interested in number theory (for example, are you interested in prime numbers or triangular number). Or in geometry (Euclidean geometry or platonic solids or ?)?? Or any other subjects?
Once you know this, we can give suggestion on topics you might like to do.

 

[Jorriss]

If I were in your position (that is, if this would keep your attention), I would treat working through Spivak Calculus as a project.

 

[homeomorphic]

Maybe reading a book about the history of math? There's a decent amount of stuff that happened before calculus was even invented.

 

[tinylights]

Micromass, the main area I've really adored so far is trig/geometry. I don't dislike limits, derivatives or linear algebra at all but they aren't as exciting for me.

Jorriss, I have heard great things about Spivak's Calculus and it's on my list of books to acquire :) I'll try working through it, for both enrichment and ideas.

 

[tinylights]

Hey guys, I hit up the bookstore and ordered a used copy of Spivak's Calculus as well as another lighter read which doesn't delve too deeply into any particular subject but discusses in a few pages each certain mathematical principles, theory and aspects of math history. It hopefully will isolate some stuff that is of particular interest to me, though so far I've found the whole thing pretty cool. :)

Also, I thought of another thing I LOVE. The main thing that got me really obsessed about math - like, I've loved this since I was around 12 years old - is the golden ratio, the Fibonacci sequence, etc. I love numbers like pi, e and phi, because they are so frequently occurring in nature. Maybe something involving these? Not sure.

I don't feel as much pressure now though, I'm happy to say, since I'm just having fun reading up and exploring a lot of different things. Thankfully the Honors chair also got her Ph.D in math so I'm sure I can bounce some ideas off of her, though I still really appreciate suggestions because I wouldn't have taken a look into the history of math or gotten Spivak's Calculus without it.