Researching Mathematics for High School Students with Calculus BC Background

[amcavoy]

I am a high school student (junior) and am looking to do some research over the summer and maybe enter a project into Intel or Siemens-Westinghouse. However, I will not have the opportunity to work with someone at a university. My background in mathematics isn't very strong, as I have only completed single-variable calculus (AP Calculus BC). I was just wondering if anyone could give me an idea of what topics I could study with this type of background. Also, where can I find a problem to tackle if I want to do research? I have gone to sites like PlanetMath, and looked through the "Unproven" section, but it is all much too advanced for me at this point. Any suggestions?

Thank you.

 

[neurocomp2003]

what field are you interested in?
biology, physics, chemistry, coding, info theory & Cryptography, social science,econ, psychology, pure math etc.

there are many projects to pursue at your level which will lead you to learning more advanced mathematics(if your willing to do so) in any chosen field

Think of a field of interest then you can discuss with others on the forums about the possibility. Once you've discovered a field and preferably a topic range then you can ask a professor about ideas on where to look. Some professors are nice enough to give you a starting point. You don't have to work for them, they'll just give you a references and stuff to look at but be prepared to do more self-reading. I once emailed a professor on parasitology and he sent me too book sin high school...i was grossed out.

Search for this book online...i think some parts are free Gary Flake's "Computational Beauty of Nature" i believe its from MIT...the math should be relatively easy. ITs a blend of math and programming with an applied science(biology for the most part).

mathematical biology may be something you might like...i enjoyed it very much. I'm waiting to study mathematical neuroscience.

 

[hhegab]

First of all, it is great to see that you are interested in conducting research in mathematics even with a limited background in the subject. With your background in AP Calculus BC, there are still many interesting topics that you can explore and potentially develop into a research project.

One suggestion would be to look into the applications of calculus in real-world situations. For example, you could research the use of calculus in physics, economics, or engineering. This would not only strengthen your understanding of calculus but also allow you to see its practical applications.

Another idea would be to delve deeper into the concepts of calculus, such as limits, derivatives, and integrals, and explore their connections to other branches of mathematics. This could lead you to study topics such as differential equations, vector calculus, or multivariable calculus.

As for finding a problem to tackle, you can start by looking at past research projects from Intel or Siemens-Westinghouse competitions and see if any of them spark your interest. You can also reach out to your math teacher or a local university for guidance and potential research opportunities.

Additionally, you can look for resources online such as math journals, research papers, or online communities where you can discuss and exchange ideas with other math enthusiasts. As you mentioned, PlanetMath is a great resource, but don't be discouraged if some of the topics seem too advanced. You can always start with simpler concepts and work your way up.

Overall, the key is to find a topic that interests you, and do not be afraid to ask for help and guidance along the way. Good luck with your research!