High school project in mathematics, original research

In summary, the individual is seeking suggestions for areas of mathematics that would be suitable for original research as a high school student. They express interest in the foundations of mathematics, specifically proof theory, set theory, and mathematical logic. However, it is noted that it may be difficult for a high school student to conduct original research in certain branches of mathematics, such as abstract algebra. The person suggests combinatorics as a potential area to explore. They also mention their preference for a "pencil-and-paper type of research project" rather than programming. Another individual suggests the boolean satisfiability problem as a potential research topic, but notes that they are not qualified to offer book recommendations on the topic.
  • #1
saltkraxen
8
0
I have been thinking about doing my 'high school project' in mathematics and I would like to do some original research.

So my question is: Which areas of mathematics would be most suited for me? Having in mind that I'm still in high school, although I have taken some (fundamental) math courses at my local university. And could you give an example of how a research question could be framed. :)

Areas that fascinates me:
Foundations of mathematics: Proof theory, set theory, mathematical logic.

Sub question: Could a high schooler do original research in say proof theory?

To mod: I put the thread here because I'm mostly interested in hearing about the foundations of mathematics (but all suggestions are of course very welcome), but if you think that it belongs elsewhere; please move it.
 
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  • #2
It's unlikely, though certainly not impossible, that a high school student could manage original research in mathematics; there are some branches of mathematics (e.g. abstract algebra) that require very extensive knowledge before you even can even understand the statement of a research question. Combinatorics might be a good branch of mathematics to look into, in that many problems have very simple formulations, can be easily understood, and often don't require extremely advanced techniques to solve.
 
  • #3
saltkraxen,
Are you skilled in writing computer programs or are you seeking a pencil-and-paper type of research project?
 
  • #4
Stephen Tashi said:
saltkraxen,
Are you skilled in writing computer programs or are you seeking a pencil-and-paper type of research project?
I have done some programming (I'm neither good or bad), although I would like a "pencil-and-paper type of research project".

Thanks for the answers and keep them coming. :D
 
  • #5
I don't claim to have any qualifications for suggesting research in mathematical logic. However, this problem has always interested me: http://en.wikipedia.org/wiki/Boolean_satisfiability_problem.
You aren't likely to solve the general problem but you might try cases where the boolean expressions have a more restricted form. Part of "research" is just looking up what is currently known about problems. I don't know enough to be helpful with that. Some other forum members probably do.
 
  • #6
Stephen Tashi said:
I don't claim to have any qualifications for suggesting research in mathematical logic. However, this problem has always interested me: http://en.wikipedia.org/wiki/Boolean_satisfiability_problem.
You aren't likely to solve the general problem but you might try cases where the boolean expressions have a more restricted form. Part of "research" is just looking up what is currently known about problems. I don't know enough to be helpful with that. Some other forum members probably do.
Thanks, this looks really interesting! Can you recommend any good books on the topic?
 
  • #7
I'm not familiar with any books that cover the boolean satisfiability problem. (But I'm no a logician, so there might be some.)
 

What is the purpose of a high school project in mathematics?

The purpose of a high school project in mathematics is to allow students to apply the concepts and skills they have learned in the classroom to a real-world problem. It also helps students develop critical thinking and problem-solving skills and encourages them to explore their own interests within the field of mathematics.

What makes a high school project in mathematics considered "original research"?

A high school project in mathematics is considered original research when it addresses a unique problem or question and proposes a new solution or approach. This could involve conducting experiments, developing models, or analyzing data to gain new insights or make original contributions to the field of mathematics.

What are some examples of high school projects in mathematics?

Some examples of high school projects in mathematics include analyzing patterns in data, creating mathematical models to solve real-world problems, exploring geometric concepts through art, and conducting statistical analyses on a topic of interest.

How do I choose a topic for my high school project in mathematics?

When choosing a topic for your high school project in mathematics, it is important to select something that interests you and aligns with your strengths and skills. You can also seek inspiration from current events, your own curiosities, or discussions with your teacher or peers.

What are some tips for successfully completing a high school project in mathematics?

To successfully complete a high school project in mathematics, it is important to start early, stay organized, and seek help from your teacher or other resources if needed. Make sure to thoroughly understand the problem or question you are addressing, and document your process and findings carefully. Finally, be creative and have fun with your project!

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