Research that highschoolers could do during the summer.

[jbmiller]

I've read in numerous places that most people applying to the higher education colleges for areas such as physics have already done some sort of research. I'm currently a freshman in high school and am looking to get into a top-notch college, but my main road block is getting started with research. I would probably hold off on the research until the end of my sophmore year, but even then I will have no idea on were to start with research.

Basically what I'm asking is that someone give me some ideas and places to start with research, I do live in Kansas if that helps at all.

 

[Bearded Man]

You cannot make a meaningful contribution to physics as a high school student (usually). To do so you would first need to be proficient in the various areas of physics, all of which have advanced mathematics as a prerequisite.

 

[jbmiller]

I know, but I wouldn't be looking to make a meaningful contribution. Just to simply show to colleges that I have more than the grades in the incredibly advanced classes and test scores.Your comment shows that I have no clue where to start and what I would even do...

 

[chiro]

I've read in numerous places that most people applying to the higher education colleges for areas such as physics have already done some sort of research. I'm currently a freshman in high school and am looking to get into a top-notch college, but my main road block is getting started with research. I would probably hold off on the research until the end of my sophmore year, but even then I will have no idea on were to start with research.

Basically what I'm asking is that someone give me some ideas and places to start with research, I do live in Kansas if that helps at all.

What experience do you have with anything (this is not a derogatory comment, but an honest question to get you thinking)?

Have you played with electronics? Done any programming? Familiar with anything particular? Familiar with any mathematics?

If you have done any of the above, then IMO you can find something small and manageable but still useful to work on. It doesn't have to (and it won't) win you the Nobel Prize or anything else but it will get you thinking about research in the way that:

a) You will be clarifying your ideas for research topics and exactly what you are trying to finf
b) You will be doing things on your own, organizing information on your own, and figuring stuff out which is what research entails in a very high degree.

The above needs to be done for any kind of research and it's important that any experience you can get doing this kind of thing is worthwhile if you want to do research of any sort no matter how big or small you may think it is (or how big or small anyone else thinks it is as well).

If you haven't done any of these things in depth but a curious then take the time out to learn something. With programming you can get everything you will possibly need off the internet including stuff that is free. There is also a lot of free stuff for electronics but you'll have to purchase some physical stuff. Lots of stuff available for mathematics and even lecture notes and books can be found for free on the internet as well.

What you will end up doing if you pursue the path of research is you will get to a point where you have clarified something specific enough to work on. It may not be as specific as it will be because it may get clearer as you progress but to get to the initial point you will need to write down specifically the problem you are trying to solve or if it's an investigation, the specific thing you are trying to investigate.

To do this you will need to understand the field enough to know what language is used (mathematics, engineering, physics, chemistry, other sciences, technical fields, whatever) so that you can describe these goals clearly in that language. If you can't describe it, you can't solve it: it's as simple as that.

Once you are able to describe what you are actually trying to solve or trying to find then you take it from there by seeing what's out there, what other people have done, what other people are thinking and so on but you can't really start until you have gotten to this point.

Also by the time you get to this point you will have probably learned enough about the field to know it in a deep way but not so deep that you are an expert and that is ok. The big things to take note of, is that you will need to know the language that is used, the concepts, the ideas currently being circulated and you will need to have in your mind a few key ideas of what it all means at a superficial level. The connections will be made with effort, thought, and time so don't worry if it doesn't all make sense straight away.

 

[jbmiller]

Thanks Chiro, this helped a lot!

I would probably start my research after my sophmore year, which means I will have taken physics, chemisty, and pre-calc.

I'm hoping one of my friends will work on the research with me, he's currently taking Pre-Calc as a Freshman. If he worked with me there's no doubt that we would get up and going and learn an incredible amount!

 

[eri]

Taking classes at a local college is probably the best place for you to start. Not a community college, but a university or 4-year college where professors are doing research. If you can take those while in high school and do extremely well in the classes (math, physics, etc) then you might be able to convince a professor there to take a chance on you as a research assistant. Keep in mind that high school students are not useful - even grad students sometimes aren't useful. Professor will not be compensated in any way for taking you on as a research assistant, but it will take up a lot of their time, so you're asking for a very large favor from them. You need to be willing to put in the work to justify them bothering to take you on. Spending the summer learning how to program (Perl, Python) would be a good start.

 

[jbmiller]

Where exactly would I start with the programming? Could you give me some softwares of books/websites that I could use to put me on a course. I'm not very familiar with programming so I would need to know what I would even be studying.

 

[eri]

This looks like a good place to start.

http://wiki.python.org/moin/BeginnersGuide

 

[micromass]

Maybe you can take part in a science fair. That's a bit more doable than research.

 

[genericusrnme]

A summer project?
I'd read all of the bourbaki books (or at least the first 2 or 3, all of them in one summer is a bit of a task) :3

 

[micromass]

A summer project?
I'd read all of the bourbaki books (or at least the first 2 or 3, all of them in one summer is a bit of a task) :3

Are you serious?

 

[genericusrnme]

Are you serious?

About reading them all in one summer? no
About reading 2 or 3? no/a little

Summer's about 3 months right?
You could probably get through 2 or 3 in 3 months if you worked hard enough at it but that being said a neophyte would probably get a little chewed up by them.
They are quite nice books though imo.

Your reaction made me chuckle a little though, something I don't regularly do whilst browsing online forums, well done.

 

[micromass]

I think that reading a book like Euclid would be a very nice thing to do during the summer though...

 

[micromass]

Actually it depends. What do you find interesting? What do you want to do in college?? Physics, math, chemistry, bio, engineering??

 

[jbmiller]

Saddly, our school doesn't have a science fair competition.

And what exactly would programming do for my science/math skills?

I'm looking for straight science, not computer science.

 

[Shaun_W]

Programming skills are extremely important for many physicists and engineers. But most importantly it is something that you can do right now, for no additional cost, as no equipment that you don't already have is required. You're probably not going to be able to create a worthy lab experiment in your bedroom over summer, but you can easily start learning to program.

 

[micromass]

You WILL have to learn programming sooner or later. Most mathematicians, physicists, engineers, etc. are familiar with programming and use it in their daily research.

And there is no reason at all why you can't combine programming with straight science. Here are some ideas of things you can do:

If your interest is mathematics, then you can try to solve things in Project Euler: http://projecteuler.net/ Very challenging exercises. They will help your math skills and your programming skills.

You try to build a simulator of a three-body problem in physics. You can use this opportunity to study some chaos theory, dynamic systems, basic physics, etc.
Or you can try to model two bodies and then investigate what happens in your simulator. You can use this to study ellipses and conic sections. Maybe you can even read up a bit on calculus to prove Kepler's laws.

A favorite hobby of mine when I was learning to program is to look at mathworld for basic stuff and then program them in a computer. I learned a lot of math and programming that way.

Or you can write a program that simulates evolution and genetics in biology, if that's your thing.

Or make some Monte Carlo simulations. An interesting problem, for example, is the following: say that you want to marry a girl. There are 100 suitors and you which to pick the best one. You are placed in a room and get to see the girls one by one. So, the first girl comes in. At that point, you have to say whether to marry her or not. If you don't marry her, then you can never marry her again. In that case, the second comes in and you will have to do the same thing. If you reject all 99 girls you see, then you will HAVE to marry the 100th one.
What's the best way to get the optimal choice? I wrote a computer program once to solve this. After you did it, you might want to derive the result theoretically.
This is one example of a Monte Carlo simulation. There are many more. Another question: what is the most popular spot on the monopoly board?? What's the best thing to buy??

Programming is certainly something you can do NOW. And you'll benefit a great deal from it in the long run. And perhaps you'll even find it fun.

It's basically impossible to do innovating research. You don't even know what you don't know and what the unsolved problems are.

Other projects can include building something: dismantle a radio and try to put it back together. Those sorts of things. If you're into engineering, then this'll be useful as well.

 

[jbmiller]

Thanks Micro, I will make it one of my main priotities this summer to begin programing.

What basic math skills would you say are required to solve things on project Euler?

 

[micromass]

Thanks Micro, I will make it one of my main priotities this summer to begin programing.

What basic math skills would you say are required to solve things on project Euler?

Depends really. I guess to understand the problems and to understand the solutions, then algebra and trig should be enough.
But to find the solutions, you'll need something more.

It's not the point to find all the solutions all by yourself. The point is that you do some research (on the internet for example) and you read results that other people have proven. You can use those results in solving the problem.

For example, in soving problem 9: http://projecteuler.net/problem=9 you need something about pythagorean triples.
This might lead you to results such as given in
http://www.math.uconn.edu/~kconrad/blurbs/ugradnumthy/pythagtriple.pdf
which might allow you to solve the problem.

The point of course is to show you diverse sides of mathematics. You could search the results and apply them without thinking. But it is more fun to actually read the proofs, derivations and the background information to everything.
The idea is to become proficient in programming and to learn techniques in mathematics.

Of course, the solutions to all the exercises can be very easy using brute force: just check every possible case. But the idea is to find an efficient and fast algorithm (the program should finish in maximum a minute). This requires mathematics.

The good thing is, once you solved a problem, you get acces to a forum where other people discuss the problems. That way, you can see other techniques people used and which might be better than your techniques. Use this to your advantage!

 

[jbmiller]

Oh ok, well I'm taking Alg II over the summer then Pre-Calc my sophmore year(I'm currently a freshman), but I might still be able to do some of the problems. Also, my mom is a genius at math, she would be totally up for figuring out challenging problems with me!

 

[AlephZero]

What basic math skills would you say are required to solve things on project Euler?

The site suggests you work through the problems more or less in sequence. The first ones don't need much specific math knowledge, they are mostly about "playing around with numbers" using basic arithmetic. Of course the real objective is to program your computer to help you do the "playing around" to solve the problem, rather than working out the complete solution by hand.

Along the way, you might discover some general results that you could write as a "formula" or a mathematical theorem, of course. For some of the seriously hard later problems, you might even discover some genuinely unknown math if you attack the problem a completely different way from what has been done in the past...

 

[jbmiller]

Oh ok, I will probably take on the problems I am capable of doing. And even yet attempting more challenging ones, it doesn't hurt to try.

I just finished downloading the Python programmer, time to start experimenting.

Any ideas on where to start with the Python program?