Math Extended Essay Ideas

[KyleAdams]

I have a few different general topic ideas, I just don't know how to turn those into a condensed RQ. Please give me suggestions if you know of any that would fit with the topic. I kind of just need something to stimulate my brain to start thinking up more ideas.

1) Combinatorics

2) Fractals

3) Golden Ratio

4) Derivatives

If you have any ideas of an RQ I could develop out of those topics please don't hesitate to respond. I am already way behind in my choosing of a topic, because I had originally wanted to do English thinking it would be easiest, but I decided to go with math, something I really enjoy.

Thanks

I did some thinking about a different topic. I started thinking about doing an EE about the math in music. I think an EE on the math of the Harmonic/Overtone Series would be doable, and I could incorporate trig functions like sine cosine based on the sound waves and show how sound waves turn into overtones and such.

Does this seem like a doable topic? I don't have enough research done to know an exact RQ, but that is the sort of outline of a topic.

[ShineeLikeMe]

Ohhhh golden ratios! My friends doing that and connecting it with religion.

[dessskris]

Hello mate, I was also about to do Math in Music too! Haha is this a fate or what?

Ok so I read stuffs about John Cage, Philip Glass, Aleatoric Music, etc. I haven't really found something doable since my first topic turned out to be not so doable, so I am still looking for ones.

I do not know how difficult your topic is, because I do not have such a background in Music. However, you should know whether it is difficult enough and worth doing. SS said that music and math ARE interrelated but it usually only involves simple maths, so it ain't difficult enough for an EE. I do not know, but I guess it would be really hard to find even a general topic, and moreover to form a research question. If you want to do that, you should make sure that your EE would be a Math EE and not leaning towards a Music EE. Your Math supervisor should also understand Music. I hate that it is so hard for us just to find an EE topic

[JoeG]

http://www.tedbursa.k12.tr/ib/html/maths.html

Well, here are some top scoring extended essays on a schools website that you can use as examples.

There's no problem with doing an extended essay in Maths, just make sure you can do the work though. One of the IB teachers who's been teaching IB for the longest amount of time (Edit: for my school lol) said there was a girl one year who had "faked" some of the math on her extended essay, and therefore got an E on it. So, pick a topic that you know you'll be able to comprehend, so you won't have to be making up formulas at 5AM before school starts lol.

Edited October 17, 2010 by JoeGuff

[KyleAdams]

I think there are sufficient topics that could be done for math that relate to music. There is the logarithmic scale, for instance, that the frequency of pitches is based on. It is something like a logarithm with a base of 1/212. I think if I do the harmonic series and overtones then I can possibly do something that relates the graphs of the sine curves that model each of the sounds and then show how they relate to the overtones and such. I don't know for sure, that is just a possibility, I just am at a loss for any other topics. If anyone has any ideas based on any of the possibilities I have presented, then please let me know.

Thanks

[JoeG]

Remember, you don't always have to stick to Maths, even though there are many topics you can write an excellent essay on. If you can't think of something/further build up a topic then don't feel bad if you have to kill it off

During the summer before IB1, I had a topic that I came up with that I absolutely loved. When I learned there wasn't anywhere to go with it and the topic would be too difficult/long for an extended essay, I decided to choose another, completely different topic. The topics were even in different subjects lol.

Edited October 17, 2010 by JoeGuff

[KyleAdams]

I know I don't have to do math, but it's the one subject I really enjoy and that I want to go on with in college most likely. I think this is something I really want to do, even if I don't have a topic yet. I think my indecisiveness is partly the problem, but I just can't tell if something is a good enough topic or not. I think there is enough to do with the harmonic series and overtone series but I am not certain.

Well I am not really sure if I will stick to the music one, but I am now looking at combinatorial game theory, and I also looked through Heinrich Dorrie's 100 Great Problems of Elementary Mathematics. Some of those problems looked interesting so I may see if I can do one of those. What do you think? Some of the better problems I saw in that book were the following:

The problems about finding location based on astronomy.

Steiner's Sphere, Circle, or Ellipse problem.

The Square as an Image of the Quadrilateral.

Berwick's Problem of the Seven Sevens.

Bernoulli-Euler Problem of the Misaddressed Letters.

Euler Problem of Polygon Division.

The Euler Number.

Nicolaus Mercator's Logarithmic Series.

Newton's Sine and Cosine Series.

Fermat-Gauss Impossibility Theorem.

Gauss' Fundamental Theorem of Algebra.

Those are some of the ones I think I could do. Anyone have any comments about them? Also, is it true that the research question has to somehow be applicable to real life? Can it not be solely theoretical or something?

[dessskris]

I am now looking at combinatorial game theory, and I also looked through Heinrich Dorrie's 100 Great Problems of Elementary Mathematics.

Also, is it true that the research question has to somehow be applicable to real life? Can it not be solely theoretical or something?

The RQ can be something theoretical, BUT it is often said that a theoretical Math EE which is not applicable to real life could only score a B. If you do not mind getting a B, go ahead. Otherwise, just play safe.

I know that finding a good topic is very hard, as I also feel it; but now that you have stuffs (ideas), show them to your MATH TEACHER first. Or probably your EE supervisor if you have already got one. They will then decide which one is good, which one is not good. They should know better than me and so I cannot say which of those problems are good since I do not know what they are all about. A lot of apologies.

However, I am also going to do my EE in Math. I currently have some ideas, but I am not sure whether they are good. Do you want to share ideas with me? You have already written some in here, though if you want to know, go PM me, so we can discuss more freely

[genepeer]

A topic (in combinatorics) I found quite interesting but barely knew where to start with it: Since my guess is "Not all solitaire games are solvable" (or are they?), what are the chances that a solitaire game is solvable? This could be extremely hard to do so one might want to look at a simplified version of the game and try extrapolating the results; or maybe play a thousand solitaire games to get an idea of the probability lol.

[KyleAdams]

http://www.tedbursa.k12.tr/ib/PDF/Mathmatics_3.pdf

I think that EE is purely theoretical,and it is on the "50 Excellent Extended Essays" list put out by IB.