Math Essay Topic

[BassamAF]

Hey

So I was fortunate enough to bare the assignment of writing a four-thousand word essay concerning Math. What I'm having trouble with at the moment is choosing a topic and a research question that falls into what is needed, which is for the research being beneficial for the society.

So I can't go into "The History of Math" or "The History of Calculus" or anything like that. Neither can I have something that is purely Math but non beneficial, for example, at first I wanted to go for Perfect Numbers and researching, testing, and trying to come up with the conclusion which is either Perfect Numbers are infinite or not, but that turned out to not be beneficial.

I am currently in Grade 11, we studied Trigonometry, Quadratic Functions & Inequalities, Functions, Polynomials, Logarithms and Exponentials, Sequences, Series and the Binomial Theorem, and currently Complex Numbers, which is interesting me more than anything else. I would really not mind the topic being something that I still haven't studied, it wouldn't really make a difference other than that if it included anything that I've learned throughly, it would be easier.

One of the past essays on Math that interested me was one trying to come up with a formula to show the amount of different combinations a Rubik's cube can have using the amount of squares, faces, colors, etc as variables, I would really like to have something of that caliber.

Excuse my lack of creativity, thanks!

 

[GundamSentinel]

How about an equation for smooth descent slopes of roller coasters? Or equation of sprinkler water pressure as function of the water level in a fixed tank that's being refilled at rate x? Optimal ways to slice a pizza?

Or mess about with chaos theory and it's impact on meteorology or astronomy. Astronomy is always a good field for mathematics problems. Mathematical analysis of rocket ascent stages or planetary orbits?

 

[BassamAF]

I'm digging the ideas, but what I'm asked (Or ordered to do) is more inclined towards pure mathematics, rather than having Physics and Astronomy related, but the Analysis of a rocket ascent stages sounds pretty awesome, thanks for the help

 

[HannesPascal]

What about this: http://escherdroste.math.leidenuniv.nl/
Explain what it's about, what Bart de Smit and the rest of the bunch did and how they did it.

 

[BassamAF]

Now that's REALLY interesting... But it would probably be rejected for it not being useful for an advance in the human race or other kinds of nonsense we're forced to oblige with.

 

[meticadpa]

Write about why e^(pi i)is -1.

Although that's not really beneficial...

Calculus. Show how it's used in everything.

 

[caselj01]

Im not really sure how you are supposed to come up with a question that is directly 'beneficial to society' without being physics/astronomy etc related. Maths does not really benefit society itself, its a tool which is used by scientists/engineers and so forth in order to discover/create things which benefit society.

 

[BassamAF]

Write about why e^(pi i)is -1.

Although that's not really beneficial...

Calculus. Show how it's used in everything.

Yeah I'm thinking of doing the Calculus thing for wave functions and such, thanks!

Im not really sure how you are supposed to come up with a question that is directly 'beneficial to society' without being physics/astronomy etc related. Maths does not really benefit society itself, its a tool which is used by scientists/engineers and so forth in order to discover/create things which benefit society.

True, but then again like the Rubik's cube example, it can be just purely math relating to just probability or just statistics... Although I can write about things that aren't completely about Physics, like for example, a few years ago somebody wrote about the Mathematical issue with the Ideal Gas Law, trying to prove that it's actually wrong or something along these lines.

 

[dWintermut3]

Im not really sure how you are supposed to come up with a question that is directly 'beneficial to society' without being physics/astronomy etc related. Maths does not really benefit society itself, its a tool which is used by scientists/engineers and so forth in order to discover/create things which benefit society.

Very well put. Math is just a model of the universe. What you do with that model, how you *apply* the math is what counts. In everything from physics to engineering to cryptography.

If you're looking for "hard math" that helps people, why not look into cryptography or computer security, where it's largely all about relatively fundamental non-applied math? An analysis of how quickly a password can be broken by various attacks (dictionary attack, sequencer attack, ect) with various attributes would be educating and a great real-life application.

You could look at several kinds of attack. One would be the straight sequencer brute-force. Go through every combination starting with 1 and ending with zzzzzzzzzzzzz. Then you could look at a dictionary attack using a good comprehensive dictionary like the OED. Then a targeted dictionary attack that started with the most common passwords (12345, common pet names, ect.)

the advantage here is that this research has already been done before so you could check your work, but it's not often fully shown with calculations for many types of attacks in one place. For instance many sources I look at for, for instance, showing how hard a password is to crack based on length, are based on only a crude sequential attack not a more sophisticated randomized augmented dictionary attack.

 

[Jacob Lucas]

Make it about what would happen if a tornado hit a volcano.

 

[BassamAF]

Very well put. Math is just a model of the universe. What you do with that model, how you *apply* the math is what counts. In everything from physics to engineering to cryptography.

If you're looking for "hard math" that helps people, why not look into cryptography or computer security, where it's largely all about relatively fundamental non-applied math? An analysis of how quickly a password can be broken by various attacks (dictionary attack, sequencer attack, ect) with various attributes would be educating and a great real-life application.

You could look at several kinds of attack. One would be the straight sequencer brute-force. Go through every combination starting with 1 and ending with zzzzzzzzzzzzz. Then you could look at a dictionary attack using a good comprehensive dictionary like the OED. Then a targeted dictionary attack that started with the most common passwords (12345, common pet names, ect.)

the advantage here is that this research has already been done before so you could check your work, but it's not often fully shown with calculations for many types of attacks in one place. For instance many sources I look at for, for instance, showing how hard a password is to crack based on length, are based on only a crude sequential attack not a more sophisticated randomized augmented dictionary attack.

I like that idea, It would also include the probability of the usual birthday password, thanks!

Make it about what would happen if a tornado hit a volcano.

No... Okay maybe

 

[Outright Villainy]

Write about why e^(pi i)is -1.

Although that's not really beneficial...

It'd be beneficial to my sanity.

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