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# Interesting mathematic topics? Watch

1. yO!!! I'm designing a poster meant to aimed at a-level students to do a mathematic related degree. But I'm not sure what I should base it on. Some interesting topics I've come across have been listed below, If you know any more please help me out !

Fractals
Chaos Theory
Zeta Function
Cryptography
Golden Ratio
Fibonacci numbers (Relation to music)
Projective Geometry
Markovian Spam Filtering
2. I'd have to say, I'm doing a maths degree and all of the things you've mentioned (with the exception of the golden ratio and Fibonacci numbers) have either not been covered or only briefly mentioned.
3. (Original post by ttoby)
I'd have to say, I'm doing a maths degree and all of the things you've mentioned (with the exception of the golden ratio and Fibonacci numbers) have either not been covered or only briefly mentioned.
Perhaps you're not doing the right courses then? Some of those are covered in a third or fourth-year course in Cambridge:

Chaos Theory - Dynamical Systems (3rd year)
Zeta Function - Number Theory (3rd year)
Cryptography - Coding and Cryptography (3rd year)
Projective Geometry - Algebraic Geometry (3rd year, 4th year)

What is true, though, is that first and second year undergraduate mathematics tends to be rather less exciting.
4. (Original post by Zhen Lin)
Perhaps you're not doing the right courses then? Some of those are covered in a third or fourth-year course in Cambridge:

Chaos Theory - Dynamical Systems (3rd year)
Zeta Function - Number Theory (3rd year)
Cryptography - Coding and Cryptography (3rd year)
Projective Geometry - Algebraic Geometry (3rd year, 4th year)

What is true, though, is that first and second year undergraduate mathematics tends to be rather less exciting.
Good point. I'm a 2nd year undergraduate in Warwick so that would probably explain why I haven't seen them yet.

To the OP: Maybe you could consider doing a three-dimensional surface plot of some function f(x,y) and calculating partial derivatives and marking them on the diagram? Then you'd have some maths that would be fairly understandable by A-level students as well as the nice pretty picture of the surface plot that would work well on a poster.
5. (Original post by ttoby)
Good point. I'm a 2nd year undergraduate in Warwick so that would probably explain why I haven't seen them yet.

To the OP: Maybe you could consider doing a three-dimensional surface plot of some function f(x,y) and calculating partial derivatives and marking them on the diagram? Then you'd have some maths that would be fairly understandable by A-level students as well as the nice pretty picture of the surface plot that would work well on a poster.
Can you expand on this? Possibly give me some links explaining this stuff ;3
6. (Original post by Zhen Lin)
Perhaps you're not doing the right courses then? Some of those are covered in a third or fourth-year course in Cambridge:

Chaos Theory - Dynamical Systems (3rd year)
Zeta Function - Number Theory (3rd year)
Cryptography - Coding and Cryptography (3rd year)
Projective Geometry - Algebraic Geometry (3rd year, 4th year)

What is true, though, is that first and second year undergraduate mathematics tends to be rather less exciting.
Is the Cambridge Number Theory course rather analysis based? Also, would you happen to know of any good books for a newcomer to the subject? (Familiar with elementary number theory and real/complex analysis, of course)

I was extremely disappointed when Bristol canceled their analytic number theory course before I had a chance to take it.
7. 'interesting' and 'maths', should not co-exist in a sentence.
8. i found cryptography horribly tiresome & boring.
9. (Original post by Kevlar)
Can you expand on this? Possibly give me some links explaining this stuff ;3
I was thinking something along the lines of putting a 3D graph like on here: http://www.wolframalpha.com/input/?i=f%28x%2Cy%29%3D-y^2+%2Bsinx then maybe doing some calculations relating to the function being plotted. I'm not really sure what to suggest specifically though.
10. (Original post by majikthise)
Is the Cambridge Number Theory course rather analysis based? Also, would you happen to know of any good books for a newcomer to the subject? (Familiar with elementary number theory and real/complex analysis, of course)
I'm not taking the course, but I suspect it's elementary algebraic number theory. We don't have an analytic number theory course, as far as I know. (Oxford does.)
11. (Original post by Zhen Lin)
I'm not taking the course, but I suspect it's elementary algebraic number theory. We don't have an analytic number theory course, as far as I know. (Oxford does.)
Probably unlikely to include zeta functions then!

Judging by walking into the wrong lectures by mistake, I think fractals are dealt with in third/fourth year analysis at Bristol- not sure about elsewhere. Possibly it's common to briefly touch upon fractal dimension in topology?

Banach-Tarski should definitely be mentioned in any list of interesting topics. Also chuck in mentions of a few random things with slightly silly names- monstrous moonshine or the Tits group, perhaps?
12. (Original post by majikthise)
Probably unlikely to include zeta functions then!
Not in depth, but the definition is given. (Yes, including the integral form and the functional equation form.)

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