IA (HL) Math Exploration Help

[Lunatic_Strider]

Hey guys ,

 

I am in a wee-bit of a spot here . I need your help for my Math IA topic . So far I have thought of two topics : Time Dilation ( with Lorentz Transformation ) wherein I thought I would model the relative rate of decay of satellite components from a static/stationary point .

 

The second topic being : investigating why Riemann's zeta function does not produce argument at 1 . 

 

Thanks in advance for any advice/suggestion .

 

PS: I am a Math HL student .

Edited August 6, 2015 by Lunatic_Strider

[Vioh]

I am in a wee-bit of a spot here . I need your help for my Math IA topic . So far I have thought of two topics : Time Dilation ( with Lorentz Transformation ) wherein I thought I would model the relative rate of decay of satellite components from a static/stationary point .

The second topic being : investigating why Riemann's zeta function does not produce argument at 1 .

 

Hi, you should read my opinions about doing maths IA on relativity here.

Now, despite the fact that I think time dilation is a very dangerous topic for HL maths, I think that your topic might work, depending on how you are going to approach the topic. This is because the problem that you've posed is quite specific and might allow some HL mathematics to be used. I like the idea with satellites because it means that you will be using general relativity rather than special relativity. And in general relativity, there are lots of advanced mathematics that you can use, such as calculus (for gravitational fields), or non-Euclidean geometry (for curved space-time). However, I'm not too sure whether this topic is actually appropriate. I need to know more about what types of mathematics you will be using and how you are going to try to solve the problem that you've posed, in order to give you more advice.

For the second topic, I don't really get what you mean.

[ctrls]

For the second topic, I would recommend avoiding the zeta function. Since the function is defined as an analytic continuation, you really need to understand and be able to explain the definition in order to investigate it. This is especially the case for showing that the value is undefined for s=1, you need to refer to the definition.

 

You could consider the series on its own though, looking at convergence/divergence (this is covered in the calculus option), determining the value when it converges and how it varies with s, etc. Dealing with infinite sums requires a fair bit of care though, plus I'm not sure of what exactly you could investigate.

[Lunatic_Strider]

Okay so since my last post , I've varied my topic quite a bit . I would now concentrate on finding the time dilation occurring between two satellites ( which I have taken as Voyager 1 and Pioneer 10 ( as they are moving in almost opposite direction ) ) during their communication with each other . Since they both have a hyperbolic trajectory : I plan to use the topology , 4-d vectors and lorentz transformation to map their positions . I would then model their respective velocity ( since they are moving away ( I could use galilean transformations but since I am using Lorentz , I will be focusing on special relativity )  with respect to ( not sure whether ) speed of light or spacetime : and then use differential equations ( not too sure about elliptical partial equations ) and evaluate the rate of change at which they would communicate on further increase of distance ( which one can find by calculating the area under the curve ) .

 

The only aspect which now worrying me is length contraction which would occur .

Edited August 23, 2015 by Lunatic_Strider