Math Extended Essay: Contour Integration is my topic too advanced?

[JesseWilkins]

I am a Sl student interested in doing my extended essay in mathematics. I became very interested in contour integration.  The thing is I am not sure if this topic will be too advance. I heard that if your topic is too advanced it goes against you. Any advice would be appreciated. 

[kw0573]

Topic too advanced by itself will not hurt you. But if you were to not explain any concept properly or misuse math then it might be used against you. Contour integrals may be too advanced. You can first try some easier multidimensional integration, such as path integrals, line integrals, or even surface integrals. The first two will be a more than sufficient challenge and will incorporate concepts from functions, trig, and vectors. 

Edited April 10, 2017 by kw0573

[JesseWilkins]

On 4/10/2017 at 5:12 PM, kw0573 said:

Topic too advanced by itself will not hurt you. But if you were to not explain any concept properly or misuse math then it might be used against you. Contour integrals may be too advanced. You can first try some easier multidimensional integration, such as path integrals, line integrals, or even surface integrals. The first two will be a more than sufficient challenge and will incorporate concepts from functions, trig, and vectors. 

 

What about Stoke's theorem?

 

[kw0573]

I mean I don't know how much calculus you know and I don't want to discourage you from doing a topic you are fully capable of. It's interesting. I have taken multivariable calculus and stokes theorem is pretty up there. I think you have to have a very solid understanding of calculus and of vectors to appreciate it. It's also important to realize in any EE, you cannot just replicate what you find in a textbook and you have to shown engagement with the material. I think it's a big challenge to include stokes theorem and do it well. 

[kw0573]

Here are some unsolicited advice
1) Just understanding what a textbook says is not research. Sure that shows some knowledge and understanding, but that is only 6/34 marks. 

2) Therefore (and you won't like this), you should start with a topic that you know well, rather than one where you have to learn all the math then do research. For example in calculus, what are some questions you are uncertain about? What do you find interesting? What do you like to know more about? How can you relate new material to what you learned in class? 

 

[SC2Player]

I'd just like to add on to @kw0573's advice in regards to finding a topic.  Try taking a theorem or concept that you already know, do a little bit of tweaking here and there, and see where it gets you.  For example, you could take something as simple as the well-known divisibility rules for integers such as 2,3 and 5, and try to prove them.  Then see if there is a pattern for various integers.  And then try to find more patterns, etc. etc.  My own math IA started with the triangular numbers, and generalizing them led to surprisingly interesting results.  

[JesseWilkins]

On 4/13/2017 at 4:45 AM, SC2Player said:

I'd just like to add on to @kw0573's advice in regards to finding a topic.  Try taking a theorem or concept that you already know, do a little bit of tweaking here and there, and see where it gets you.  For example, you could take something as simple as the well-known divisibility rules for integers such as 2,3 and 5, and try to prove them.  Then see if there is a pattern for various integers.  And then try to find more patterns, etc. etc.  My own math IA started with the triangular numbers, and generalizing them led to surprisingly interesting results.  

 

I'll take that into consideration.

On 4/12/2017 at 9:53 PM, kw0573 said:

Here are some unsolicited advice
1) Just understanding what a textbook says is not research. Sure that shows some knowledge and understanding, but that is only 6/34 marks. 

2) Therefore (and you won't like this), you should start with a topic that you know well, rather than one where you have to learn all the math then do research. For example in calculus, what are some questions you are uncertain about? What do you find interesting? What do you like to know more about? How can you relate new material to what you learned in class? 

 

 

Don't worry about that. I was thinking about just that all the way through. I was thinking of a lot of other things as well. Thanks for your help tho.