Math HL IA topic help

[JustanotherIBstudent]

Sorry for yet another IA help thread, but I seriously need some help deciding which topic to do my Math HL IA on. I've been thinking of doing my IA on types of cryptography, but my teacher shot down both of my ideas (RSA and Elliptic curve cryptography) saying they were too hard for an IA.

I could investigate the modular arithmetic side of RSA encryption, but I'm not sure if that's enough. My teacher also suggested to me to find earlier methods of encryption, but I don't know how to approach such a topic.

Other ideas I came up with are Gabriel's horn, but my class didn't learn integral calculus yet so I basically have to each myself in a week. I also thought about just picking a random lake and measuring the volume and surface area using calculus, which would involve the shoreline paradox and similar mathematics. Can you guys give me any recommendations? Thanks.

[JustanotherIBstudent]

Bump

Also I've been thinking of doing mine on the Enigma machine, although I'm not sure if there's enough mathematics to be explored there. Thanks guys.

[kw0573]

For these topics outside of syllabus, it's more important to demonstrate near complete understanding of basic stuff rather than superficial understanding of the whole thing, with the exception that if looking at multiple perspectives lightly can demonstrate how different topics of math are interconnected then it would be ok. 

So if you want to proceed with any of these topics, you should do preliminary researches and prove to your teacher that you can indeed understand and engage with these topics. IB sets the bar for difficulty only up to syllabus level, so you don't have to go much/anywhere beyond. Especially since your teacher thinks RSA/elliptical curve crytography may be too advanced, you should be fine. But the important thing to note is that some of these out-of-syllabus do terrible because students don't understand much and end up repeating what others have said without making any attempt making the knowledge their own. As long as you remember that the goal is to interact with any mathematics at least at the level of study (HL) without a huge emphasis on how "difficult" it may appear. 

[JustanotherIBstudent]

40 minutes ago, kw0573 said:

For these topics outside of syllabus, it's more important to demonstrate near complete understanding of basic stuff rather than superficial understanding of the whole thing, with the exception that if looking at multiple perspectives lightly can demonstrate how different topics of math are interconnected then it would be ok. 

So if you want to proceed with any of these topics, you should do preliminary researches and prove to your teacher that you can indeed understand and engage with these topics. IB sets the bar for difficulty only up to syllabus level, so you don't have to go much/anywhere beyond. Especially since your teacher thinks RSA/elliptical curve crytography may be too advanced, you should be fine. But the important thing to note is that some of these out-of-syllabus do terrible because students don't understand much and end up repeating what others have said without making any attempt making the knowledge their own. As long as you remember that the goal is to interact with any mathematics at least at the level of study (HL) without a huge emphasis on how "difficult" it may appear. 

Thank you so much for replying. I understand what you mean by proving to my teacher I can handle the topic, but my teacher also said it may be 'too much' for a math IA, as opposed to an extended essay. He said not only is the topic too hard to explain to my peers, but also does not allow a focused scope of analysis that the IA has room for. What do you think about my idea of the enigma machine? He recommended I do the IA on a specific type of encryption, but I'm not sure if there is enough math involved or just combinatorics/permutations. With more simpler forms of encryption and codes I can demonstrate personal engagement by creating my own code based on the ideas of the one I'm investigating, or come up with methods to crack them. Thank you.

[kw0573]

I am not very familiar with the Enigma machine. If I may rephrase my response, you should first prove to yourself that this is a good topic. And my previous reply would indicate that it would be enough even if you only describe the combinatorics and permutations (but you need to do it really really well). I certainly don't think it's bad topic, it just depends on how deep and what math and implications of math you want to dive in. IB encourages you to draw connections to seemingly unconnected math topics so even if there were only combinatorics and permutations, you would be awarded for making connections to the less visible aspects of math if you do it properly. 

[JustanotherIBstudent]

15 minutes ago, kw0573 said:

I am not very familiar with the Enigma machine. If I may rephrase my response, you should first prove to yourself that this is a good topic. And my previous reply would indicate that it would be enough even if you only describe the combinatorics and permutations (but you need to do it really really well). I certainly don't think it's bad topic, it just depends on how deep and what math and implications of math you want to dive in. IB encourages you to draw connections to seemingly unconnected math topics so even if there were only combinatorics and permutations, you would be awarded for making connections to the less visible aspects of math if you do it properly. 

Thank you, that makes a lot of sense. I think I can try to connect it to modular arithmetic. Are there any other types of encryption that you would recommend, perhaps easier forms? I feel like RSA has lots of modular arithmetic for me to explore, but it does seem slightly complicated. The enigma machine also seems like the mathematics involved is more rigorous rather than 'difficult'.