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Ideas for undergrad research

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Had a lot of fun with my undergrad math reading in quantum information. I understand there is some graph theory in that area WRT cluster and graph states.

Not sure how much serious undergrad level research there is but it’s a bit of a sexy area atm and might interest you.
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You should talk to a faculty member in your department about having them mentor you in a project. Doing research (even without novel results) on your own is not advisable as an undergraduate.
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Working through the four-colour problem would probably be a solid project.
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If you’re into graph theory, existence of strongly regular graphs is an interesting topic. You can also get into some spectral analysis and algebraic graph theory with just a basic knowledge of linear algebra. That being said, it is usually best to find a professor you like and work on whatever they’re doing though. The passion tends to follow the work, and you want to collaborate with professionals that you interact with on a regular basis. Good luck! Undergrad research is super fun and rewarding
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The discrete math behind a multiply and accumulate unit.
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Take a look on category theory, judging by the topics you've stated to be of your taste, I think you're gonna like it.
A good undergrad study linked to the topics you've stated would be something BASIC about model theory.

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