@Anon hey. It is quite hard question. The "undergraduate knowledge" is not something well defined, you haven't given the purpose (hobby, project, etc.).

@Anon And the level - how hard it should be.

@Evil I just want to kind of break into TCS research. The purpose is for a project in order to produce something substantial. I know the basics of advanced mathematics; as in, some combinatorics, how to prove things, and some basic number theory.

I'm reading sipsers and Ullman's respective texts right now, but I was wondering if someone could give me more personalized advice.

There are open problems with substantial outcomes - deterministic linear time hashing, deterministic linear time uniqueness problem, Collatz conjecture from number theory ;)

Interesting

I will write those down, thank you!

@Evil. Would you recommend for me to prioritize number theory over statistics?

Personalized advice might just go wrong, those are open problems, so it is very hard.

@Anon I do not know, what do you expect? What is the goal?

I want to try to get my foundation knowledge as quick as possible

I apologize if these questions are a bit annoying, but right now I have Statistics, Linear Algebra, and Discrete Mathematics planned for this semster; however, I'm thinking of switching the statistics out with number theory and differing it.

deferring&

@Anon so maybe some easier problems? Well, in that case I would recommend to get as much as possible, not switching.

@Evil If you have any easier problems, I would love to hear them.

Fast detection of number being a^2 * b without factorization, fast (minimal) perfect hashing.

@Anon so you are going to be researcher?

@anon hi welcome to the site/ chat. research is usually very personalized & connects with your own strengths/ interests. so what are they? TCS is very broad now. for ideas try browsing this eg via the sections, can reply on questions on it etc vzn1.wordpress.com

you mention number-theory. have seen a few undergrad senior papers on eg the collatz conjecture & theres a lot on the site wrt that

what country/ school are you at?

I live in the United States.

@Evil Thank you for the reply. Yes, I want to try to be a TCS Reseacher.

@Anon what state? school confidential for now? what is your undergrad degree in? have you done any undergrad prjs?

@vzn, I'm a bit shy to share that information but it's a state school as in like university of x state.

I'm an incomming junior and my degree, hopefully, is going to be one in mathematics and computer science.

@vzn I have not done any undergraduate research, unfortunately.

@Anon how are your grades in math/ science classes? research is hard and requires creativity/ imagination etc

I have Aced all my Science and Mathematics courses, so far.

@vzn , I know Research is very hard and requires creativity. However, I want to make an attempt.

Maybe my own little hash question ;)

@Anon so now go read a zillion scientific papers & see which ones appeal to you. have you read any?

@vzn Negative. I have been dedicating most of my time right now to get through ullman and Sipser. However, I will heed your advice and go read papers.

I forgot to mention that I did speak with the TCS guy at my university. He told me I must gain proper footing by reading through Sipers and Ullman during the summer, so that's what i have been doing primarily.

@Anon ok try paying special attn to citations in ullman/ sipser esp areas that appeal to you. think of each chapter as covering some area that has frontiers/ boundaries that can be pushed

@Anon what area is he researching? yes anyone at your school may be a resource. also, occasionally exceptionally gifted/ motivated undergrads take grad classes

sipser/ ullman are a good place to start. but keep in mind there is no "fast" way to get into research.

@vzn Complexity Theory and Quantum Computing.

@Anon excellent mainstream topics with lots of active research. defn try to leverage him as a resource as much possible. hey there is a talk on QM computing in the physics chat room coming up if youre interested. ~6wks. what about research appeals to you? what gave you the idea etc?

@vzn I will take note of that.

have you heard of this site yet?

@vzn Well, oddly enough it came from my interest in Philosophy. After learning about what Abstract Mathematics was and the works of Leibniz it just kind of came naturally.

I became very interested in pure mathematics; however, I always dabbled in computer science on the side. I felt like TCS was a good compromise between the two.

@Anon ah, have you taken any philosophy classes? yeah have been musing some, it might seem that leibnitz' rational calculator idea (heard of it?) might have seen some realization in the turing machine if you ask me. anyway we were just talking about aaronsons paper on philosophy of computer science, check it out... very unique, nothing like it...

Yes I took a few in my time at university. Yes, I find that Leibniz was a early computer scientist and should gain more praise. I have never heard of his rational calculator idea but I think it is related to his attempts to make a calculating machine. Thank you for the other resources by the way, I will look into it.

yw :)

anyway poke thru that Theoretical Computer Science site sometime to see if its your thing. its quite searchable and surfable. it also has a chat room with lots of history/ transcript/ citations etc

Alright

@vzn I will read through Aaronsons paper by the way, looks interesting. I have to go now but I appreciate the advice.

sure. ps a personal fan, Shallit is a neat CS researcher that crosses into number theory quite a bit, see if any of his papers look interesting.

Wow, how is it possible to get 10years suspension?

@Evil who?