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Going to research talks while being an undergraduate can be very challenging (frustrating I would say). This is a subjective answer, from my own experience and some friends'. Empirically (very subjective too) it appears that taking exhaustive notes of what is happening in a talk is usually not so efficient. The pace is not really the same as in a classical ...


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Manoli, algebra is a broad field of mathematics, so it is not clear which parts of algebra precisely appeal to you. In fact it is so broad that there are people who do research in one part of algebra and completely loathe another. In general, because of the advent of computer science and the recent preeminence of structures in science and industry, certain ...


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In learning there are two goals, one is obtaining knowledge and the other is obtaining skill. Having knowledge without skill means you can talk about it, but when it comes time to act, you lack the tools to produce results. Having skill without knowledge means you can generally produce results, but your limited understanding of the world has you relying on ...


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Reviewing the topics here at MSE is also a good way to provide new interesting series to OEIS. I would suggest you to use the tags of MSE and read all the great questions other users did here, that will give you insights and new ideas. In my case it was so, I have published only two sequences, and both were related with topics I just asked here and later ...


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Firstly, The submission stack at OEIS is pretty large at the moment. You could help by registering and editing some of the submissions if you feel competent doing that. You might learn a bit in the process. You could also help by finding un-submitted sequences in peer reviewed literature, if you have access to that. Nothing really, Submitting a sequence ...


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You can come up with any sequence you like. If you look around OEIS, you'll find from the ubiquitous Fibonacci numbers to the Look and say sequence. But consider that they prominently state that they have a huge backlog of proposed sequences, so you should make sure (a) it isn't a variant of something already in there, and (b) is is a really interesting ...


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Best advice might depend on your area of interest in mathematics, where you are located (and if not in your home country, what visa restrictions apply), and what your long-term career goals are after you finish your PhD. Answer those questions and I (we) might have more to say. Community college teaching might be feasible depending on location, but good ...


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Functional analysis is the study of topological vector spaces. That is, a vector space with a topology. If you took graduate topology, and did well, you should have the background for the topology aspect. The other aspect is the vector space part. I'm sure you've taken linear algebra, right? However a one line platitude means nothing when you're asked to ...


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Well as a former math contestant I wanted to share my thoughts on this question. First and foremost you have to understand that the competition and the result you'll achieve are by no means a measurement of your mathematical ability. A very nice example is a friend of mine. In my life I've participated in about 40 math contests (regional, county, national, ...


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You can always become a professor: get good pay, get grants from industry, and continue your focused research that you say keeps you excited in hopes of advancing your field, at least that's what your application will say. Companies are intersted in one thing: making money. Pure theoratical math rarely, if ever, can be used in a away to attain money. Thats ...


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Give Coursera, Khan Academy & edX a go. Try and go for anything that will help you understand the underlying concepts. If you're studying a subject, maybe look into the history. Learning how something was created may be a very interesting way of learning and one that will stick with you.


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As others have pointed out, Rudin's book is a little bit hard even for people who has more mathematical maturity. You should try some other alternatives, for example: Bryant's: And Yet Another Introduction To Analysis It's perhaps a good idea to use: Hairer/Wanner's: Analysis by It's History This book explained me a lot about the hierarchy of the ...


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I'd recommend learning these subjects from Coursea - Introduction to Mathematical Thinking, Calculus One and Calculus Two. (I am sorry but for this class I can't put hyperlink). Coursea is great place to start. And I want to recommend you youtube channel of Professor Leondard - he also has a great video where he explain students form university calculus and ...


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Man to to be honest with you, here is what I think why most people fail calculus classes. Students think that you should know the answer once you look at the question which is far from truth when dealing with university level mathematics.It's not a sociology class.You should try to be analytic, meaning that , You should see a problem and then try ...


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Euclid's axioms of geometry provide only one model, which works for most purposes in real life (building a pyramid, putting carpet in your house, etc.). If we need a different geometry for other purposes (e.g., mapping the globe, mapping the universe) we change axioms and try to make an appropriate non-Euclidean geometry. Maybe with more or less than 180 ...


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There are a few types of proofs. For this post I organize them as (I know it's very arbitrary to label proofs this way, I just use these "types" to break down different characteristics of proofs for this post): 1) Proofs for classes that you're expected to create 2) Proofs for classes that you aren't expected to create 3) Research level proofs The first ...


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Try looking at Vilenkin's introductory 1968 book on Representation Theory and Special Functions. Then look at his 3 volumes on the same subject with a more detailed treatment.



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