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Thread: Advice for someone starting a PhD programme without Real Analysis

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    Advice for someone starting a PhD programme without Real Analysis

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    Beginning Math camp in a few weeks. I spent a few years out of school, so I'm rusty on my Calc1-3 and Linear Algebra, although I'm starting to recap it now.

    My fear is about Real Analysis. If I get through Calc and Linear Algebra, then I plan to self-study Analysis. What's the best way to balance everything?

    I've been told two different ways of proceeding:

    1) Carry on with Calc and LA, and self-study relevant RA as I go through the PhD. I.e. designate 1/2 hours in the evenings during the PhD to focus on Math. Will I have enough time on top of the existing material to do this?

    2) Someone said do this course Real Analysis, Lecture 1: Constructing the Rational Numbers - YouTube now instead of refreshing Calc and LA (which I can use Math camp for). However, will this course be too much for me?

    Any advice would be really appreciated. Thanks!

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    Re: Advice for someone starting a PhD programme without Real Analysis

    I'm really not the right person to answer this as I don't have real analysis experience myself and I'm starting my PhD this Fall too, but for question 1, speaking from my experience from MS program, you will barely have any time to devote for things outside of your stated courses, research, and TA/RA duties. I was working for 7 days a week for MS, so I can imagine how it would be like for PhD. So if it is under your coursework, then that's a good idea to devote a couple of hours (or even more) on it, but not otherwise.

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    Re: Advice for someone starting a PhD programme without Real Analysis

    Personally I won't be able to have extra time for maths when studying my PhD courses so I don't think your first way of proceeding would be viable. On the other hand, without refreshing Calculus and Linear Algebra, you won't be able to fully comprehend the YouTube course you suggested.

    My advice would be to refresh Calculus and Linear Algebra and try your very best to understand every proof (on top of knowing how to use the Theorems in concrete questions). After that, you could start with the YouTube videos. Most likely you won't be able to finish it, but it is still better than not doing it.

    I would not count on the Math Camp. Typically it goes very fast (depending on your institution of course). It is very hard to refresh unless you already had solid mathematics foundation and the only thing you forgot is the statements of some theorems.

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    Re: Advice for someone starting a PhD programme without Real Analysis

    My advice has always been to take it easy the summer before beginning your PhD. Watch some youtube videos on calc review, if you must, but don't stress out about math.

    My second piece of advice is, assuming you have X hours to devote to preparation, that the MB of getting ahead on research exceeds the MB of working more on math.

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    Re: Advice for someone starting a PhD programme without Real Analysis

    You've gotten several good pieces of advice above, but let me add one more thought based on your being out of school for a few years and saying that you feel rusty. In many ways math is like a language. If you're really fluent, you can go for years without using it and then pick it up again pretty quickly. But if you're only at an intermediate level and you don't use it for a long time, it can take a while to get back into the swing of things.

    So while I generally think the summer before grad school is a good time to relax, given where you left off with math you might want to spend some time getting back into practice. The specific subject matter is probably less important than just getting back into practice manipulating symbols.

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    Re: Advice for someone starting a PhD programme without Real Analysis

    For studying analysis, I highly recommend Elementary Analysis:The Theory of Calculus by Kenneth Ross. It is a book that gives you detailed explanations on the structures of proofs and it is incredibly easy to understand(unlike Baby Rudin which has a lot of implicit statements). The book by Kenneth Ross will also help you brush up on your calculus.

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    Re: Advice for someone starting a PhD programme without Real Analysis

    Summer before grad school is a good time to relax before the endless grind towards the PhD in the years after

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    Re: Advice for someone starting a PhD programme without Real Analysis

    Thank you everyone for the advice. Will take it on board. Fingers crossed...

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