Soft question: how do I get back to studying maths after taking a long break?

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I'm studying for a Master's degree in mathematics at the moment, after taking a break from studying for several years. As was then, my current area of interest is combinatorics and graph theory, which I suppose require a little less calculus and analysis than some other areas. Regardless, I still have to either read or perform algebraic manipulations sometimes, and I'm frequently at a loss in doing so. I'm talking about things like trigonometry, inequalities, limits, integrals, differential equations, etc., i.e. things usually covered in the first one or two years of college-level maths education. How do I bridge those gaps? Should I just re-learn those things as I go, or should I do the courses again?

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Case in point: I've just read a proof that requires the use of the identity $$\displaystyle \lim\limits_{n \to \infty} (1 + \frac{x}{n})^n = e^x$$, which I got stuck at since several steps in between were skipped. Once someone pointed out that that is the identity used (and after I looked up the proof for the identity), everything became clear. Yet it's frustrating since this situation happens more than it should.

romsek

Math Team
Patience. Your brain will only absorb it so fast anyway. I would re-learn things as you go up until it becomes absurd.

That identity isn't one that typical math students will have up their sleeve. I know it because it comes up frequently on these sites.

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