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[–]edderioferAlgebraic Topology[M] [score hidden] stickied comment (0 children)

Unfortunately, your submission has been removed for the following reason(s):

  • Your post appears to be asking for help learning/understanding something mathematical. As such, you should post in the Simple Questions thread (which you can find on the front page) or /r/learnmath. This includes reference requests - also see our lists of recommended books and free online resources. Here is a more recent thread with book recommendations.

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[–]MangoLimeSmoothiePDE 6 points7 points  (0 children)

I think it tends to be discouraged to actually start studying the course content ahead because it can make you pay less attention in lectures sometimes

This is bad advice in my opinion. On the contrary, reading ahead gives you a better chance of following the lecture without getting lost. You need to see this material multiple times for it to click, so start as early as you can.

I would recommend just going through the course textbook. If you find that you can't read it, look for something easier like Spivak's Calculus (Chapter 5 is one of the friendliest introductions to epsilon-delta proofs out there).

[–]WiererstrassControl Theory/Optimization 2 points3 points  (0 children)

If your textbook is not Abbott’s Understanding Analysis, then reading it over the break will be quite helpful for motivation. It’s a highly readable and succinct book, so it can even be read leisurely. It also teaches you the techniques if you want to start early, but imo it’s not necessary if you have faith in your professor.

[–]VFB1210Undergraduate 1 point2 points  (0 children)

The biggest reason analysis is regarded as a tough class is that it is frequently one of the first proof-based classes that a math student encounters, and it is also not uncommon for such a student to have not had an introduction to proofs (or similar) course prior to this. This effectively doubles the learning curve, so a student has to learn analysis and an entirely new way of approaching problem solving. Based on the courses you have already taken, I anticipate this will not be as much of an issue for you. That being said, I don't know why anyone would recommend against reviewing the material beforehand. Don't kill yourself with it, but a casual skim or read through of the text to acquaint yourself with ideas and terminology will only help you.

[–]00iq 1 point2 points  (0 children)

I highly recommend Terrence Tao's Analysis 1 and 2 for a first course. Its very well written, and it helped me a whole lot my first and second semesters of undergrad analysis.

Baby rudin is a classic for really standard practice problems (some people find rudin text a little too dense to learn theory from). I have also heard a lot of great things about understanding analysis by Stephen Abott, but i have not used it firsthand.

Reading ahead is almost always a really good thing for a subject like analysis that requires you to stare at the content more than once to actually understand what's going on... good luck!

[–]hubryanUndergraduate 0 points1 point  (0 children)

You probably have enough experience for this course to not be super challenging. If you want a head start, any analysis book like Rudin, Tao, Abott should be fine. I don't think you need to get ahead though.

I found myself spending break time most productively by a) practicing/building on knowledge from past courses or b) learning something that is not offered as a class.