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Ha! It took me 3+ years to really understand real analysis. How? I tried to imagine 10, 20, 30 etc examples for every abtract definition in the books. E.g. take
by starchild_3001 9y ago
Ha! It took me 3+ years to really understand real analysis. How? I tried to imagine 10, 20, 30 etc examples for every abtract definition in the books. E.g. take the definition of open set. Try to imagine 10s of examples of open sets. Then try 10s of examples of closed sets. And similar. Then in your mind, you should develop the intuition that "open set is something that looks like one of these" vs "close set is something that looks like the others" etc. Then take the definition of continuous function, try to imagine every example possible! Just work on defn's with many, many, many examples. Henceforth, the theorems and proofs will become obvious... and presumably you'll end up being a good theorem-proof style mathematician.
No books necessary! If anything, I liked The Elements of Real Analysis by Bartle.
- rocqua 9y agoI have one thing to add. Whenever you meet a new example, check that example against your intuitions. When they mismatch, that is a great learning moment. These also help in finding 'counter-examples' which tend to be very constructive.
- thraway180306 9y agoThis is sometimes called inquiry-based teaching or Moore method, and… there is a textbook advertised as adhering to this particular style, Carol Schumacher's Closer and Closer: Introducing Real Analysis, haven't had it in hand though.