That sort of thing.Now Available in Paperback! In Einstein Never Used Flashcards highly credentialed child psychologists, Kathy Hirsh-Pasek, Ph.D., and Roberta Michnick Golinkoff, Ph.D., with Diane Eyer, Ph.D., offer a compelling indictment of the growing trend toward accelerated learning. with proofs maybe just look at it through the corner of your eye and see how much you can reproduce. write a little star or something in the margin if its important or you have a harder time with it. Just get to a definition and block out the text. The information is already laid out like flashcards anyway. A math book in particular is set up in a way that makes this really easy already. These days, I've been experimenting with essentially just letting the book be the flashcard deck. So these kinds of things start gumming up the works and taking up more time than they are worth. This means that some hard proofs keep coming up over and over, which would be okay but sometimes a subject has proofs that are tougher but that actually aren't all that important. Spaced repetition systems mean that cards you fail more often also show up more often. Time which would have been better spent studying. Even with a pretty streamlined process, it still took a ton of extra time to set them up. Just having the text of some definition to deal with didn't help understand it very much. Taking the information out of context to put it on a card made it harder to gain intuition. The problems I ran into were, in no particular order My set up was that I had cards for definitions, theorems, and examples/exercises. I absolutely think that it can work for mathematics, but I'm not sure I recommend it. Well, I used to do this digitally with spaced repetition (I used emacs' org-drill, which is the emacs answer to Anki). I use flashcards to this day whenever I want to learn a new subject in math. One person picks, the other proves at the board and must be able to explain all the steps, then switch. We'd plunk down the flashcards on a desk in the office and challenge each other to "pick and prove". He also insisted that the front of the flashcards had the statement of the theorem and that the back contained the proof. He pointed out that I had absolutely no hope of using, say Ascoli's Thm, if I didn't know exactly what Ascoli's thereom said. When we started studying for quals together he insisted I make them and taunted me until I did it. A friend used them and I was always stunned with how well fast and how thoroughly he learned the material in the classes he took. I thought they were dumb, that people who use them were "just memorizing", and that I was better than that because I didn't have to "memorize" because I "understood". Putting definitions and theorems to use is the best way to understand and remember them. Do all the practice problems you can find, and try to understand all the steps you’re performing. My advice is to focus less on memorization, and more on practice. Additionally, ‘memorization’ of important theorems and objects tends to come naturally when you use them repeatedly. Like, it’s not going to do you any good to verbatim memorize the first isomorphism theorem if you do not have the conceptual understanding of what it’s doing, and if you do have that conceptual understanding, you won’t have to memorize it since you know what’s going on. However, as you progress, you really need to be able to internalize the WHY, rather than just simple memorization. If you’re doing some version of “qualifier courses” (required courses in the first year or two, usually algebra, topology, and analysis), I could see flash cards being slightly useful for memorizing a bunch of theorems. Depends on what level you’re at in grad school.
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