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One approach is to look at a few different but overlapping primers on the same matter and do the exercises. If one treatment doesn't click, another might. And f
by medymed 10y ago
One approach is to look at a few different but overlapping primers on the same matter and do the exercises. If one treatment doesn't click, another might. And for well-known subjects, topics are often covered in roughly the same order. Maybe not for graduate classes, not sure, but linear algebra, set theory, group theory, analysis it's generally the case.
Unless you can afford a tutor to teach it several different ways until it clicks, which is functionally similar.
- jwdunne 10y agoI can verify this approach works for me. The other thing I suggest is use "getting stuck" as a way to identify gaps - go look for books that fill those gaps. Recently I cracked open Principle of Analysis by Rudin. I got stuck pretty much straight away and looked it up - I saw a few suggestions for a bridge between high school maths and the rigor required by that book. I'm now reading another book that took inspiration from the previously mentioned book but gives a bit shallower a slope towards the rigor required.
- mrkgnao 10y agoPugh, by any chance?
- jwdunne 10y agoKrantz. Seems to be at a decent pace. No idea if it's any good though - problem of not having a mentor!
- gtani 10y agoThat book got good reviews. /r/math has lots of threads on this, recommend Abbott, Tao, Pugh, Spivak etc https://www.reddit.com/r/math/comments/50m4ib/what_are_the_main_differences_between_rudin_and/ https://www.reddit.com/r/math/comments/50m4ib/what_are_the_m... https://www.reddit.com/r/math/comments/4jopme/is_it_premature_for_me_to_start_reading_baby_rudin/ https://www.reddit.com/r/math/comments/4jopme/is_it_prematur... https://www.reddit.com/r/math/comments/512p2p/analysis_text_for_selfstudy/ https://www.reddit.com/r/math/comments/512p2p/analysis_text_...
- jwdunne 10y agoThank you :) I'm currently reading Calculus by Spivak too. Fantastic book. I find getting a taste and moving forward breadth-first keeps things fresh.
- deleted 10y ago[deleted]
- xemdetia 10y agoIt is also important to look for primers from multiple decades because what sometimes can be confusing is the current state of the art, thesis papers (PhD students are struggling to learn it the first time too, but often they hold the complete supporting material with references), and the original paper for the field. A lot of those papers are struggling to explain the new concept so they draw more analogies and you can see where they are going compared to a worked example.
- mindcrime 10y agoIt is also important to look for primers from multiple decades because what sometimes can be confusing is the current state of the art, thesis papers (PhD students are struggling to learn it the first time too, but often they hold the complete supporting material with references), and the original paper for the field. True, but the fly-in-the-ointment here is that sometimes notation changes over the years, and comparing papers / textbooks across textbooks can add even more cognitive overhead in that sense. :-(
- xemdetia 10y agoI agree but if you get enough books in the same area you can start to figure out the mapping. Even books released in the same subfield at the same time can have wildly different notation and only by having enough references can you have a chance.
- mindcrime 10y agoThat should have read: ... comparing papers / textbooks across decades can add even ...
- godelski 10y agoI fully suggest this, but also some other things. Try different media. I've found, at least for me, sometimes just reading it won't click. I pull up some ocw or a random video on youtube and presto. It is important to remember that when it clicks that what you've been reading makes sense and to reread. Sometimes I'll go through like 5/6 videos, it is just finding the right one. Try problems. Struggling is the key to success in mathematics. There is no doubt in my mind that this is true. If you REALLY have problems look up a professor at a local university or community college. Find out when their office hours are and send a polite email asking that if they have time you'd appreciate the help. This will be hit or miss, but many are glad to help (no one does academics for the money). Many will even let you sit in on their classes (less will grade your work).
- Chris2048 10y agoperhaps one approach to this is a wiki linking to different approaches for describing the same concepts? Plus, there are enough old math books (out of copyright) to just include scans directly. I actually collect math books, have a few infitesimal calculus books even.