A good collection of hints, fits to my experiences in autodidactism. But you need a very good library at hand for such browsing (I used as teenager what a mathematician had designed as “Bibliothekskontinuum” ). “Don’t … study … as if you had to pass a test on it” is IMO very good too. Skimming connects with the subconscious procedures of memory and learning and works much better that one usually expects. In a similar way, I would suggest to take interesting looking books at home, laying them aside your bed and browsing like you please each evening before sleeping. That helps very much in identifying fitting themes and texts. But then one should stick on one issue and dig deeper, learn and think about a specific topic. After that, the cycle starts again, but on a higher level. Making notices is simplified by having a small paper notebook all the time around.
And, of course, it helps not to be frightened by sensing how small one’s knowledge is. When I first entered the math library, I took a book by chance, and understood nothing, not even what the author told about. Then I tried an other one, with the same result. This continued until I came across a “Basic Number Theory” (by A. Weil) and could not believe that I even did not understand the first page. That was a bit too much for my taste—I stopped browsing then, sat down and worked systematically until I found out what to understand in which order for digesting that “Basic Number Theory”—a really tough job for me then. Some more than a few months later I happily finished it’s last page and asked some professor lurking in the library for “the 2nd volume”. He barely could supress laughter, as there was no “2nd volume”, I already was in some sense at the top of the mountain.
But you need a very good library at hand for such browsing
The internet is basically all you need. Anyone with that has access to a whole bunch of resources, including Wikipedia, OpenCourseWare and Khan Academy. Journal articles are often less available, but it is increasingly easy to gain access to journal articles through a combination of Google Scholar, the researchers’ websites, and open access journals.
No, for several reasons (drawn from experiences in math, I am sure in physics and other sciences it is even worse):
Even if one includes hidden download-sites and special access by university subscriptions, only sources at the low or medium levels are available in a sufficient amount. The contents of an advanced level are only insufficient there, even some of the decades old and basic ones.
Suitable and really good existing texts on the web can be found only if one knows very precisely what one is looking for. But someone who wants to learn needs to find the better stuff, which is in part outside his/her mental frame. In contrast, good texts, even if found, still become hard to detect because of the noise by shallow pseudo-substitutes.
Browsing a real library makes your brain detect very quickly much more information and orientation, e.g. experiments (by friends who tutor at the local university) with beginning university students who were grouped and then asked to look for literature (in physics) by web/library only, for an hour, showed a very huge difference. An other experiment with students showed that students using a library have much better learning techniques that the other, but the later don’t notice. Maybe it is a special case of this. On the interesting ways of how subconscious learning and “active” memory gets connected by seemingly irrelevant sensory inputs may play a role then, a famous extreme case here.
University libraries are usually very good and have good long distance services. Have you looked for one? I would not buy books, as most of them one reads only once and science books are expensive. But one can suggest university libraries to buy them, I use those opportunities as the cheapest and fastest way to get them.
If you’re in London, and want access to some book that you don’t otherwise have access to, you can can apply for a reader’s card at the British Library. I don’t know if this is useful, as you can then only access the works while in the Reading Rooms (and so, while the library is open), but I find the Reading Rooms in there are a good place to get work done.
They’re also probably the only place that you’ll be able to access recent journals without being at a university (or asking people who are at a university to get them for you, but that doesn’t suit the “browsing” style of learning).
On the other hand, I pretty much agree that you don’t really need access to physical books. In CS areas of maths, at least, most people tend to make a draft of their textbook available for free online.
I never had a problem with free access as non-student to a university library (and usually to it’s computing center). I would suggest to contact the people and to try it. And are there no good other libraries in London?
I find it hard to believe that there are no better solutions, esp. in London—do you really think London offers it’s inhabitants so little? By far less than remote districts in Germany or the US?
Conc. books: A good way to orient is to define the field of one’s interests and to look at the websites of seminars and workshops in good universities on those and related topics. This helps to formulate a few possible learning routes and with some luck you find the sources free online. But if you want to avoid to crash (because low altitude flights of learning always crash into dead ends) , you need to follow Ravi Vakil’s advise: “(mathematics) is so rich and infinite that it is impossible to learn it systematically, and if you wait to master one topic before moving on to the next, you’ll never get anywhere. Instead, you’ll have tendrils of knowledge extending far from your comfort zone. Then you can later backfill from these tendrils, and extend your comfort zone; this is much easier to do than learning “forwards”. (Caution: this backfilling is necessary. There can be a temptation to learn lots of fancy words and to use them in fancy sentences without being able to say precisely what you mean. You should feel free to do that, but you should always feel a pang of guilt when you do.)” BTW, here is a good collection of math related reading tips.
Even if one includes hidden download-sites and special access by university subscriptions, only sources at the low or medium levels are available in a sufficient amount.
How advanced are you referring to? There are many resources at the advanced undergraduate or beginning graduate level (this is biased towards computer science and math, so maybe this is not true for the sciences):
To get to the research level you certainly need journal access, which, as far as I know, is pricy for an individual, hence unrealistic. Hopefully more journals switch to open acccess.
In mathematics, I would call “advanced” roughly what is above the average of “Springer Graduate Text” book series level. Of course, I do not say that one finds nothing, e.g. the Bourbaki seminar series is very good for autodidacts, or this site. It is a bit like the difference between a complex organism and the bunch of isolated cells.
A good collection of hints, fits to my experiences in autodidactism. But you need a very good library at hand for such browsing (I used as teenager what a mathematician had designed as “Bibliothekskontinuum” ). “Don’t … study … as if you had to pass a test on it” is IMO very good too. Skimming connects with the subconscious procedures of memory and learning and works much better that one usually expects. In a similar way, I would suggest to take interesting looking books at home, laying them aside your bed and browsing like you please each evening before sleeping. That helps very much in identifying fitting themes and texts. But then one should stick on one issue and dig deeper, learn and think about a specific topic. After that, the cycle starts again, but on a higher level. Making notices is simplified by having a small paper notebook all the time around.
And, of course, it helps not to be frightened by sensing how small one’s knowledge is. When I first entered the math library, I took a book by chance, and understood nothing, not even what the author told about. Then I tried an other one, with the same result. This continued until I came across a “Basic Number Theory” (by A. Weil) and could not believe that I even did not understand the first page. That was a bit too much for my taste—I stopped browsing then, sat down and worked systematically until I found out what to understand in which order for digesting that “Basic Number Theory”—a really tough job for me then. Some more than a few months later I happily finished it’s last page and asked some professor lurking in the library for “the 2nd volume”. He barely could supress laughter, as there was no “2nd volume”, I already was in some sense at the top of the mountain.
The internet is basically all you need. Anyone with that has access to a whole bunch of resources, including Wikipedia, OpenCourseWare and Khan Academy. Journal articles are often less available, but it is increasingly easy to gain access to journal articles through a combination of Google Scholar, the researchers’ websites, and open access journals.
No, for several reasons (drawn from experiences in math, I am sure in physics and other sciences it is even worse):
Even if one includes hidden download-sites and special access by university subscriptions, only sources at the low or medium levels are available in a sufficient amount. The contents of an advanced level are only insufficient there, even some of the decades old and basic ones.
Suitable and really good existing texts on the web can be found only if one knows very precisely what one is looking for. But someone who wants to learn needs to find the better stuff, which is in part outside his/her mental frame. In contrast, good texts, even if found, still become hard to detect because of the noise by shallow pseudo-substitutes.
Browsing a real library makes your brain detect very quickly much more information and orientation, e.g. experiments (by friends who tutor at the local university) with beginning university students who were grouped and then asked to look for literature (in physics) by web/library only, for an hour, showed a very huge difference. An other experiment with students showed that students using a library have much better learning techniques that the other, but the later don’t notice. Maybe it is a special case of this. On the interesting ways of how subconscious learning and “active” memory gets connected by seemingly irrelevant sensory inputs may play a role then, a famous extreme case here.
I haven’t found my library particularly useful for the most part and I’ve bought very few books, but I’ve still largely managed to get up to speed.
University libraries are usually very good and have good long distance services. Have you looked for one? I would not buy books, as most of them one reads only once and science books are expensive. But one can suggest university libraries to buy them, I use those opportunities as the cheapest and fastest way to get them.
I’m in London—how does one get access to a University library as a non-student? Surely they’d want money for that?
If you’re in London, and want access to some book that you don’t otherwise have access to, you can can apply for a reader’s card at the British Library. I don’t know if this is useful, as you can then only access the works while in the Reading Rooms (and so, while the library is open), but I find the Reading Rooms in there are a good place to get work done.
They’re also probably the only place that you’ll be able to access recent journals without being at a university (or asking people who are at a university to get them for you, but that doesn’t suit the “browsing” style of learning).
On the other hand, I pretty much agree that you don’t really need access to physical books. In CS areas of maths, at least, most people tend to make a draft of their textbook available for free online.
I never had a problem with free access as non-student to a university library (and usually to it’s computing center). I would suggest to contact the people and to try it. And are there no good other libraries in London?
£220/year. I can get books on inter-library loan, but it’s slow and time-consuming.
Partly though it’s that I’m still not convinced I need physical books enough to hurdle these barriers—what sort of books do you have in mind?
I find it hard to believe that there are no better solutions, esp. in London—do you really think London offers it’s inhabitants so little? By far less than remote districts in Germany or the US?
Conc. books: A good way to orient is to define the field of one’s interests and to look at the websites of seminars and workshops in good universities on those and related topics. This helps to formulate a few possible learning routes and with some luck you find the sources free online. But if you want to avoid to crash (because low altitude flights of learning always crash into dead ends) , you need to follow Ravi Vakil’s advise: “(mathematics) is so rich and infinite that it is impossible to learn it systematically, and if you wait to master one topic before moving on to the next, you’ll never get anywhere. Instead, you’ll have tendrils of knowledge extending far from your comfort zone. Then you can later backfill from these tendrils, and extend your comfort zone; this is much easier to do than learning “forwards”. (Caution: this backfilling is necessary. There can be a temptation to learn lots of fancy words and to use them in fancy sentences without being able to say precisely what you mean. You should feel free to do that, but you should always feel a pang of guilt when you do.)” BTW, here is a good collection of math related reading tips.
How advanced are you referring to? There are many resources at the advanced undergraduate or beginning graduate level (this is biased towards computer science and math, so maybe this is not true for the sciences):
This is a link to a freely available 4-volume set on measure theory
Here is a book on information-theoretic approaches to machine learning and inference
Here is one on statistical learning theory
Here is one on a “computational” approach to classical mechanics (Hamiltonians and Lagrangians abound)
To get to the research level you certainly need journal access, which, as far as I know, is pricy for an individual, hence unrealistic. Hopefully more journals switch to open acccess.
In mathematics, I would call “advanced” roughly what is above the average of “Springer Graduate Text” book series level. Of course, I do not say that one finds nothing, e.g. the Bourbaki seminar series is very good for autodidacts, or this site. It is a bit like the difference between a complex organism and the bunch of isolated cells.