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Particularly of note: 1.3 What is requested from the student The only way to learn mathematics is by doing exercises. One does not get fit by me

Particularly of note: 1.3 What is requested from the student The only way to learn mathematics is by doing exercises. One does not get fit by merely looking at a treadmill or become a chef by merely reading cookbooks, and one does not learn math by watching someone else do it. There are about 300 exercises in this book. Some of them have solutions in the text, others have solutions that can only be accessed by professors teaching the class. A good student can also make up his own exercises or simply play around with the material. This book often uses databases as an entry to category theory. If one wishes to explore categorical database software, FQL (functorial query language) is a great place to start. It may also be useful in solving some of the exercises.[0] This is not a novel, and you don't learn by just reading things. You need to engage topics like this in hand-to-hand combat, and if you're not willing to do that - give up now. Your knowledge will be superficial, and ultimately useless. Added in edit: To reply to both (currently) comments, you don't learn how to program by just reading and not doing. You can learn about programming, but you won't actually be able to program, and your knowledge will be superficial. If that's your objective, just to know about this topic, and others in math, then fine. If you want to be able to use your knowledge in any meaningful way, my comment stands. It's not enough just to read. You have to engage, and do the work. [0] http://category-theory.mitpress.mit.edu/chapter001.html#lev_1-3 http://category-theory.mitpress.mit.edu/chapter001.html#lev_...

Koshkin 10y ago
To be fair, you can and do learn a lot about things by simply reading and trying to understand the material. Notice I said "about", and that is an important distinction. Not everybody needs and or wants to have a working knowledge of the category theory or any other subject. Rather, many either want to satisfy their curiosity or get a basic understanding of a subject before deciding whether it would be worthwhile for them to invest more time in learning it. Philosophers of science, for instance, do need to know a lot about, say, modern physical theories, and many of them do - down to a level of astonishing mathematical detail; yet, no one would expect them to be able to work as a theoretical physicist.
- p4wnc6 10y ago
  I learned a ton about my car from reading the car's manual. And, can you believe it, the manual has no exercises in it!
  - nine_k 10y ago
    But did you ever drive the car?
    - p4wnc6 10y ago
      In theory, I did. There was a lot of commuting, so I can't say for sure that category theory wasn't involved.
mcguire 10y ago
"Some of them have solutions in the text, others have solutions that can only be accessed by professors teaching the class." And this is why I don't usually end up doing the exercises.
- CarolineW 10y ago
  That's your choice, but in my experience that simply means that you don't end up able to apply the knowledge you think you have acquired by reading about a topic. That might be fine for you, but it's an inherent limitation in reading about something, rather than actually engaging in it. I've edited my original comment to make a comparison, and expand on why I say this. But to take you up on this - some exercises have answers in the text. You could do just those. Other exercises don't have the answers, just like code that you write doesn't already exist. When you write the code you then have the ability to check that it does what it's supposed to do. The idea of having exercises without answers it to foster the ability to understand when your answers are right. Most of the time it's easy to know if you got the right answers, but it's finding the answer that's the challenge. If you choose not to learn this topic, fine, that's your choice. My comment just says: don't expect to understand the material at anything other than a superficial level if all you do is read about it. As it says in the quoted section: One does not get fit by merely looking at a treadmill.
- wfo 10y ago
  Usually in college-and-up mathematics, if you get the answer, you know when you have the answer, because you have a correct proof. You don't need the solutions, the whole point is to write your own, which is much more work and which will invariably differ from the official ones -- sometimes slightly, sometimes drastically.
teamhappy 10y ago
> You need to engage topics like this in hand-to-hand combat Fortunately, doing the exercises in books isn't the only way to do that.
gone35 10y ago
The only way to learn mathematics is by doing exercises. This, in my experience, is utterly false. It does seem to be a pervasive bias in the community, though --cf. the ubiquitous "[missing step] is left as an exercise to the reader", and so forth.
- CarolineW 10y ago
  Fantastic. Can you tell me how you learned mathematics without doing any exercises?
  - Noseshine 10y ago
    > without doing _any_ exercises? I suggest you ask a question about what he actually said (wrote) if you want an answer. In the current form the question doesn't seem to be that (a question) at all but a cheap rhetorical method to pretend the other party said something ridiculous by taking a few words but adding exaggeration until the original contents no longer exists. http://dilbert.com/strip/2015-06-07 http://dilbert.com/strip/2015-06-07
    - CarolineW 10y ago
      OK, so I said: The only way to learn mathematics is by doing exercises. To this, gone35 replied: This, in my experience, is utterly false. To me, that says that it's not true that the only way to learn mathematics is by doing only exercises. Logically, that means there is some way to learn mathematics by doing something other than exercise, possibly in addition to exercise, admittedly, but certainly something that is not exercises. The word "utterly" seems additionally to imply that this extra something completely outweighs the exercises, perhaps even to the point of no longer requiring exercises at all. And so my question. So I believe my question to have been completely reasonable. Rephrasing gone35: In my experience, is utterly false that the only way to learn mathematics is by doing exercises. So let me be very much more specific. gone35: I would be very interested to know what methods of learning mathematics you espouse other than, or perhaps in addition to, doing exercises. Is that better?
jknoepfler 10y ago
for the sake of precision it should be pointed out that learning about mathematics by reading alone is not the logical compliment of learning about mathematics through reading and book exercises. the term "exercise" by its nature implies something that is "practice". one may, however, simply learn by doing (rather than "exercising"). for a programmer, there is a clear distinction. this might not be the case for a mathematician.

Koshkin 10y ago

To be fair, you can and do learn a lot about things by simply reading and trying to understand the material. Notice I said "about", and that is an important distinction. Not everybody needs and or wants to have a working knowledge of the category theory or any other subject. Rather, many either want to satisfy their curiosity or get a basic understanding of a subject before deciding whether it would be worthwhile for them to invest more time in learning it. Philosophers of science, for instance, do need to know a lot about, say, modern physical theories, and many of them do - down to a level of astonishing mathematical detail; yet, no one would expect them to be able to work as a theoretical physicist.

p4wnc6 10y ago
I learned a ton about my car from reading the car's manual. And, can you believe it, the manual has no exercises in it!
- nine_k 10y ago
  But did you ever drive the car?
  - p4wnc6 10y ago
    In theory, I did. There was a lot of commuting, so I can't say for sure that category theory wasn't involved.

mcguire 10y ago

"Some of them have solutions in the text, others have solutions that can only be accessed by professors teaching the class." And this is why I don't usually end up doing the exercises.

CarolineW 10y ago
That's your choice, but in my experience that simply means that you don't end up able to apply the knowledge you think you have acquired by reading about a topic. That might be fine for you, but it's an inherent limitation in reading about something, rather than actually engaging in it. I've edited my original comment to make a comparison, and expand on why I say this. But to take you up on this - some exercises have answers in the text. You could do just those. Other exercises don't have the answers, just like code that you write doesn't already exist. When you write the code you then have the ability to check that it does what it's supposed to do. The idea of having exercises without answers it to foster the ability to understand when your answers are right. Most of the time it's easy to know if you got the right answers, but it's finding the answer that's the challenge. If you choose not to learn this topic, fine, that's your choice. My comment just says: don't expect to understand the material at anything other than a superficial level if all you do is read about it. As it says in the quoted section: One does not get fit by merely looking at a treadmill.
wfo 10y ago
Usually in college-and-up mathematics, if you get the answer, you know when you have the answer, because you have a correct proof. You don't need the solutions, the whole point is to write your own, which is much more work and which will invariably differ from the official ones -- sometimes slightly, sometimes drastically.

teamhappy 10y ago

> You need to engage topics like this in hand-to-hand combat Fortunately, doing the exercises in books isn't the only way to do that.

gone35 10y ago

The only way to learn mathematics is by doing exercises. This, in my experience, is utterly false. It does seem to be a pervasive bias in the community, though --cf. the ubiquitous "[missing step] is left as an exercise to the reader", and so forth.

CarolineW 10y ago
Fantastic. Can you tell me how you learned mathematics without doing any exercises?
- Noseshine 10y ago
  > without doing _any_ exercises? I suggest you ask a question about what he actually said (wrote) if you want an answer. In the current form the question doesn't seem to be that (a question) at all but a cheap rhetorical method to pretend the other party said something ridiculous by taking a few words but adding exaggeration until the original contents no longer exists. http://dilbert.com/strip/2015-06-07 http://dilbert.com/strip/2015-06-07
  - CarolineW 10y ago
    OK, so I said: The only way to learn mathematics is by doing exercises. To this, gone35 replied: This, in my experience, is utterly false. To me, that says that it's not true that the only way to learn mathematics is by doing only exercises. Logically, that means there is some way to learn mathematics by doing something other than exercise, possibly in addition to exercise, admittedly, but certainly something that is not exercises. The word "utterly" seems additionally to imply that this extra something completely outweighs the exercises, perhaps even to the point of no longer requiring exercises at all. And so my question. So I believe my question to have been completely reasonable. Rephrasing gone35: In my experience, is utterly false that the only way to learn mathematics is by doing exercises. So let me be very much more specific. gone35: I would be very interested to know what methods of learning mathematics you espouse other than, or perhaps in addition to, doing exercises. Is that better?

jknoepfler 10y ago

for the sake of precision it should be pointed out that learning about mathematics by reading alone is not the logical compliment of learning about mathematics through reading and book exercises. the term "exercise" by its nature implies something that is "practice". one may, however, simply learn by doing (rather than "exercising"). for a programmer, there is a clear distinction. this might not be the case for a mathematician.