Target audiences are different. More competent people prefer absorbing more dense presentation that leaves out obvious steps and communicates more sophisticated ideas faster, while newcomers need all steps spelled out for a simple enough version of the ideas. Video lectures are usually targeted as people new to the field, or generally less technically sophisticated, such as average university students. By looking for video lectures, you apply a heavy selection bias for this kind of target audience, and so you should expect the presentation to be more transparent. Written material, on the other hand, may target different groups of people. By searching for a random paper or book on the subject, you are more likely to encounter more difficult material. On the other hand, if the topic is popular enough, you should be able to find easy introductory written material as well, you’d just need to filter the material by less obvious cues than it being a video lecture course. One heuristic is to look for lecture notes.
That’s not always the case. Plenty of times competent people are called upon to implement a new method, and want to see for themselves the precise steps that the techniques’ discoverer has gone through. I don’t always have time, and it’s not always instructive to have to fill in the blanks.
I don’t see any reason why more competent people would prefer omission of a key step in a proof with remark “left to readers as an excercise”. If you want to save time, you can surely skip it while reading. Why shall the author make the choice for the reader?
Especially in math, even textbooks which are intended to present complete overview of some subject have these excercises to the reader. I like to read books from the beginning to the end, but this is exactly what makes it impossible for me to do with math books. It can be refreshing to stop reading at some moment and have to think about some detail, but to do it repeatedly, knowing that I am losing time trying to figure out something which could be explained on two lines, is frustrating. I read books and papers because I want to get the information as efficiently as possible, not because I want to eventually rediscover it for myself. Not much to do with competence, I believe.
Added: I also find “excercise to the reader” mildly offensive, as the author is saying that it is trivial for him, but not for the readers, who should improve their skills by making the excercise. Such sentences aren’t surprising in undergraduate course textbooks, but when the audience are competent people, it seems inappropriate.
Target audiences are different. More competent people prefer absorbing more dense presentation that leaves out obvious steps and communicates more sophisticated ideas faster, while newcomers need all steps spelled out for a simple enough version of the ideas. Video lectures are usually targeted as people new to the field, or generally less technically sophisticated, such as average university students. By looking for video lectures, you apply a heavy selection bias for this kind of target audience, and so you should expect the presentation to be more transparent. Written material, on the other hand, may target different groups of people. By searching for a random paper or book on the subject, you are more likely to encounter more difficult material. On the other hand, if the topic is popular enough, you should be able to find easy introductory written material as well, you’d just need to filter the material by less obvious cues than it being a video lecture course. One heuristic is to look for lecture notes.
That’s not always the case. Plenty of times competent people are called upon to implement a new method, and want to see for themselves the precise steps that the techniques’ discoverer has gone through. I don’t always have time, and it’s not always instructive to have to fill in the blanks.
I don’t see any reason why more competent people would prefer omission of a key step in a proof with remark “left to readers as an excercise”. If you want to save time, you can surely skip it while reading. Why shall the author make the choice for the reader?
Especially in math, even textbooks which are intended to present complete overview of some subject have these excercises to the reader. I like to read books from the beginning to the end, but this is exactly what makes it impossible for me to do with math books. It can be refreshing to stop reading at some moment and have to think about some detail, but to do it repeatedly, knowing that I am losing time trying to figure out something which could be explained on two lines, is frustrating. I read books and papers because I want to get the information as efficiently as possible, not because I want to eventually rediscover it for myself. Not much to do with competence, I believe.
Added: I also find “excercise to the reader” mildly offensive, as the author is saying that it is trivial for him, but not for the readers, who should improve their skills by making the excercise. Such sentences aren’t surprising in undergraduate course textbooks, but when the audience are competent people, it seems inappropriate.