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I think the writer is understating the importance of the exercises. In graduate level math textbooks, the exercises frequently serve as a truncated exposition o

I think the writer is understating the importance of the exercises. In graduate level math textbooks, the exercises frequently serve as a truncated exposition of related topics and concepts.

nanolith 8y ago
This is true. Complete understanding rarely occurs until one can understand how to wield this knowledge.
- thomasfortes 8y ago
  My calculus teacher used to say that you learn calculus through your wrists, when you read the theory you get a grasp of how to solve some problems, when you learn to solve the problems is when you really can start to understand the theory. The same is valid for writing software, reading code is great, but you need to write a lot to learn how to program.
whatshisface 8y ago
In my experience I never learned a single thing except from the exercises.
DRMacIver 8y ago
> I think the writer is understating the importance of the exercises. I think it's not so much that I'm understating the importance of the exercises as that I'm coming from a position where by the time I want to read a textbook these days I effectively have my own exercises to work on. That being said, it's true that I've always had a more-than-healthy aversion to actually doing the textbook exercises, and it's something I should work on.
kleopullin 8y ago
I agree for undergraduate math. I love math textbooks, but it never occurred to me that one reads them without doing the exercises. And yes to the other post that points out many math texts contain cumulative knowledge making picking a random topic a method from someone not doing math. Intro geology text, sure. Some math textbooks have a few core chapters, too. Generally not reasonable to struggle through a random topic in chapter 5 when its underpinnings are clearly given in the first three chapters. In school I read all of my math textbooks, cover to cover. But, I never sat down to read them, until after doing the exercises. I go through a chapter with pencil and paper, doing all of the examples, then attempting the easy set of exercises. Then I go through the chapter, reading the text and reworking the examples, then do all the exercises. For differential equations and linear algebra this was sufficient to do the homework and ace tests. For calc I and II, I needed class also, calc III a study group helped, crystallography I worked with one other person. It's highly dependent on the topic. Other than crystallography, I haven't taken any graduate math courses. I did work through maybe half of my mom's advanced engineering math text, and it's not overboard or harder than the first two years. The exercises are where you learn math.

I think the writer is understating the importance of the exercises. In graduate level math textbooks, the exercises frequently serve as a truncated exposition of related topics and concepts.

nanolith 8y ago

This is true. Complete understanding rarely occurs until one can understand how to wield this knowledge.

thomasfortes 8y ago
My calculus teacher used to say that you learn calculus through your wrists, when you read the theory you get a grasp of how to solve some problems, when you learn to solve the problems is when you really can start to understand the theory. The same is valid for writing software, reading code is great, but you need to write a lot to learn how to program.

whatshisface 8y ago

In my experience I never learned a single thing except from the exercises.

DRMacIver 8y ago

> I think the writer is understating the importance of the exercises. I think it's not so much that I'm understating the importance of the exercises as that I'm coming from a position where by the time I want to read a textbook these days I effectively have my own exercises to work on. That being said, it's true that I've always had a more-than-healthy aversion to actually doing the textbook exercises, and it's something I should work on.

kleopullin 8y ago

I agree for undergraduate math. I love math textbooks, but it never occurred to me that one reads them without doing the exercises. And yes to the other post that points out many math texts contain cumulative knowledge making picking a random topic a method from someone not doing math. Intro geology text, sure. Some math textbooks have a few core chapters, too. Generally not reasonable to struggle through a random topic in chapter 5 when its underpinnings are clearly given in the first three chapters. In school I read all of my math textbooks, cover to cover. But, I never sat down to read them, until after doing the exercises. I go through a chapter with pencil and paper, doing all of the examples, then attempting the easy set of exercises. Then I go through the chapter, reading the text and reworking the examples, then do all the exercises. For differential equations and linear algebra this was sufficient to do the homework and ace tests. For calc I and II, I needed class also, calc III a study group helped, crystallography I worked with one other person. It's highly dependent on the topic. Other than crystallography, I haven't taken any graduate math courses. I did work through maybe half of my mom's advanced engineering math text, and it's not overboard or harder than the first two years. The exercises are where you learn math.