> Of the books that I explored, Baby Rudin came the closest to this ideal. While many of the individual chapters contains long runs of mostly linear development, the interdependence of the chapters is complex, and apparently very carefully considered.
and I removed what was "complex".
Many students hear bad things about Baby Rudin and don't try it. Of students who do try it, too many don't finish well. Of the students who do finish, only a small fraction take a second pass where they will get some of the clarity I typed in for you.
For my Ph.D., there were five qualifying exams. I did the best on four of them, and one of those was Analysis and fairly close to Baby Rudin. The department didn't offer a course to help students prepare for the Analysis exam. So, I was likely the only student who had taken two passes through Baby Rudin; the first pass was in a course; I did okay; the second pass was on my own and slowly; it was fun! The second pass is the main reason I did the best on that exam. The next year the department tried teaching a course from Baby Rudin: They did that for only one year; I can believe that few or none of the students did well with the course. A friend from another department wanted to learn Baby Rudin, took the course, had a hard time, and dropped it. He went away unhappy, and that was sad and not really necessary.
So, my experience with Baby Rudin suggests (i) take a formal course, (ii) use advice such as I gave here to see during the course some clarity in what is going on, how, and why; (iii) also study or glance at one or two other competitive or similar books, e.g., Spivak, Calculus on Manifolds, Fleming, Functions of Several Variables, Kolmogorov and Fomin, Apostol, and more, and (iv) take a second pass through Baby Rudin.
Net, Baby Rudin has discouraged a lot of students, too many. To many students, Baby Rudin looks forbiddingly severe and abstract; students can't figure out what the heck is going on, how, or why. E.g., your view was "complex" -- it can be "simple". With some help, e.g., as I typed in here for you, Baby Rudin can be okay.
You are misunderstanding my use of the word "complex".
I'm saying that after encoding the graph structure I found Baby Rudin contained more complexity (i.e. connectedness) than the other texts that I repeated the excersise for.
You wrote
> Of the books that I explored, Baby Rudin came the closest to this ideal. While many of the individual chapters contains long runs of mostly linear development, the interdependence of the chapters is complex, and apparently very carefully considered.
and I removed what was "complex".
Many students hear bad things about Baby Rudin and don't try it. Of students who do try it, too many don't finish well. Of the students who do finish, only a small fraction take a second pass where they will get some of the clarity I typed in for you.
For my Ph.D., there were five qualifying exams. I did the best on four of them, and one of those was Analysis and fairly close to Baby Rudin. The department didn't offer a course to help students prepare for the Analysis exam. So, I was likely the only student who had taken two passes through Baby Rudin; the first pass was in a course; I did okay; the second pass was on my own and slowly; it was fun! The second pass is the main reason I did the best on that exam. The next year the department tried teaching a course from Baby Rudin: They did that for only one year; I can believe that few or none of the students did well with the course. A friend from another department wanted to learn Baby Rudin, took the course, had a hard time, and dropped it. He went away unhappy, and that was sad and not really necessary.
So, my experience with Baby Rudin suggests (i) take a formal course, (ii) use advice such as I gave here to see during the course some clarity in what is going on, how, and why; (iii) also study or glance at one or two other competitive or similar books, e.g., Spivak, Calculus on Manifolds, Fleming, Functions of Several Variables, Kolmogorov and Fomin, Apostol, and more, and (iv) take a second pass through Baby Rudin.
Net, Baby Rudin has discouraged a lot of students, too many. To many students, Baby Rudin looks forbiddingly severe and abstract; students can't figure out what the heck is going on, how, or why. E.g., your view was "complex" -- it can be "simple". With some help, e.g., as I typed in here for you, Baby Rudin can be okay.