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I'm annoyed that "Pre-calculus," "Calculus I," and "Calculus II" are deemed distinct areas of mathematics. Do additional dimensions necessitate a new category?

acangiano 17y ago
They are not distinct areas. However, I feel that dividing them up helps the reader compare apples to apples, rather than having a list of 10 calculus related books.
- Sukotto 17y ago
  If you take that sort of approach, I would much rather you present the topics in some sort of directed graph format to clearly show which areas depend on knowledge of other areas. I realize that's a non-trivial exercise and no matter what you did you'd likely catch flack from people that don't agree with your prereqs. However, I think that would be particularly valuable to people who don't know what they don't know. (edit) I mean non trivial outside of relationships like basic math -> algrebra -> precalc -> calc1 -> calc2
  - eru 17y ago
    > (edit) I mean non trivial outside of relationships like basic math -> algrebra -> precalc -> calc1 -> calc2 What do you mean by Algebra? In university we had Analysis and Linear Algebra starting at the same time, and Algebra only came later on as a more advanced topic.
  - jacobolus 17y ago
    At some point they get mixed up and interdependent. Go read until you run into some concept that gets you stuck, and then switch topics and work through until you understand it. Unless you’re taking university classes, no one cares what order you follow.
jacobolus 17y ago
Precalculus, at least in US high schools, means something like “trigonomety and limits, plus applications”. “Calculus I” means single variable calculus, though the Spivak book they list is much more rigorous than a typical first-year calculus course. “Calculus II/III” in this case means vector calculus, which is enough of its own material to get at least its own semester course. I don’t think I’d quite put Spivak’s Calculus on Manifolds in the same category – maybe more like basic differential geometry/differential topology – but hey, this isn’t my list.
roundsquare 17y ago
If you look at the divisions being made, its pretty clearly based on how people would look for books. For calculus, lots of people buy books based on classes they take. Hence the division. No one of any mathematical repute or who took anything beyond calculus would be confused by this so I'm okay with the menu as is.

acangiano 17y ago

They are not distinct areas. However, I feel that dividing them up helps the reader compare apples to apples, rather than having a list of 10 calculus related books.

Sukotto 17y ago
If you take that sort of approach, I would much rather you present the topics in some sort of directed graph format to clearly show which areas depend on knowledge of other areas. I realize that's a non-trivial exercise and no matter what you did you'd likely catch flack from people that don't agree with your prereqs. However, I think that would be particularly valuable to people who don't know what they don't know. (edit) I mean non trivial outside of relationships like basic math -> algrebra -> precalc -> calc1 -> calc2
- eru 17y ago
  > (edit) I mean non trivial outside of relationships like basic math -> algrebra -> precalc -> calc1 -> calc2 What do you mean by Algebra? In university we had Analysis and Linear Algebra starting at the same time, and Algebra only came later on as a more advanced topic.
- jacobolus 17y ago
  At some point they get mixed up and interdependent. Go read until you run into some concept that gets you stuck, and then switch topics and work through until you understand it. Unless you’re taking university classes, no one cares what order you follow.

jacobolus 17y ago

Precalculus, at least in US high schools, means something like “trigonomety and limits, plus applications”. “Calculus I” means single variable calculus, though the Spivak book they list is much more rigorous than a typical first-year calculus course. “Calculus II/III” in this case means vector calculus, which is enough of its own material to get at least its own semester course. I don’t think I’d quite put Spivak’s Calculus on Manifolds in the same category – maybe more like basic differential geometry/differential topology – but hey, this isn’t my list.

roundsquare 17y ago

If you look at the divisions being made, its pretty clearly based on how people would look for books. For calculus, lots of people buy books based on classes they take. Hence the division. No one of any mathematical repute or who took anything beyond calculus would be confused by this so I'm okay with the menu as is.