Mixing
![How would I go about finding how many combinations based on this criteria. [closed]](https://lh3.googleusercontent.com/-XdUIqdMkCWA/AAAAAAAAAAI/AAAAAAAAAAA/4252rscbv5M/s72-c/photo.jpg?sz=32)
geometry and topology in the universities
0
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I was wondering if universities teach geometry and topology in the same course or separately?
I tried to search among the popular universities but could not find a specific answer.
general-topology geometry
asked Feb 2 at 10:13
yanoyano
6
$endgroup$
|
show 1 more comment
0
$begingroup$
I was wondering if universities teach geometry and topology in the same course or separately?
I tried to search among the popular universities but could not find a specific answer.
general-topology geometry
asked Feb 2 at 10:13
yanoyano
6
$endgroup$
3
$begingroup$
Geometry is very wide ! As topology...
$endgroup$
– idm
Feb 2 at 10:21
1
$begingroup$
Separate courses at UGA. Even just the broad-strokes, undergrad version of differential geometry has a ton of material, as does general topology, and this material is fairly disjoint (though there's certainly interplay). For instance, differential geometry AFAIK is done inside of a metric space, whereas a lot of general topology asks what happens when your space isn't even Hausdorff, let alone metric. Combining them into a mere semester-long course would do both a disservice, so I suspect they're separate courses at most universities. I don't know for certain though.
$endgroup$
– Kaj Hansen
Feb 2 at 10:25
1
$begingroup$
There is no single "geometry" or "topology"... E.g. non-commutative algebraic geometry and differential topology are quite different so cannot be taught in a single course.. But maybe metric geometry and metric topology are more compatible (but ask very different questions and have different methods etc.)
$endgroup$
– Henno Brandsma
Feb 2 at 10:25
$begingroup$
My major (back in the 80's) was called AMT (Algebra, Geometry (Meetkunde in Dutch), Topology) and the courses were all quite distinct and mostly non-overlapping.
$endgroup$
– Henno Brandsma
Feb 2 at 10:27
1
$begingroup$
A course in "geometric topology" can be given, if the students already have a good background in (general) topology and parts of geometry, as an advanced course.
$endgroup$
– Henno Brandsma
Feb 2 at 10:38
|
show 1 more comment
0
0
0
$begingroup$
I was wondering if universities teach geometry and topology in the same course or separately?
I tried to search among the popular universities but could not find a specific answer.
general-topology geometry
asked Feb 2 at 10:13
yanoyano
6
$endgroup$
I was wondering if universities teach geometry and topology in the same course or separately?
I tried to search among the popular universities but could not find a specific answer.
general-topology geometry
general-topology geometry
asked Feb 2 at 10:13
yanoyano
6
asked Feb 2 at 10:13
yanoyano
6
asked Feb 2 at 10:13
yanoyano
6
asked Feb 2 at 10:13
yanoyano
6
asked Feb 2 at 10:13
yanoyano
6
6
3
$begingroup$
Geometry is very wide ! As topology...
$endgroup$
– idm
Feb 2 at 10:21
1
$begingroup$
Separate courses at UGA. Even just the broad-strokes, undergrad version of differential geometry has a ton of material, as does general topology, and this material is fairly disjoint (though there's certainly interplay). For instance, differential geometry AFAIK is done inside of a metric space, whereas a lot of general topology asks what happens when your space isn't even Hausdorff, let alone metric. Combining them into a mere semester-long course would do both a disservice, so I suspect they're separate courses at most universities. I don't know for certain though.
$endgroup$
– Kaj Hansen
Feb 2 at 10:25
1
$begingroup$
There is no single "geometry" or "topology"... E.g. non-commutative algebraic geometry and differential topology are quite different so cannot be taught in a single course.. But maybe metric geometry and metric topology are more compatible (but ask very different questions and have different methods etc.)
$endgroup$
– Henno Brandsma
Feb 2 at 10:25
$begingroup$
My major (back in the 80's) was called AMT (Algebra, Geometry (Meetkunde in Dutch), Topology) and the courses were all quite distinct and mostly non-overlapping.
$endgroup$
– Henno Brandsma
Feb 2 at 10:27
1
$begingroup$
A course in "geometric topology" can be given, if the students already have a good background in (general) topology and parts of geometry, as an advanced course.
$endgroup$
– Henno Brandsma
Feb 2 at 10:38
|
show 1 more comment
3
$begingroup$
Geometry is very wide ! As topology...
$endgroup$
– idm
Feb 2 at 10:21
1
$begingroup$
Separate courses at UGA. Even just the broad-strokes, undergrad version of differential geometry has a ton of material, as does general topology, and this material is fairly disjoint (though there's certainly interplay). For instance, differential geometry AFAIK is done inside of a metric space, whereas a lot of general topology asks what happens when your space isn't even Hausdorff, let alone metric. Combining them into a mere semester-long course would do both a disservice, so I suspect they're separate courses at most universities. I don't know for certain though.
$endgroup$
– Kaj Hansen
Feb 2 at 10:25
1
$begingroup$
There is no single "geometry" or "topology"... E.g. non-commutative algebraic geometry and differential topology are quite different so cannot be taught in a single course.. But maybe metric geometry and metric topology are more compatible (but ask very different questions and have different methods etc.)
$endgroup$
– Henno Brandsma
Feb 2 at 10:25
$begingroup$
My major (back in the 80's) was called AMT (Algebra, Geometry (Meetkunde in Dutch), Topology) and the courses were all quite distinct and mostly non-overlapping.
$endgroup$
– Henno Brandsma
Feb 2 at 10:27
1
$begingroup$
A course in "geometric topology" can be given, if the students already have a good background in (general) topology and parts of geometry, as an advanced course.
$endgroup$
– Henno Brandsma
Feb 2 at 10:38
3
3
$begingroup$
Geometry is very wide ! As topology...
$endgroup$
– idm
Feb 2 at 10:21
$begingroup$
Geometry is very wide ! As topology...
$endgroup$
– idm
Feb 2 at 10:21
1
1
$begingroup$
Separate courses at UGA. Even just the broad-strokes, undergrad version of differential geometry has a ton of material, as does general topology, and this material is fairly disjoint (though there's certainly interplay). For instance, differential geometry AFAIK is done inside of a metric space, whereas a lot of general topology asks what happens when your space isn't even Hausdorff, let alone metric. Combining them into a mere semester-long course would do both a disservice, so I suspect they're separate courses at most universities. I don't know for certain though.
$endgroup$
– Kaj Hansen
Feb 2 at 10:25
$begingroup$
Separate courses at UGA. Even just the broad-strokes, undergrad version of differential geometry has a ton of material, as does general topology, and this material is fairly disjoint (though there's certainly interplay). For instance, differential geometry AFAIK is done inside of a metric space, whereas a lot of general topology asks what happens when your space isn't even Hausdorff, let alone metric. Combining them into a mere semester-long course would do both a disservice, so I suspect they're separate courses at most universities. I don't know for certain though.
$endgroup$
– Kaj Hansen
Feb 2 at 10:25
1
1
$begingroup$
There is no single "geometry" or "topology"... E.g. non-commutative algebraic geometry and differential topology are quite different so cannot be taught in a single course.. But maybe metric geometry and metric topology are more compatible (but ask very different questions and have different methods etc.)
$endgroup$
– Henno Brandsma
Feb 2 at 10:25
$begingroup$
There is no single "geometry" or "topology"... E.g. non-commutative algebraic geometry and differential topology are quite different so cannot be taught in a single course.. But maybe metric geometry and metric topology are more compatible (but ask very different questions and have different methods etc.)
$endgroup$
– Henno Brandsma
Feb 2 at 10:25
$begingroup$
My major (back in the 80's) was called AMT (Algebra, Geometry (Meetkunde in Dutch), Topology) and the courses were all quite distinct and mostly non-overlapping.
$endgroup$
– Henno Brandsma
Feb 2 at 10:27
$begingroup$
My major (back in the 80's) was called AMT (Algebra, Geometry (Meetkunde in Dutch), Topology) and the courses were all quite distinct and mostly non-overlapping.
$endgroup$
– Henno Brandsma
Feb 2 at 10:27
1
1
$begingroup$
A course in "geometric topology" can be given, if the students already have a good background in (general) topology and parts of geometry, as an advanced course.
$endgroup$
– Henno Brandsma
Feb 2 at 10:38
$begingroup$
A course in "geometric topology" can be given, if the students already have a good background in (general) topology and parts of geometry, as an advanced course.
$endgroup$
– Henno Brandsma
Feb 2 at 10:38
|
show 1 more comment
1 Answer
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Personally I was taught Geometry and Topology as separate courses but the Differential Geometry modules touched on topological aspects as there is an inexplicable link between them (see John McLeary's book for example).
answered Feb 2 at 10:57
user452221user452221
233
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Personally I was taught Geometry and Topology as separate courses but the Differential Geometry modules touched on topological aspects as there is an inexplicable link between them (see John McLeary's book for example).
answered Feb 2 at 10:57
user452221user452221
233
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Personally I was taught Geometry and Topology as separate courses but the Differential Geometry modules touched on topological aspects as there is an inexplicable link between them (see John McLeary's book for example).
answered Feb 2 at 10:57
user452221user452221
233
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add a comment |
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Personally I was taught Geometry and Topology as separate courses but the Differential Geometry modules touched on topological aspects as there is an inexplicable link between them (see John McLeary's book for example).
answered Feb 2 at 10:57
user452221user452221
233
$endgroup$
Personally I was taught Geometry and Topology as separate courses but the Differential Geometry modules touched on topological aspects as there is an inexplicable link between them (see John McLeary's book for example).
answered Feb 2 at 10:57
user452221user452221
233
answered Feb 2 at 10:57
user452221user452221
233
answered Feb 2 at 10:57
user452221user452221
233
answered Feb 2 at 10:57
user452221user452221
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3
$begingroup$
Geometry is very wide ! As topology...
$endgroup$
– idm
Feb 2 at 10:21
1
$begingroup$
Separate courses at UGA. Even just the broad-strokes, undergrad version of differential geometry has a ton of material, as does general topology, and this material is fairly disjoint (though there's certainly interplay). For instance, differential geometry AFAIK is done inside of a metric space, whereas a lot of general topology asks what happens when your space isn't even Hausdorff, let alone metric. Combining them into a mere semester-long course would do both a disservice, so I suspect they're separate courses at most universities. I don't know for certain though.
$endgroup$
– Kaj Hansen
Feb 2 at 10:25
1
$begingroup$
There is no single "geometry" or "topology"... E.g. non-commutative algebraic geometry and differential topology are quite different so cannot be taught in a single course.. But maybe metric geometry and metric topology are more compatible (but ask very different questions and have different methods etc.)
$endgroup$
– Henno Brandsma
Feb 2 at 10:25
$begingroup$
My major (back in the 80's) was called AMT (Algebra, Geometry (Meetkunde in Dutch), Topology) and the courses were all quite distinct and mostly non-overlapping.
$endgroup$
– Henno Brandsma
Feb 2 at 10:27
1
$begingroup$
A course in "geometric topology" can be given, if the students already have a good background in (general) topology and parts of geometry, as an advanced course.
$endgroup$
– Henno Brandsma
Feb 2 at 10:38