Timeline for What should be offered in undergraduate mathematics that's currently not (or isn't usually)?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 23, 2013 at 19:57 | comment | added | roy smith | I agree, David. Even after reading tomes like Spivak's first couple volumes, it took me decades to realize that the classical euclidean and non euclidean geometries were just those Riemannian surfaces which were simply connected and of constant curvature. Thus the natural progression would have been to learn Euclidean geometry as flat geometry, then spherical/projective and hyperbolic geometry as universal constant non zero curvature geometry, then quotients of these as other constant curvature geometries, and finally more generally curved surfaces. Nikulin/Shafarevich is a good source. | |
| Aug 30, 2012 at 18:24 | comment | added | janmarqz | on the beginning missing duality of finite dimensional vector spaces (preferable over the real field) garanties from minor to almost no understanding :P | |
| Jan 8, 2012 at 7:32 | history | edited | J W | CC BY-SA 3.0 |
Improved clarity.
|
| Jun 16, 2010 at 8:12 | comment | added | David Corwin | I actually would love to see non-euclidean geometry (from a more elementary perspective) and differential geometry unified into one course. You always see elementary books which give you bits and pieces of the idea that there are other geometries, and that the sophisticated way of doing this is differential geometry - then much later in life you get thrown into a course where you pick up from multivariable calculus and define manifolds, tangent spaces, tensor fields, etc... There should be an attempt to show the connection between the two. | |
| May 7, 2010 at 4:56 | comment | added | The Mathemagician | Read John and Barbara Hubbard's VECTOR CALCULUS,LINEAR ALGEBRA AND DIFFERENTIAL FORMS:A UNIFIED APPROACH,2nd edition,to see how it's done,Jacques. | |
| Mar 15, 2010 at 11:18 | comment | added | darij grinberg | But, please, with motivation. Understanding manifolds is THE hardest part of "elementary" advanced mathematics. Just introducing them by an abstract definition and then doing proofs by "local-global" handwaving doesn't do the job; the students will neither have an idea what the definition signifies, nor why the handwaving is allowed. Maybe some non-Euclidean geometry as a nontrivial motivating example would be useful... | |
| Mar 14, 2010 at 16:36 | history | edited | Jacques Carette | CC BY-SA 2.5 |
fix latex
|
| Nov 30, 2009 at 16:55 | history | answered | janmarqz | CC BY-SA 2.5 |