Pillars of Mathematics' Building
Following are 4 pillars of Mathematics upon which its building is established:
Things will go more smoothly, if one already has had some experience with continous functions, open and closed sets, metric spaces, and the like, although none of is actually assumed.
The teaching of topology aafords the instuctor opportunity not only to impart necessary mathematical contents, but also to expose the students to both riger and abstraction.
Since the axiomatic methods is fundamental to mathematics, the student should become acquainted with it as early as possible.
- Topology, (Read More)
- Algebra,
- Geometry, and (Read More)
- Analysis
Topology
The only pre-requisite for topology is study of some analysis; even the traditional "Advanced Calculus" should be sufficient.
No part of this require the material sometime labelled "Modern Algebre".
Naive Way = Non-axiomatically
Things will go more smoothly, if one already has had some experience with continous functions, open and closed sets, metric spaces, and the like, although none of is actually assumed.
The teaching of topology aafords the instuctor opportunity not only to impart necessary mathematical contents, but also to expose the students to both riger and abstraction.
Since the axiomatic methods is fundamental to mathematics, the student should become acquainted with it as early as possible.
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