Introduction to Concrete Supermath:

We cover basics of supernumbers, superanalysis and super geometry. This involves generalizing course work from linear algebra, real analysis, advanced calculus, complex analysis and naturally calculus. Our goal will be to find some new examples to add depth to the concept of a supermanifold.Supermath is not the endgoal of this exercise, ideally we hope to understand more about ordinary math by thinking about how it can be abstracted. Incidentally, this is why algebra teachers should take abstract algebra.

The concreteness of our approach is that our models mirror those of ordinary differential geometry. We have points, functions, vector fields, forms etc... these are a bit more abstract, but the procedure is usually that of replacing real or complex numbers with supernumbers. In contrast, the ringed-space approach, or the other more abstract approaches to supermath involve much more machinery from algebraic geometry. There are advantages to both approaches. You can read Supermanifolds: Theory and Applications by Alice Rogers to gain some appreciation of the advantages and disadvantages of the concrete approach.

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Last Modified: 8-17-12