## Guideline

On syntax $\blacktriangleright$ Guideline |

### Note

##### What's different between 'An apple pie from scratch' the AoC graph itself

- Book-like character and hence linear. To read it, follow the red path in the axiomsofchoice graph.
- The concepts are development in a logical/mathematical fashion too, while the graph shows a not necessarily linear web of dependencies.

##### Approach

- I do math for physics sake, not for mathematics. So provable theorems are just used right away. Emphasis on concepts relevant for physics are generally emphasized (e.g. Green functions $\gg$ Dedekind cuts).
- The tour guide is
**Self-contained**. Also as concise as possible and hence completely**top-down**: Always introduce the mathematical object first which*a)*needs least and more rudimentary tools*b)*has most models and special cases.**Theorem hierarchy**is developed (studied). - Syntax and semantics: One should try to differntiate the general syntactic theory and its semantics. Especially for the more general framworks, I try to keep track of core semantics/examples at the same time.

##### Focus

The focus of the presentation is motivated in Perspective. We care for general mathematical structures and versatile computational knowledge…

Framework emphasis(versatile):

Universal properties

Sets

Structure emphasis(established important structures for physics):

Lie-Groups

Geometrical formulations of theories

(Hamiltonian formulations of Dynamical systems)

Computational knowledge

Evaluations of integrals and sums

Formal power series, Difference Calculus, Falling powers etc.

integrals over differential equations (as motivation, remember: stochastic differential = integral relation)

Green functions