===== 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 [[http://graph.axiomsofchoice.org/?to=boltzmann_equation|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

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=== Sequel of ===
[[On syntax]]