===== Todo =====
==== Meta ====
<code>
d = 3;
a = 5;
r = 1/3;
f[z_] = ((z + d)^a - d^a)^r;

Series[f[z], {z, 0, 6}]
</code>

>IMPORTANT:
>formal power series
>[[Tensor product]]
>[[ε-δ function limit]]

== Theormodyanmics ==

atm. there are only some notes under [[On phenomenological thermodynamics . Note]].

== topoi ==

>subobject classifier
>[[Base change functor]]
>
>
>

=== Topics ===

To solve 
$f(x)=x$ 
via fixedpoint iteration, one may consider the sequence
$f^n(x_\text{guess})$.

However, 
$g(x):=\dfrac{h(x)}{h(f(x))}\cdot f(x)$
should converge to it too and 
$g^n(x_\text{guess})$ 
may converge faster.

I saw this at [[https://en.wikipedia.org/wiki/Omega_constant#Computation | Omega_constant#Computation]] (Wikipedia) with $h(x):=1+x$.



=== Articles waiting to be created ===
//Type theory//

> [[Function type]]
> [[Dependent product type]] (for its use int the entry [[Category theory]])

//descrete math//

> [[multiset]]

//graph theory//

>[[source . graph theory]]/[[sink . graph theory]] of a graph - vertices where all adjacent edges are outgoing/ingoing

>[[directed acyclic graph]] - directed graph (connected?) without directed circle as subset

>[[Boolean circuit]] - directed acyclic graph where all non-sink/source vertices have either 1 or 2 ingoing vertices and there is a function assigning "$\neg$" to all of the former and another symbol (out of an alphbet "\land,\lor,\dots") to the latter.

//CS//

> [[Polynomial time Turing machine]]

//logic//

> [[Kleene star]]

//Set theory//

>supremum, bounds, etc.

<code haskell>
mnmInt :: [Int] -> Int
mnmInt [] = error "empty list" 
mnmInt [x] = x
mnmInt (x:xs) = min x (mnmInt xs)
</code>

//category theory//

> [[Set]]
> [[Category theory]]
> [[Hask]]
> several special arrows. In particular (for [[Natural isomorphism]])
> [[isomorphism . category theory]] 

>NOTE:
>- pullbacks + terminal object ⇒ equalizers + binary products
>- binary products + terminal object ⇒ all finite products
>- equalizers ⇒ all finite equalizers
>- finite products + finite equalizers ⇒ finitely complete (= all finite limits)
>- http://math.stackexchange.com/questions/591302/show-the-following-conditions-are-equivalent-for-a-category-c

// Number theory //

>[[prime-counting function]], see [[Riemann zeta function]], [[Offset logarithmic integral]]

//set theory, topology//

>[[Euclidean topology]]

// Analysis //

>TODO: make individual entries for models of ${\mathbb R},{\mathbb Q}$ and ${\mathbb C}$ and the entries called [[real numbers]], [[rational numbers]] and [[complex numbers]].

>[[Real coordinate space]]

>shift operator $T_a=\exp\left(a\frac{\partial}{\partial x}\right)$, and more generally http://en.wikipedia.org/wiki/Lagrange_reversion_theorem

// Complex analysis //

>[[Complex argument]] (see [[Natural logarithm of complex numbers]])
>[[Continuously differentiable finite lines]] (see [[Complex line integral]])

>Zeidler QFT 1
>p. 515: Polchinsky equation
>p.514: reg $\int$
>p. 512: Weierstrass product Theorem (for entire functions) - discussion: that's an infinite generalization of the factoring w.r.t. roots of a function. Similarly, I think, the infinite partial fraction decomposition is given by the //Mittag-Leffler's theorem//.

// diffgeo, analysis //

>[[Differentiable manifold]]
>[[Total derivative]]
>[[Hamiltonian vector field]]

//physics//

>[[Grand canonical partition function]]
>[[Quantum canonical partition function]]
>
>[[Classical Hamiltonian system]]
>[[Classical statistical ensemble]]

-----
=== Related ===
[[Nikolajs notebook]]