Todo

Meta

d = 3;
a = 5;
r = 1/3;
f[z_] = ((z + d)^a - d^a)^r;

Series[f[z], {z, 0, 6}]
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 Omega_constant#Computation (Wikipedia) with $h(x):=1+x$.

Articles waiting to be created

Type theory

descrete math

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

logic

Set theory

supremum, bounds, etc.
mnmInt :: [Int] -> Int
mnmInt [] = error "empty list"
mnmInt [x] = x
mnmInt (x:xs) = min x (mnmInt xs)

category theory

Set
Category theory
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

set theory, 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.
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

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

physics 