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

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

subobject classifier
Base change functor

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 $h(x):=1+x$.

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.

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

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

Nikolajs notebook