Graph and model transformations play a central role for visual modeling and model-driven software development. Within the last decade, a mathematical theory of algebraic graph and… 59 more words

## Tags » Algebraic

#### Raspberry Springtime Lemonade

Oh, the things I might show you

The pleasures you might experience

If only life were like that

If our judgments weren’t pretense.

Oh, the things I could tell you… 63 more words

#### Time-Evolution in Quantum Mechanics is a “Flow” in the (Abstract) Space of Automorphisms of the Algebra of Observables

In quantum mechanics, time is not a geometrical flow. Time-evolution is characterized as a transformation that preserves the algebraic relations between physical observables. If at a time t = 0 an observable – say the angular momentum L(0) – is defined as a certain combination (product and sum) of some other observables – for instance positions X(0), Y (0) and momenta PX (0), PY (0), that is to say… 325 more words

#### Diophantine Approximation: Liouville’s Theorem

Diophantine approximation deals with the approximation of real numbers by rational numbers.

## Liouville’s Theorem

In the 1840’s Liouville obtained the first lower bound for the approximation of algebraic numbers: 169 more words

#### Transcendental Numbers

A transcendental number is a number that is real or complex, but it not algebraic, meaning that it is not the root of a polynomial with non-zero integer coefficients. 223 more words

#### Transitivity of Algebraic Extensions

Let be a tower of fields. If and are algebraic, then is algebraic.

**Proof:**

(Hungerford pg 237, reworded)

Let . Since is algebraic over , there exists some () such that… 41 more words

#### Arithmetic Operations

There are only 4 binary operations which we call “arithmetic operations”. These are:

- Addition (+)
- Subtractions (-)
- Multiplication (×)
- Division (÷)

Reading this fact, an obvious question is: 398 more words