====Mathematics and crisis ====

By Tamuraj (http://www.tamuraj.com)

=== Mathematical prerequisites ===

  * Algebraic prerequisites
    * Real numbers, Complex numbers, Matrix algebra,...
  * Mathematical functions
  * Properties of mathematical functions
    * Continuity
    * Differentiability
  * Mathematical equations
    * Linear equations
    * Differential equations
  * The basic principles of mathematical logic
    * First order logic
    * Deduction systems
    * Meta logic
  * Probability theory


===Digital chaos
===

  * Random processes: natural and digital random processes
    * Brownian movements, the digital randomizer
  * Infinity
    * Different versions of infinity: 
    * Countable overcountible sets e.g. Cantor sets
  * Self similarity
    * Sierpinski triangle
  * Chaos theory
  * The linear fake model

===The artificial dream===

  * Introduction into [[Artificial Intelligence]]
    * Short overview of history
    * Definition and the Turing test
  * Hilberts program
  * Gödel’s theorem
  * The artificial brain
  * Emotive computing
  * Quantum mechanics and Artificial Intelligence


===Mathematical modeling===

  * Basic principles of mathematical modeling
    * Hypothesis testing
    * Error manipulation
  * Predictive modeling
    * Linear modeling with example
    * Outliers and instability

  * Overview of different mathematical models
    * Multilinear regression models
    * Polynomial regression models
    * Hazard models
    * General linear models
    * Timeseries analysis
    * ...


  * The curse of non linearity

  * The curse of assumptions
    * Normality
    * Linearity
    * Distributional assumptions


===Mathematical models of ecological  systems
====

  * Introduction into biostatistics
  * The outlier problem 
  * Rare events 
  * Recursive patterns
  * Linearization
  * Risk modeling
  * Maths and ecological policy

===Mathematical models of economical systems
===
  * Gödel’s theorem in a capitalist world
    * Loan systems
    * The monetary hyperspace
  * Capitalism and infinity
  * Introduction into econometric modeling
  * Linearization
  * Politics of complexity