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maths_and_crisis

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

maths_and_crisis.txt · Last modified: 2014/08/05 21:27 by nik