Sunday, March 2, 2014

How Mathematics Has Got Broader With Time

How Mathematics has got broader with time
  • Early Mathematics: the study of Quantities and Shapes
    • Areas: Number System, Algebra, Number Theory, Geometry 
      • Foundational work by Euclid (Elements) and Pythagoras
  • Calculus
    • Mathematics of change 
    • Still the study of quantities, but changing ones
    • 17th century invention
    • Newton and Leibniz
  • Probability
    • Mathematics of chance
    • 17th century invention 
    • Fermat, Pascal & Others 
  • Analysis
    • Generalization of the ideas of Calculus - limit, continuity, differentiability, etc.
  • Abstract Algebra
    • Generalization of Classical Algebra
    • Study of Algebraic Structures
    • Mathematics of symmetry (Not just calculation of "quantities")
    • Flourished in 19th & 20th Century 
  • Extensions of geometry
  • Automata, Languages, Computability - Discrete Mathematics 
    • 20th century  
    • Advent of Computers - finite state machine
    • Interest in Number Theory, Combinatorics, Graph Theory exploded
  • Network Science
    • Dynamic graph
    • Work begun in earnest in the late 20th and into the 21st century
    • Proliferation of Computer, Telecommunications and Social Networks. 

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