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Mathematics in 10 levels.

  1. Mar 13, 2013 #1
    I saw somewhere that mathematics can be divided into 10 sections, i quote:

    "1-Arithmetic
    2-Basic Logic and Set Theory: proof techniques and reasoning, Sets,
    operations on sets, mappings, binary relations (you'll need that
    if you expect to go anywhere beyond arithmetic..)
    3-Combinatorics and Elementary Number Theory
    4-Basic Abstract Algebra: groups, rings, fields
    5-Linear Algebra: Linear spaces, subspaces, linear mappings, matrices, polynomials
    6-Affine and Euclidian Geometry
    7-Basic Point-Set Topology
    8-Analysis
    9-More Linear Algebra
    10-More Abstract Algebra"

    How much of this is true?
     
  2. jcsd
  3. Mar 25, 2013 #2
    To be honest, I see no reason to make this categorization...

    Of course, if you learn math e.g. at a university, you will have different subjects, like algebra, linear algebra, analysis, etc. However, after learning enough, you will see, that everything is connected with almost everything in mathematics. Graph theorists use extereme advanced analysis techniques, analysists often use algebraic tools, and set theorists created non-standard analysis (where the "infinitesimal" quantity is defined in a precise sense!) etc, so these categories are rather artificial in my opinon.
     
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