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Order of mathematical concepts

  1. Jan 4, 2012 #1
    I have taken courses in math up to calculus 2, after which my math ambitions came to a quick hault. I would like to pick it back up and attempt to casually learn some math on my free time. So I would like to know the sequence/order of math concepts that someone would normally take at a given school. I will start this off to give an example and show what i know so far, anyone feel free to further elaborate my list or branch out on your own. My goal is to be able to conceptually understand all mathematical concepts, even if i cannot caculate. thanks ahead.
    • algebra
    • geometry
    • trigonometry
    • pre calculus
    • calculus1: limits, derrivatives
    • Calculus 2: integration, techniques of integration, volumes, divergence and convergence
    • Calculus 3: ....?
    • ....
  2. jcsd
  3. Jan 4, 2012 #2
    After calc II, there is no longer a linear connection between topics. That is, you can study a lot of independent things. Some things you can do:

    - Linear algebra: matrices, vector spaces, transformation. After this, you can take abstract algebra

    - Calculus III: studies multivariable derivatives and integrals. After this, you can study vector calculus or calculus on manifolds.

    - Analysis: You can study real analysis (which is just the rigorous version of calculus), then complex analysis or functional analysis or ...

    - Discrete mathematics and/or logic: studies discrete systems like graphs or generating functions. Logic studie axiomatic systems. The two topics are fairly different, but a first course usually combines the two.

    All these things are very much proof-based. So be sure to know proofs before embarking on your journey.
  4. Jan 4, 2012 #3


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    Calculus 3 typically extends the concepts of Calculus 1 and 2 to higher dimensions, dealing with functions from Rn to R or from R to Rn. "Analysis" deals with the theory behind Calculus. After that would come "Linear Algebra", "Abstract Algebra", "Differential Equations", "Partial Differential Equations", "Complex Analysis", "Functional Analysis", ...

    Of course, there is no standard "ordering" of most of those.
  5. Jan 4, 2012 #4


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    arithmetic, algebra 1, logic, geometry, linear algebra 1, elementary number theory, calculus, diff eq 1, adv calc, elementary differential geometry, abstract algebra 1, algebraic plane curves, linear algebra 2, real analysis 1, topology 1, complex analysis 1.

    now you can take grad algebra, grad real analysis, grad complex analysis, grad number theory, grad algebraic topology, basic algebraic geometry, grad differential geometry, pde, all in any order you like.
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