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Quick 1-paragraph summary of all of math

  1. Mar 29, 2007 #1
    Go!

    Actually I want to pose this hypothetical question:

    If you wanted to self-learn most of the higher level mathematics most efficiently, starting with a calculus level knowledge, how would you go about doing it?
     
  2. jcsd
  3. Mar 29, 2007 #2
    * 01. Logic and Foundations
    * 02. Algebra
    * 03. Number Theory
    * 04. Algebraic and Complex Geometry
    * 05. Geometry
    * 06. Topology
    * 07. Lie Groups and Lie Algebras
    * 08. Analysis
    * 09. Operator Algebras and Functional Analysis
    * 10. Ordinary Differential Equations and Dynamical Systems
    * 11. Partial Differential Equations
    * 12. Mathematical Physics
    * 13. Probability and Statistics
    * 14. Combinatorics
    * 15. Mathematical Aspects of Computer Science
    * 16. Numerical Analysis and Scientific Computing
    * 17. Control Theory and Optimization
    * 18. Applications of Mathematics in the Sciences
    * 19. Mathematics Education and Popularization of Mathematics
    * 20. History of Mathematics

    The best path of study depends on your goals with Math. If you want to be a Mathematician, you can't go wrong with Abstract Algebra and Analysis (advanced calculus).
     
  4. Mar 29, 2007 #3
    Crosson,

    Is there a book, understandable to a Mathematics B.S., which overviews the topics you list?
     
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