Quick 1-paragraph summary of all of math

[Fletcher]

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?

 

[Crosson]

* 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).

 

[Loren Booda]

Crosson,

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