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> My goal here is to provide a roadmap for anyone interested in understanding mathematics at an advanced level. Anyone that follows and completes this curriculu

> My goal here is to provide a roadmap for anyone interested in understanding mathematics at an advanced level. Anyone that follows and completes this curriculum will walk away with the knowledge equivalent to an undergraduate degree in mathematics. NO, NO, NO. There is no real way to go up to the real deal without having understood elementary Functional Analysis, which the article doesn't even mention. FA is roughly what Linear Algebra would look like if instead of finite dimensional vector spaces we considered infinite dimensional vector spaces. It opens the rigorous path to non-linear optimization, analysis of pdes, numerical analysis, control theory, an so on. What this article mentions is a way to work around things, but nowhere near an undergraduate degree in mathematics. I'm astonished that the PDE section has such books, they look like the calculus aspect of partial differential equations. A more appropriate book would be L. C. Evans' Partial Differential Equations. Same with ODEs, no mention of Barreira's or Coddington & Levinson's books.

ratzkewatzke 5y ago
I'm a fan of functional analysis, but even in my (very competitive) undergraduate curriculum, it wasn't required for a bachelor's in mathematics. I think Susan's guide covers most of what the undergraduate programs I've seen require.
- mbustamanter 5y ago
  It was for me (french school of math), that and also measure theory.
davidmr 5y ago
This is certainly not universally the case, even in very well-regarded departments. The University of Chicago, for example, does not require it: http://collegecatalog.uchicago.edu/thecollege/mathematics/ http://collegecatalog.uchicago.edu/thecollege/mathematics/.
- secabeen 5y ago
  For those of you interested in the Chicago approach, a bibliography of textbooks used in Chicago UGrad math is maintained here: https://github.com/ystael/chicago-ug-math-bib https://github.com/ystael/chicago-ug-math-bib
BeetleB 5y ago
My undergrad institution does not require FA to graduate. It doesn't even list as an elective. There's a very good reason for this: FA is not all that useful if you're more on the algebra side of things.

ratzkewatzke 5y ago

I'm a fan of functional analysis, but even in my (very competitive) undergraduate curriculum, it wasn't required for a bachelor's in mathematics. I think Susan's guide covers most of what the undergraduate programs I've seen require.

mbustamanter 5y ago
It was for me (french school of math), that and also measure theory.

davidmr 5y ago

This is certainly not universally the case, even in very well-regarded departments. The University of Chicago, for example, does not require it: http://collegecatalog.uchicago.edu/thecollege/mathematics/ http://collegecatalog.uchicago.edu/thecollege/mathematics/.

secabeen 5y ago
For those of you interested in the Chicago approach, a bibliography of textbooks used in Chicago UGrad math is maintained here: https://github.com/ystael/chicago-ug-math-bib https://github.com/ystael/chicago-ug-math-bib

BeetleB 5y ago

My undergrad institution does not require FA to graduate. It doesn't even list as an elective. There's a very good reason for this: FA is not all that useful if you're more on the algebra side of things.