[proginthebox]

This is terrible advice. Apart from the last sentence. A better advice would be to specify which subject to learn.

For example, (since I don't really have much time)

1. Topology (book by Munkres)

2. Real Analysis and Measure Theory (book series by Stein Shakarchi)

3. Algebra (book by Aluffi)

4. Linear Algebra (book by Friedberg Insel)

5. Measure Theoretic Probability (book by Cinlar)

6. Differential Geometry (book Smooth Manifolds by Lee)

7. Numerical Analysis (book by Quarteroni)

8. Set Theory and Propositional Logic (books by Goldrei)

This is what one will mainly learn in a strong undergrad/grad math program. Once this is done, then there are different tracks to follow.

[abnry]

The advice I gave is not exclusive to working through the typical undergraduate books.

I was questioning why the OP wants to self-study an undergrad math curriculum to begin with.

It's probably not to become a pure mathematician. So I suggested, instead of creating a massive goal of getting through a collection of books just for the sake of being a completionist, to have a concrete personal goal. Otherwise, people can throw books "you have to read" at you until the cows come home. Especially since this person is talking about applied math.

[proginthebox]

I see. Well, you have a point, but the OP did specifically ask for a plan like that Susan Fowler's blog post. And I am an applied mathematician working mostly on computational physics and I can attest to the requirements I mentioned.

But your advice has a point, just going through books mindlessly is not motivation enough/ can lead to wandering. And it is always good to have specific tasks at hand. Like, solving a particular ordinary differential equations numerically.

[xenihn]

Is this the recommended order to read/learn them in? If I was primarily concerned with getting up to par with math for the sake of being able to actually understand everyone's favorite algorithms textbooks, would you still suggest working through all of these, or could you recommend an abridged list?

[proginthebox]

If you want to understand algorithms, you need a computer science curriculum, not a mathematical curriculum.

Also, unfortunately, its not the recommended order to learn them in.