- #1

MexChemE

- 237

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It’s been a while since I last posted. I am looking for a critique and recommendations regarding my study plan towards Functional Analysis and applications (convex optimization, optimal control), but first, some background:

- This plan is in preparation for my master’s thesis, I will be working on optimization techniques and I want to be as rigorous as possible.

- ChemE degree, and just beginning a MEng in Systems Engineering, might be able to take some graduate math electives.

- My strengths are a solid intuitive understanding of single variable calculus and transport phenomena modeling.

- Never had a formal course in linear algebra during undergrad, and I don’t remember much of my multivariable class. 5 years have passed since my graduation.

- No previous proof-writing experience.

Now, for the actual plan:

For the first phase I intend to study linear algebra and multivariable calculus. My options for LA are Applied Linear Algebra by Shores and Linear Algebra and its Applications by Strang. By what I’ve seen by skimming the table of contents, both books are quite similar in content although I think Shores includes more proofs and also more interesting exercises, but Strang is a classic, which one would you recommend? I also think it is interesting Strang includes a small section on Hilbert spaces.

For multivariable calculus I am set on Lang’s Calculus of Several Variables.

Then for the second phase I intent on studying a more advanced LA book and mathematical analysis. For this phase I am pretty much decided on Lax’s Linear Algebra and Its Applications. For analysis though, I think I am going for Apostol’s Mathematical Analysis, however, I also like the contents in Zorich’s two-volume book, but it is pretty long. What is your opinion on Apostol vs. Zorich?

After that I think I should be ready to tackle functional analysis. Axler’s graduate analysis book seems like a good choice, however, maybe it would be best to read a dedicated FA book such as Rudin, Kreyszig, Kolmogorov. Could you please share your thoughts on this?

I think on parallel with my study of FA, I could begin studying advanced optimization at the level of Luenberger, Rockafellar or Sasane.

The timeline I have for this is one year before starting the program, and then one and a half years before having to start to work on my thesis, so 2.5 years in total.

Thank you very much for your insights!