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tl;dr : Is the dependency in the figure attached accurate?

Long Version : I am through with my engineering and am shifting to math for grad school. I am looking forward to re-learning (reviewing) everything (Calculus on wards) that is relevant to me. I have created a rough diagram of what I have to learn, which books I have to refer and the dependency I predict by checking out course prerequisites at Stanford, Princeton, UCLA etc.

I am not entirely new to any of these subjects; there is always a little familiarity but what I want now is mastery. I will be learning by myself.

Dependency

For Differential Equations, I am thinking of using Simmons and for Numerical Optimization, Nocedal and Boyd for Convex Optimization. Fluid Mechanics is Batchelor. Numerical Analysis I am yet to decide a book on but it could be a Numerical Methods for Engineers type book. Link to the Computational Science Part : Here.

Does this sequence seem OK? Should I do anything differently

Note: I'll be spending about 15 days - a month per subject (which I think will be sufficient since I only have to fill in some holes). All subjects on the same horizontal level, I will working on together.

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@Whoever down voted, Please explain the reason. The question is objective (People can have facts not opinions about prerequisites)and non-localized (every engineer who wishes to shift to math needs to brush up these things). –  Inquest Mar 17 '12 at 6:47
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1 Answer

up vote 1 down vote accepted
+50

It is certainly a good idea to start with linear algebra as this subject is basic to most other subjects. However since you are shifting to math for grad school i would recommend looking at some other text book because Strang is to obsessed with matrices. It is helpful to view linear algebra from little more abstract point of view if one considers doing more math in the future. Also for ordinary differential equations your going to need jordan canonical forms wich are not covered much in Strang.

You can do numerical analysis after linear algebra and multivariable calculus, but it is not a prerequisite for most subjects that follow in your graph. The book on functional analysis by Kreyszig for instance can be read without any knowledge of numerics (I did that myself.). Knowing a bit about functional analysis might make learning numerical analysis simpler. I do not know anything about fluid mechanics but i think you should study this subject after functional analysis because the theory of partial differential equations involves a lot of functional analysis.

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So, Should I go LA > Multivariable > Functional > Numerical and then the rest? –  Inquest Mar 17 '12 at 9:03
    
Yes, that would be a way to do it. One thing that is not on your list, but could be very useful would be real analysis. Real analysis is used heavily in some probability books and also in more advanced books on functional analysis. –  readingframe Mar 17 '12 at 9:10
    
Where do you recommend I put that? –  Inquest Mar 17 '12 at 10:10
    
After multivariable calculus. –  readingframe Mar 17 '12 at 10:31
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