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Analysis

Since no-one else has bothered to reply, you can't get very far in numerical analysis without understanding some real analysis. Off the cuff, understanding the reals and how the rationals fit in, understanding the different kinds of convergence (pointwise, uniform), understanding the uniform convergence of various power series.
 
CGiuliano said:
Which is more advantageous to have as an undergraduate:

Intro to Analysis

Courses of Study 2008-2009

or

Numerical Analysis.

Courses of Study 2008-2009

/

Courses of Study 2008-2009

Also, Which is more important to FE: linear/nonlinear numerical analysis or, diffEQ numerical analysis.

Thanks.
Click to expand...

Analysis is the foundation of virtually all that follows. Nothing can be properly understood without a solid grasp of Analysis. Do it right and build your math career on Analysis. Good Luck!
 
What people have posted below is all true. You need to crawl before you can run. This is what you're being told. From a practical standpoint, you will use numerical analysis way more than real analysis. In fact, you will probably never directly use real analysis on the job. This is because numerical analysis concerns implementing various numerical algorithms (root-finding, DE solving, etc.) and studying their efficiencies. Obviously, if you're a quant, you'll be doing a whole lot of this. What you need to understand is that math isn't just about jumping in naked. In order to meaningfully understand numerical analysis (which is ultimately what you really want), you need to first have a solid grasp of real analysis. (FYI: You use real analysis in numerical analysis to understand how quickly/efficiently numerical algorithms converge/work - this is a BIG part of numerical analysis.) You would be doing yourself a disservice to take numerical analysis without first knowing a good deal about real analysis, linear algebra, ODEs, PDEs, and basic programming. You should first solidify your foundation in these areas, and only then should you start taking numerical analysis courses.
 
financeguy- well put thank you =D>.

Already have a strong foundation in Linear and ODE's and I'm taking real analysis & PDE's in the Fall, so I should be ready for Numerical by Spring. Again, linear/nonliner, or diffEQ numerical Analysis?

Thanks
 
If you had to choose one, then take the DE numerical analysis. You should, however, consider a second course in real analysis as well since the first one does not cover all the necessary topics to lay a foundation for a more thorough understanding of more advanced subjects. Most people take at least two courses in real analysis, not just one - I think this is pretty standard. I guess if you're super-eager to take numerical, you can take the second course of real analysis at the same time.
 
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