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Which topics are considered "graduate-level" for the following subjects:

  • Linear algebra
  • Multivariable calculus

On Internet, it is said that you need "graduate level" Linear algebra and multi-variable calculus for understanding Stochastic calculus, but topics are not mentioned.

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I would definitely add being very comfortable with measure-theoretic Probability and Real Analysis. –  gt6989b Oct 23 '12 at 15:59
    
@gt6989b, thanx, but subject/topics that you mentioned are my step number 2, but I also learned from net that you need some LA and MVC, how much is my question, I am an engineer, if I already know this "how much", then I cam happily start with RA and Measure theory –  Vikram Oct 23 '12 at 16:07
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Basically, you need to understand the abstract properties of Linear Algebra, e.g. group theoretic properties, etc. This is in contrast to "undergraduate" Linear Algebra, which focuses primarily on computational aspects and some basic algebraic properties (e.g. rank-nullity theorem, etc.).

For graduate-level multivariable calculus, you need to understand rigorous proofs regarding integration and differentiation in $\Bbb R^n$, as well as analytic properties of differential forms. This differs from undergraduate multivariable calculus, which again is typically computational, and focuses on vector calculus and use of Green's/Stoke's Theorems, rather than their construction and proof.

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Of course, for any given undergraduate program, your mileage may vary. –  Arkamis Oct 23 '12 at 15:57
    
thanx, can you tell which chapters of Linear algebra by Shilov will constitute "graduate level" linear algebra and same for Multi Variable Calculus by Edwards –  Vikram Oct 23 '12 at 16:03
    
I cannot, because I do not own those books. Perhaps I can find the TOC on Google. –  Arkamis Oct 23 '12 at 18:48
    
@Vikram Looking at previews in Google, I would say that probably none of the chapters in either of those books covers true graduate-level material. Maybe some of the later chapters in Shilov covers some material, but it appears to largely be computational. –  Arkamis Oct 23 '12 at 21:54
    
thank you, but unfortunately you increased my worries/tension( :s hehe..), don't know how much I will have to cover before embarking on Stochastic Calculus... (phew...)! –  Vikram Oct 24 '12 at 5:32
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