How hard is Real Analysis 2 compared to Real Analysis 1?

[SMA_01]

Is it a lot harder? I'm taking Real Analysis 1 this semester, and am planning on taking the second part to the course in the Winter.
Also, would it be a bad idea to take Real Analysis 2 and Elementary Number Theory in one semester?

Thanks

 

[homeomorphic]

I found it noticeably harder, but it's not a really big leap or anything.

 

[PieceOfPi]

Please post the course descriptions of both Real Analysis 1 and 2; those course titles mean completely different things between different schools.

 

[SMA_01]

Please post the course descriptions of both Real Analysis 1 and 2; those course titles mean completely different things between different schools.

Analysis 1:

Properties of the real number system; point set theory for the real line including the Bolzano-Weierstrass theorem; sequences, functions of one variable: limits and continuity, differentiability, Reimann integrability.

Analysis 2:

Includes the rigorous study of functions of two and more variables, partial differentiation and multiple integration. Special topics include: Taylor Series, Implicit Function Theorem, Weierstrass Approximation Theorem, Arzela-Ascoli Theorem.

 

[romsofia]

I can't comment on the analysis part, but elementary number theory is not very hard. All the theorems involve basic algebraic manipulations, and mods (which you should be use to by now).

 

[micromass]

Analysis 1:

Properties of the real number system; point set theory for the real line including the Bolzano-Weierstrass theorem; sequences, functions of one variable: limits and continuity, differentiability, Reimann integrability.

Analysis 2:

Includes the rigorous study of functions of two and more variables, partial differentiation and multiple integration. Special topics include: Taylor Series, Implicit Function Theorem, Weierstrass Approximation Theorem, Arzela-Ascoli Theorem.

If you got through Analysis 1 alive, then you won't find Analysis 2 much harder. In fact, I think Analysis 1 is the hardest course since you got to get used to the techniques and proofs of analysis. In analysis 2, you're already used to that. So you won't find it too difficult.

 

[PieceOfPi]

Analysis 1:

Properties of the real number system; point set theory for the real line including the Bolzano-Weierstrass theorem; sequences, functions of one variable: limits and continuity, differentiability, Reimann integrability.

Analysis 2:

Includes the rigorous study of functions of two and more variables, partial differentiation and multiple integration. Special topics include: Taylor Series, Implicit Function Theorem, Weierstrass Approximation Theorem, Arzela-Ascoli Theorem.

Thanks! Based on the course descriptions, Analysis 2 sounds like a very reasonable sequence that follows Analysis 1. It can hard in a sense that the materials build upon what you learned in analysis 1 (afterall, you need to be solid on the analysis of R^1 in order to learn the analysis of R^n). On the other hand, if you have a solid understanding of analysis 1, analysis 2 shouldn't be too hard, since you will see same kinds of techniques from analysis 1 again.

 

[SMA_01]

Thank you, that was helpful