Equivalent to Real Analysis? Also, related question

[metaserve]

My school doesn't have a class named "real analysis". Is the following class it but under a different title?

Advanced Calculus I:
"Rigorous review of elementary calculus. The real number system. Continuous functions. Taylor’s formula. Infinite series. Convergence criteria."

Seems similar from the description.

I have taken Calculus I-III. I am signed up to take Mathematical Proofs and Differential EQ's in the Fall, which are the prerequisites for the Adv. Calc course. But I am not sure if it is offered in the Spring, which is my last semester before I plan to graduate. Is it necessary to take if I want to have a shot at top-30 programs?

Thanks

[mathemagician]

Eh... not really. Seems like watered down real analysis.

This is the description from my university:
A rigorous treatment of the real number system, Euclidean spaces, metric spaces, continuity of functions in metric spaces, differentiation and Riemann and Riemann–Stieltjes integration of real-valued functions, and uniform convergence of sequences and series of functions.

[chisquared]

Eh... not really. Seems like watered down real analysis.

This is the description from my university:
A rigorous treatment of the real number system, Euclidean spaces, metric spaces, continuity of functions in metric spaces, differentiation and Riemann and Riemann–Stieltjes integration of real-valued functions, and uniform convergence of sequences and series of functions.

Sounds almost like the table of contents of Baby Rudin.

[Popolo2]

While we're on the topic of real analysis, are most people here doing a two-semester sequence (at my school, "mathematical analysis I and II", using Rudin), followed by a graduate semester of "functional analysis"?

[kevinp123]

While we're on the topic of real analysis, are most people here doing a two-semester sequence (at my school, "mathematical analysis I and II", using Rudin), followed by a graduate semester of "functional analysis"?

I don't think most people on here have taken that much analysis.

In regards to OP's question, I think a lot of schools call Real Analysis Advanced Calculus. Mine does, but I don't really go to a top school. Even if it is a "watered-down" version of analysis, that is the school's fault and there is nothing you can do about it, so I think your best shot would be to take it.

[Baby Varian]

What about this?

1. Number Systems (§1):
   ordered fields
   rational, real and complex numbers
   Archimedian property
   supremum, infimum, completeness
2. Sequences and Series of Real Numbers (§3):
   limits of sequences, algebra of limits
   Bolzano-Weierstrass Theorem
   Cauchy sequences, liminf, limsup
   limits of series, convergence tests, absolute and conditional convergence
   power series
3. Metric Spaces (§2):
   metric spaces
   convergence, completeness, completion
   open sets, closed sets, compact sets, Heine Borel Theorem
   connected sets
4. Continuity (§4):
   functions, cardinality
   continuity
   continuity and compactness, existence of minimizers and maximizers, uniform continuity
   continuity and connectedness, Intermediate Value Theorem
   monotone functions and discontinuities
5. Differentiation (§5):
   differentiation
   Mean Value Theorem
   L'Hôpital's Rule
   Taylor's Theorem

Is this real analysis?

[Charis]

I am actually at a school with a similar system (I've taken the watered down real analysis class) but they also teach a more advanced version of the class next semester (using Rudin). Having taken the watered down analysis my first preference would be to jump right into Grad Micro and Econometrics, but do you think I should back pedal and take the real analysis taught with Rudin now instead of the grad classes.

[_nanashi]

What about this?

1. Number Systems (§1):
   ordered fields
   rational, real and complex numbers
   Archimedian property
   supremum, infimum, completeness
2. Sequences and Series of Real Numbers (§3):
   limits of sequences, algebra of limits
   Bolzano-Weierstrass Theorem
   Cauchy sequences, liminf, limsup
   limits of series, convergence tests, absolute and conditional convergence
   power series
3. Metric Spaces (§2):
   metric spaces
   convergence, completeness, completion
   open sets, closed sets, compact sets, Heine Borel Theorem
   connected sets
4. Continuity (§4):
   functions, cardinality
   continuity
   continuity and compactness, existence of minimizers and maximizers, uniform continuity
   continuity and connectedness, Intermediate Value Theorem
   monotone functions and discontinuities
5. Differentiation (§5):
   differentiation
   Mean Value Theorem
   L'Hôpital's Rule
   Taylor's Theorem

Is this real analysis?

Yes that course is real analysis. I'm guessing the title is Math 320: Real Variables I?
(if it is give me a p.m.)

[treblekicker]

suggestion to anyone who ever wants to make one of these threads:

instead, visit the math department websites for top universities and see what they describe ug real analysis as

[metaserve]

Okay. But is it the consensus that the class I listed is close to real analysis?

There is also "Adv. Calculus II", as another person mentioned. It continues with fourier series and coordinate trasnformation.