Which Class Should I Drop?

[YoungEconomist]

Unfortunately, I won't have a chance to take all of the math classes I'd like to take. So, I'd like to ask all you TMers which one of the classes below should I drop from my schedule?

Advanced Multivariable Calculus I
Topics include the chain rule, Lagrange multipliers, double and triple integrals, vector fields, line and surface integrals. Culminates in the theorems of Green and Stokes, along with the Divergence Theorem.

Introductory Real Analysis I
Limits and continuity of functions, sequences, series tests, absolute convergence, uniform convergence. Power series, improper integrals, uniform continuity, fundamental theorems on continuous functions, theory of the Riemann integral.

Probability II
Random variables; expectation and variance; laws of large numbers; normal approximation and other limit theorems; multidimensional distributions and transformations.

Introduction to Mathematical Statistics
Probability, generating functions; the d-method, Jacobians, Bayes theorem; maximum likelihoods, Neyman-Pearson, efficiency, decision theory, regression, correlation, bivariate normal.

[pevdoki1]

Originally Posted by YoungEconomist

Unfortunately, I won't have a chance to take all of the math classes I'd like to take. So, I'd like to ask all you TMers which one of the classes below should I drop from my schedule?

Advanced Multivariable Calculus I
Topics include the chain rule, Lagrange multipliers, double and triple integrals, vector fields, line and surface integrals. Culminates in the theorems of Green and Stokes, along with the Divergence Theorem.

I wonder why this is called advanced M.C... I always thought that these topics are part of any run of the mill multivariate calc course. They always seemed fairly important to me, so I wouldn't suggest dropping it.

[YoungEconomist]

It turns out that I might not be able to take Real Analysis, depending on what time they offer it that quarter. So I have 1 more question: What is the Rubin book everyone talks about on this forum? I've tried to find it on amazon, but didn't have any luck. I want to find out what the book is, because if I can't take the class I plan on studying the book before school starts.

[semischolastic]

That might because it is Rudin, rather than Rubin.

Amazon.com: Principles of Mathematical Analysis, Third Edition: Walter Rudin: Books

[pevdoki1]

I think you'll have a really hard time digging through Rudin on your own (I speak from experience, since I bought it before I took real analysis).

You really need a professor to guide you through it. Another benefit is that the professor will point out places where Rudin leaves parts of proofs up to the reader (some of these can be tricky). Also, you'll get feedback on your homework proofs (how else will you know what the hell you're doing???)

[ForTheWin!_08]

Only the multivariable calculus stuff will not be heavily used in graduate school. Unless you plan on skipping econometrics entirely and becoming an 19th-century physicist instead, I wouldn't worry about not knowing Stokes' theorem. You will, however, need to be conversant with all of the topics you mentioned from the latter three courses.

[octavio]

So I know a bit about the UW's courses and felt like pointing out that Advanced Multivariable Calculus I isn't really advanced. This is students' first exposure to things like Lagrange multipliers, multivariate integration, and the chain rule in a multivariable context. I would consider this to be basic and pretty important stuff -- it was covered in my standard calculus sequence at another university. What do you all think?

[YoungEconomist]

Originally Posted by semischolastic

That might because it is Rudin, rather than Rubin.

Well, that explains a lot.

By the way, if a Real Analysis class does not use this textbook, does that mean it's not really worth taking?

[pevdoki1]

No. I learned Analysis 1 without Rudin, and only Analysis II out of Rudin (we went straight to later chapters).

[GymShorts]

Your advanced multivariate calculus I class covers exactly what my calculus III class covered. When schools say you need at least three semesters of calculus at a minimum, this class is included.