Castial

Ah I see. As for my post regarding no prior background, I ment it more in the context of point-set topology and primarily measure theory since papa rudin usually assumes intermediete knowledge of both before starting the book. I think you might be referring to his other book " Principles of Mathematical Analysis ", i.e baby rudin. I think your class is following a different syllabus though so never mind. Good luck with the class, Cheers !

Just wondering but what book does your school use for "Honors Analysis" ? I ask only because this is supposedly the first analysis class you'll be taking and it's listed as a graduate class in your post. Most graduate schools jump into Papa rudin typicallly for a graduate analysis class and I'd be shocked if you could follow that without any prior background in analysis whatsoever.

It's funny how different the definition of Real Analysis is at different schools. Measure Theory/ Functional Analysis/ Fourier Analysis is still considered undergrad material at McGill for example though that's because they have Anal 1/2/3/4 as undergrads instead of just 1/2 like most other schools.

joint honours econ/math at McGill I presume?

Lol, thats strange. I dont know much about Queens but mcgills honours econ/math program is crazy difficult by any standards. I assumed the rest of Canada was like that aswell.

Your masters coursework seems to be undergrad courseswork at better math departments. I mean typically arnt you suppose to do a fair bit of algebra/analysis as an undergrad and generally do advanced topics at the grad level? It's quite odd to see a course called linear algebra at the grad level given that nearly every grad school considers linear algebra a special case of abstract algebra and this is further explored in galois theory. For example at my school math undergrads usually finish up til galois theory in algebra and fourier analysis/measure theory in real analysis.

Are you at McGill by any chance?

At my school the Applied Math masters typically includes a 2-term course on Measure Theory probability with 4 courses of real analysis as a pre req. Typically applied math masters also do take courses which require alot of pure mathematics.

I should have been more clear. When I mentioned Micro 1/2 and Macro 1/2, I essentially ment Honours Intermediete Micro/Macro 1/2. There is no higher level at my school. As for Econometrics 1, it was an honours joint senior undergrad/grad course. We did the first 9 chapters of Davidsons Book which I believe is considered a graduate book by several universities. I prefer to do a masters in math because it would also allow me to take some graduate econ courses alongside the math and the converse is not possible because of some faculty regulations. Also, the econ professors that I know pretty much told me to do the math as well since the grad econ program here isnt particularly good while the math is.

These are regular semester courses, Fall/Winter Real Analysis 1 - The Real Numbers, Sequences, Limits, Continuity, Differentiation Real Analysis 2 - Metric Spaces and Multivariable Analysis, Numerical Series, The Riemann Integral and Lebesque Theorem, Sequence of Functions, Power Series, Analysis of the Elementary Functions. Real Analysis 3 - Review of point-set and Metric Space topology, topological space, dense sets, completeness, compactness, connectedness and path-connectedness, separability. Arzela-Ascoli, Stone-Weierstrass, Baire category theorems. Measure theory: σ-algebras, Lebesgue measure. Real Analysis 4 - Continuation of measure theory. Abstract integration. Functional analysis: Lp spaces, linear functionals and dual spaces, Hahn-Banach theorem, Riesz representation theorem. Hilbert spaces, weak convergence. Spectral theory of compact operator. Fourier analysis, Fourier transforms.

Need some advice, I'll try to be as clear as possible. I expect to graduate next year from a Top 3 Canadian school and I'm wondering If I should apply for a PhD in my final year or not. Here are the Facts : Math Courses taken till date : Calculus 2/3/4, Real Analysis 1/2, Abstract Algebra, Linear Algebra, ODE's, Numerical Analysis Math Courses Expected to take next year : Graduate Probability, PDE's, Real Analysis 3/4, Complex Analysis Econ Courses taken till date : Micro 1/2, Macro 1/2, Econ Stats 1/2, Econometrics 1 I've done well in all the courses I've taken till date, Solid A's in all of them. However I'm not particularly close to any Professor and I dont think that I would be able to get a great reference. Here are my options : Option 1 : Apply directly for the PhD with possibly "decent" but not great recommendation letters. Option 2 : Stay on at my current school for a masters in math and take some graduate economics courses as well. Also, get to know my Econ Professors better. I have no doubt that I would be able to get better recommendation letters if given time. Other Relevant Facts : The masters is fully funded so I dont lose anything financially. Also I could possibly see a masters helping me in the long run in fields like econometrics. Suggestions?

I've sort of alternated between 5 courses and 4 courses throughout my undergrad. The reason being primarily because I work 20 hours during the week apart from school and alot of the time my work timings conflict with some class which prevents me from taking a 5th. Also, it's quite exhausting to do 5 courses and work. Do I mention this in my application or do they not really care if you do 4 or 5 each term?

I'd skip it then. The only thing I found remotely useful in my Calc 4 class was the fourier series/pde's section. If you dont have something like that, then it's not worth it imho. Vector Calculus in it's own right isn't a very long course so most schools usually add something to it.

What is Calculus 4 in your school? For me, it's Vector Calculus ( Stokes, Gauss, Green etc ) + Fourier Series to solve the Heat/Wave/Laplace partial differential equations.

In the long run, a skilled computer scientist would not really be judged on where he graduated from. Most if not all, comp sci graduates depend on their work and code to sell themselves later on. It's in fact even more impressive to most people if you graduate at a lower school and still have great code skills, experience etc. Your point is well noted though if you're talking about something like investment banking where there's alot of value throughout your life by getting to say that you went to harvard. Doesn't matter even if you went there for women's studies.