PDA

View Full Version : Math Preperation Question



YoungEconomist
02-23-2008, 10:49 PM
I will definitely take the following courses:

Calculus with Analytic Geometry I
First quarter in calculus of functions of a single variable. Emphasizes differential calculus. Emphasizes applications and problem solving using the tools of calculus.

Calculus with Analytic Geometry II
Second quarter in the calculus of functions of a single variable. Emphasizes integral calculus. Emphasizes applications and problem solving using the tools of calculus.

Calculus with Analytic Geometry III
Third quarter in calculus sequence. Sequences, series, Taylor expansions, and an introduction to multivariable differential calculus.

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.

Introduction to Differential Equations
Introductory course in ordinary differential equations. Includes first- and second-order equations and Laplace transform.

Matrix Algebra with Applications
Systems of linear equations, vector spaces, matrices, subspaces, orthogonality, least squares, eigenvalues, eigenvectors, applications. For students in engineering, mathematics, and the sciences.

Introduction to Mathematical Reasoning
Mathematical arguments and the writing of proofs in an elementary setting. Elementary set theory, elementary examples of functions and operations on functions, the principle of induction, counting, elementary number theory, elementary combinatorics, recurrence relations.

Probability I
Sample spaces; basic axioms of probability; combinatorial probability; conditional probability and independence; binomial, Poisson, and normal distributions.

My question is: What will be the marginal benefit of adding the courses below in terms of being prepared to succeed in a PhD program? (just for the record, I am not worried about the signaling benefit of the following courses, because they won't be on my transcript anyway because I would be taking them around the time I get admits/rejects) Also, out of the courses below, which ones are most crucial? Are any of them more important than some of the classes I've listed above which I plan on taking for sure?

Advanced Multivariable Calculus II
Elementary topology, general theorems on partial differentiation, maxima and minima, differentials, Lagrange multipliers, implicit function theorem, inverse function theorem and transformations, change of variables formula.

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

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.

In case it matters for the advice, I don't aspire to top 10 programs (in fact, I won't be applying anywhere in the top 10, and possibly not even in the top 20). The overwhelming majority of programs I'll be applying to are in the range of 20 - 40 (according to US News Rankings).

apropos
02-23-2008, 11:07 PM
Probability 1 sounds kind of incomplete. The adcoms will not notice that since they don't read course descriptions, but if you care about knowing the material well enough to take courses that assume prior knowledge of probability, you should probably take a course that also covers random variables, transformations, CLT, etc.

Enough has been said about real analysis, just search the archives. It's very important to have it although there are strong applicants who get into very good PhD programs without it. In the end, it may also depend on who is going to teach your theory courses. At Purdue, Micro 1 and Micro 2 are both taught by mathematical economists, and yet they're so different in their approach. Micro 1 is taught in such way that all math you need is a working knowledge of multivariate calculus and optimization. Homeworks were mind-twisting, but they're rarely about math. Micro 2 is a different story. It's taught by professor Aliprantis who likes to prove and derive every simple little result very carefully. You will have much easier time in a course like that if you have taken a decent undergraduate real analysis course (e.g. something that covers elementary point-set topology well, you'll get to use much of it). Also, both of our first year Macroeconomics courses make references to various parts of SLP, which again has very mathematically rough parts, but I don't think mastering this book is essential to doing well in our first year courses.

reactor
02-23-2008, 11:21 PM
All the extra courses have material that is used in the first year econ PhD (even in not top 10 schools). Maybe it is not the core material (i.e. it is not economics or econometrics) but you have to prepare for whatever you can. If during the first year you already know this stuff (math & probability), you will have more time for the other stuff (economics).
I think that it is important to start the PhD with an advantage in at least one area (say mathematics or statistics or advanced economics=not essays) so you can "draw from your background" and devote more time to your weaker areas.

pevdoki1
02-23-2008, 11:48 PM
I applied mostly in the 20-50 range, and I have 2 semesters each of real analysis and mathematical statistics.. It seems to me that my math preparation is pretty basic (and IT IS compared to some of the foreign applicants). I don't consider myself a mathematician at all; I simply tried to learn some elementary things.

I would REALLY suggest taking analysis.

bauble
02-23-2008, 11:51 PM
The calc that you listed will be very useful for micro. The probability will be useful for econometrics. That said, if you have a strong basic foundation (the calc 1/2/3 and matrix algebra you listed), you'll do just fine.

YoungEconomist
02-23-2008, 11:53 PM
Assuming I've already taken the courses at the top, can you guys rank/compare the importance of these 3 classes.

Advanced Multivariable Calculus II
Elementary topology, general theorems on partial differentiation, maxima and minima, differentials, Lagrange multipliers, implicit function theorem, inverse function theorem and transformations, change of variables formula.

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

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.

pevdoki1
02-23-2008, 11:55 PM
1. Advanced multivariate
2. Analysis (VERY CLOSE)
3. Probability

But I'm not a PhD student yet, so you might as well ignore my advice. :p

Olm
02-24-2008, 12:16 AM
I would definitely take analysis, no ifs, ands, or buts. And I would take it so that it appears on my transcript. Most places only require cal 1 and cal 2 for it.

If you have a choice, I would drop the advanced multivariate calculus and differential equations courses. Definitely take probability 2. Also, you should have at least one course in mathematical statistics.

YoungEconomist
02-24-2008, 12:16 AM
1. Advanced multivariate
2. Analysis (VERY CLOSE)
3. Probability

Did you notice that it was multi-variable calc 2? Likewise, it was probability 2. I just wanted to clarify in case you thought it was going to be my first multi-variable calc class and probability course.

Karina 07
02-24-2008, 12:20 AM
In terms of what will save you the most time in first year, imho:

1. Probability 2
2. Advanced multivariate 2
3. Real analysis 1

But all are good stuff.

macroeconomicus
02-24-2008, 12:50 AM
If you ask me, I would say it is better to take analysis before going to graduate school. The reason is that the econ departments will generally teach multivariate calculus and probability well enough for what you need to know in the econ program.. Analysis, on the other hand is much harder to pick up if you wait all the way until you need to actually use it. Again, not all econ courses might make use of it. It probably depends on who's teaching what course.

pevdoki1
02-24-2008, 01:09 AM
While we're discussing math courses, what about differential equations?

I have taken all the calculus courses, a semester of linear algebra, and intro to proofs course, and 2 semesters each of math. statistics and real analysis (as mentioned before)

However, I don't know how to solve differential equations (beyond calc 2-style separable ones). Is this something I'll learn when I'm in the PhD program, or should I have some beforehand familiarity?

Olm
02-24-2008, 01:15 AM
Differential/difference equations are solved by either formulas (the easy ones) or computers (the hard ones). And I haven't seen a single differential equation in my PhD courses I have taken (micro, macro, a lot of metrics) and we use all the standard textbooks.

Read up on it if you like in Schaum or Chiang if you want to be sure.

YoungEconomist
02-24-2008, 01:19 AM
I'm having somewhat of a crisis here trying to figure out what to do. If I took 4 math courses this summer and 3 next fall I could have all the neccessary courses on my transcript by the time I apply. Could I pull this off and still get solid grades in these courses? Or is this too difficult? I've been told that I should never try to take more than 2 math courses in one quarter, is that solid advice?

If I did it this way my schedule would look like this:

Summer

Probability 1
Matrix Algebra
Intro Proofs
Multi-variable Calc 1Fall

Probability 2
Real Analysis
Multi-variable Calc 2
I guess I could also drop Multi-variable calc 2, and go:

Summer

Probability 1
Intro Proofs
Matrix AlgebraFall

Probability 2
Real Analysis
Multi-variable Calc 1I'm just so confused about what I should do.

Karina 07
02-24-2008, 02:35 AM
I'm having somewhat of a crisis here trying to figure out what to do. If I took 4 math courses this summer and 3 next fall I could have all the neccessary courses on my transcript by the time I apply. Could I pull this off and still get solid grades in these courses? Or is this too difficult? I've been told that I should never try to take more than 2 math courses in one quarter, is that solid advice?

If I did it this way my schedule would look like this:

Summer

Probability 1
Matrix Algebra
Intro Proofs
Multi-variable Calc 1Fall

Probability 2
Real Analysis
Multi-variable Calc 2I guess I could also drop Multi-variable calc 2, and go:

Summer

Probability 1
Intro Proofs
Matrix AlgebraFall

Probability 2
Real Analysis
Multi-variable Calc 1I'm just so confused about what I should do.


Option 2 sounds good; if you find it hard going over the summer (on the easier courses) you'll know to drop one of the 3 from your list in the fall. Or you could slog through all 3 and not send your fall grades.

C152dude
02-24-2008, 02:47 AM
I've been told that I should never try to take more than 2 math courses in one quarter, is that solid advice?

I am currently just taking math courses and it has been smooth sailing (however, I am on semesters).

Also, I like option one, but have no experience with summer classes - especially their intensity. I think your motivation will help you get through all these courses in such a short period of time.

macroeconomicus
02-24-2008, 02:54 AM
Option 2 sounds ok. Just make sure you don't overload yourself with math. Having a bad grade on your transcript is a lot worse than not having that course at all. If there are some courses that are not essential to be on your transcript, like probability 2, but which you still want to take, shift them to your last spring semester in school.

signal08
02-24-2008, 02:57 AM
4 classes in the summer is alot. especially since they're all math.... what year are you in now? it might be easier if you take multivariable calc before real analysis.

YoungEconomist
02-24-2008, 04:25 AM
4 classes in the summer is alot. especially since they're all math.... what year are you in now? it might be easier if you take multivariable calc before real analysis.

What about 3 classes? I'm currently a fifth year senior, so in the summer and next fall I'll be sixth year I guess.

I could also see if my university will let me stay an extra quarter, and then I could go "option 3"

Summer

Multi-variable Calc 1
Matrix AlgebraFall

Probability 1
Intro ProofsWinter

Probability 2
Multi-variable Calc 2
Real Analysis 1

YoungEconomist
02-24-2008, 04:35 AM
Some of you said I should go with option 2, but I just found out that Probability 2 is not offered next fall.

Interestingly enough though, they do have a way that you can take Probability 1 and 2 for the whole summer (I guess it'd just be an accelerated course).

If I took that I could go:

Summer

Probability 1
Probability 2
Intro ProofsFall

Matrix Algebra
Multi-variable Calc 1
Real Analysis 1

YoungEconomist
02-24-2008, 04:46 AM
Out of the 2 classes below, Diff Eq will be easier right? If so, do you think it will be much easier? The reason I am asking is because I just found out about the accelerated Probability 1 & 2 over the summer (it meets for 2 hours 3 times a week, as opposed to just 1 hour 3 times a week).

I was thinking maybe I could switch to taking Intro to Mathematical Reasoning for spring quarter (instead of Diff Eq). Then, over the summer I could take Probability 1 & 2, Diff Eq, and Matrix Algebra. What do you guys think?

Introduction to Differential Equations
Introductory course in ordinary differential equations. Includes first- and second-order equations and Laplace transform.

Introduction to Mathematical Reasoning
Mathematical arguments and the writing of proofs in an elementary setting. Elementary set theory, elementary examples of functions and operations on functions, the principle of induction, counting, elementary number theory, elementary combinatorics, recurrence relations.

macroeconomicus
02-24-2008, 04:51 AM
The summer session is about as long as a quarter I suppose. You propose taking three courses (probability, diff eq, and matrix algebra). Do you already feel comfortable taking three math courses per quarter? Anyways, in my opinion picking up the math reasoning course early on is fairly important. If you plan on taking it, you should certainly take it before real analysis (otherwise, you will learn math reasoning as you go in real analysis, but possibly in a more painful way). Diff. eq. is recommended to have for admissions at some places, but IMHO, as it has been already mentioned, it's not essential for coursework. Leave it to your final quarter or something.

Olm
02-24-2008, 05:25 AM
Yes, switch to Intro to math reasoning. Differential equations can go **** themselves. :)

Internationalstudent08
02-24-2008, 05:35 AM
I think that a class called analysis on your transcript will make things much better. other than that, be careful and try to get good grades in all those classes, or even a rec letter if you need one! btw, i'm one of the few people applying without too much math. i have m. calculus, linear algebra, intro to proofs and probability and i have good grades in most of them. this fall i took an optimization class, but i didn't send fall semester grades. now i take real analysis just in case i need to reapply... I hope that in two weeks I will list myself as another exception of the math rule...

btw, why do you say that you are not going to apply to any top-20 schools? Is there anything bad about your profile? If you think that you have good chances to get into a school in the 20-40 range, then you should apply to a few top20 schools just to try!

signal08
02-24-2008, 06:14 AM
Some of you said I should go with option 2, but I just found out that Probability 2 is not offered next fall.

Interestingly enough though, they do have a way that you can take Probability 1 and 2 for the whole summer (I guess it'd just be an accelerated course).

If I took that I could go:

Summer
Probability 1
Probability 2
Intro ProofsFall
Matrix Algebra
Multi-variable Calc 1
Real Analysis 1

that looks do-able. all of those classes are essential.
what other classes (if any) are you planning to take concurrently? i.e. any more econ classes? and i'm assuming you're all finished with general university requirements?

YoungEconomist
02-24-2008, 07:01 AM
Differential equations can go **** themselves. :)

LOL. Unfortunately, none of the times work, so I can't switch diff eq and proofs next quarter.



btw, why do you say that you are not going to apply to any top-20 schools? Is there anything bad about your profile? If you think that you have good chances to get into a school in the 20-40 range, then you should apply to a few top20 schools just to try!

I might apply to some top 20 programs depending on how I do over the next few quarters. I guess I just think I probably wouldn't be competetive at many top 20 programs for admissions, but when I'm a little further along I'll post my profile and see what all you TM gurus think.


that looks do-able. all of those classes are essential.
what other classes (if any) are you planning to take concurrently? i.e. any more econ classes? and i'm assuming you're all finished with general university requirements?

Well, If I only took 3 math courses I'd need some other course to keep me at full-time status. If I took 4 math classes though, that'd be enough.

Olm
02-24-2008, 07:59 AM
As long as your GPA is 3.5 or above, you should shoot for a pair of schools in the top 20 that closely fit your interests. I'm sure you can do it!

econofrosh!
02-24-2008, 11:02 AM
what would you guys say is the marginal benefit of taking Topology after having had at least two semesters of Analysis?

Olm
02-24-2008, 06:39 PM
Topology is great because many micro results use topological proofs. :)

YoungEconomist
02-24-2008, 08:30 PM
Here are the two options I am considering.

Option 1
Summer: Probability 1 & 2, Intro Proofs, Matrix Algebra
Fall: Multi-variable Calc, Readl Analysis, two non-math courses

Option 2
Summer: Probability 1 & 2, Intro Proofs, one non-math course
Fall: Matrix Algebra, Multi-variable Calc 1, Real Analysis 1, one non-math course

Notice the only difference is that I'd be moving Matrix Algebra to fall quarter. Also, keep in mind that I will be filling out applications in the fall in case this changes things.

Edit: Started a poll here: http://www.urch.com/forums/phd-economics/85612-one-more-math-poll.html

pevdoki1
02-24-2008, 08:36 PM
Option 1 for sure!!!!