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polkaparty
02-08-2008, 12:38 AM
I'm wondering, what program do you think has the most mathematically advanced courses? Note: The subset I'm thinking of ordering is the top 20 or so programs, but please feel free to provide any information useful for making pairwise comparisons among any programs.

I would particularly like to hear from people with personal or 2nd hand experience.

For example, I know that Penn's math camp is 6 weeks long and appears to cover a lot of fairly advanced material, allowing them to cover even more in their Fall "math for econ" course. In this respect, MIT seems less mathematically advanced since they are still covering Rudin level material during their fall math for econ course. [this all from syllabi, etc. I found online]

Also, Cassin said that their micro theory course (at Princeton) proved everything, which of course MWG does not even approach. I'm not sure how literal he was in saying this though. How do other school's micro sequences compare from this kind of mathematical perspective? (I.e., in supplementing MWG; the text is good, but nowhere near the standards of a real math text)

If I had to guess, I'd say that the theory schools are going to be more advanced for the obvious reason, but perhaps this isn't true.

Other schools that may be relatively more advanced: NYU, if their mathematics sequence just follows Efe Ok's text (through the end of course). Purdue also seems to have a good mathematical side, since James Moore was (is?) a prof. there when he wrote his excellent 2 volume methods texts and Aliprantis is there as well.

As one final benchmark, Harvard also appears relatively less advanced (in micro 1 at least), if the Nolan Miller notes are still used.

econdreamer
02-08-2008, 12:56 AM
I would say Kellogg's MEDS is also mathematical advanced.

Mr.Keen
02-08-2008, 01:11 AM
I would say Minnesota is among the most advanced.

Karina 07
02-08-2008, 01:25 AM
Just a quick note: I'm not sure if looking at first-year coursework will give you a good idea of how mathematically advanced a program is; I'd think that field courses probably matter more in terms of how mathematically advanced people come *out* of a program. Nor do 2nd year courses necessarily follow the difficulty level of 1st year courses; for instance, the econometrics field at Berkeley is reputed to be a HUGE, MASSIVE jump up in difficulty from the 1st year econometrics courses. Though the right courses to look at undoubtedly depends on why you're wondering.

ekonomiks
02-08-2008, 02:17 AM
On the same topic, which well-known mainstream programs are the least mathematical?

zsla
02-08-2008, 02:26 AM
Chicago's program does not require advanced math knowledge at all. But the funny thing is, I see a very strong correlation here between the job market performances and math knowledge of students. The reason is: fundamentals and basic ideas are given very well to the students. Those who can combine the two are the stars.

But, I think one can get a Chicago PhD in 5 years with only Multivariate Calculus, Linear Algebra and Diff. Eq. knowledge.

IMHO, one of the most math-advanced depts is Caltech. Others are: Yale, Penn, Cornell, CMU, Northwestern.

But, as a general rule, mathematically advanced fields is a control variable in most schools (except the first year).

apropos
02-08-2008, 02:45 AM
I wonder, are there any schools that make a systematic attempt to cover a significant portion of Stokey and Lucas's dynamic programming book during first year? It seems like at many places professors of macroeconomics just say: "Here is how to work with a dynamic program analytically and numerically. However, if you want to convince yourself that this actually works then read Stokey and Lucas's book, but we're not going to focus on it much in this course."

I mean, that's a tough book. If there is a school that covers the first say 5-6 chapters rigorously, then I would say that that program is more mathematical than almost all other schools out there (at least if you look at the first year coursework).

savingtheplanet
02-08-2008, 02:46 AM
U Penn is often said to be very mathematically rigorous. Evidence from our math econ instructor who is from Penn and constantly jokes about the math jocks he was surrounded by.

zsla
02-08-2008, 02:50 AM
I wonder, are there any schools that make a systematic attempt to cover a significant portion of Stokey and Lucas's dynamic programming book during first year? It seems like at many places professors of macroeconomics just say: "Here is how to work with a dynamic program analytically and numerically. However, if you want to convince yourself that this actually works then read Stokey and Lucas's book, but we're not going to focus on it much."

Minnesota students use it almost everyday during their PhDs. Also they use it as a pillow at night.

TruDog
02-08-2008, 02:55 AM
We were told that although the book is almost unreadable because it is so dense (professors here use their own course notes), the exercises are very important to master before prelims. And the exercises follow Stokey and Lucas very closely.

zsla
02-08-2008, 03:07 AM
We were told that although the book is almost unreadable because it is so dense (professors here use their own course notes), the exercises are very important to master before prelims. And the exercises follow Stokey and Lucas very closely.

I think it is not that unreadable. Last year Sargent told us the following about Bob Lucas:

"Bob writes like a novelist, but in the precision of a physicist!"

That really describes the book. You should proceed slow, spend lots of time on each page (read twice if you have time), prove everything yourself and try to use Matlab as much as you can while reading it. Visualization is very important for dynamic models. Programming allows you get into the model as a residual term :) (Of course there is no residual in the book).

You should have MWG with you while reading it. I would also keep a good Econ101 textbook around all the time.

Also note that the book is written for discrete time dynamic programming. Even Lucas is working with continuous time models today. So, you should also try to translate everything from discrete time to continuous time. It will be really helpful.

Thesus
02-08-2008, 04:32 AM
The professors I asked to write letters for me unanimously chose Berkeley as the most technical program - over Minnesota and Princeton.

imperfectinformation
02-08-2008, 04:33 AM
It is true, Minnesota students go through most of SLP in the first semester and can basically recite all of the theorems with corresponding assumptions and proofs from SLP ch 4 and 9. This paired with one-week homework assignments that begin with 9 or 10 non-book questions followed by #11: all of chapter 6 S&L, #12: all of chaper 8 S&L.
Haha... awesome

jbs02002
02-08-2008, 04:46 AM
This is actually really promising for me. Math is my only concern, and I have already been accepted at Minnesota this year.

pevdoki1
02-08-2008, 05:06 AM
one-week homework assignments that begin with 9 or 10 non-book questions followed by #11: all of chapter 6 S&L, #12: all of chaper 8 S&L.

Ouch.

sonicskat
02-08-2008, 05:10 AM
In our math (for Macro) course we started this semester and on real analysis and are working our way through the all of the nitty gritty proofs of dynamic programming. Needless to say, we are following a lot of material from S&L&P rather closely while the prof does not explicitly say so.

Macro is also using this text somewhat....of course it doesn't help when you have one of the authors' son as the professor...

andyecon
02-08-2008, 06:38 AM
This was our Final for the first half of the first semester last year here at Minnesota.
http://www.econ.umn.edu/%7Ecslavik/teaching/final.pdf

Question 1 is essentially the proof of existence and uniqueness of the value function in SLP chapter 4 (or is that in 3? I can't remember right now)

Next look at question II.1 from this Fall's macro prelim:
http://www.econ.umn.edu/prelims/f07/f07-macro.pdf

and compare it to chapter 6 in SLP (the first part on global stability).

In short, if you come here, be prepared for chapters 1-6 in about 8 weeks. The second half of the first semester still uses it a lot too, but that mini is a bit of a blur for most people.

doubtful
02-08-2008, 07:12 AM
interesting.. the first question of the first final is essentially a functional analysis/dynamic optimization question.. I don't see any economics... eeheheh

trjohnson
02-08-2008, 07:44 AM
TAMU is covering SLP Ch 3 - 13 in four weeks. It's been a blur so far, and probably will continue to be when we jump into fiscal policy.

econphilomath
02-08-2008, 01:00 PM
Why do you think the places with the best placements do not have (following this thread) the most advanced math in first year sequences? I'm taking about MIT and Harvard.

jazzcon
02-08-2008, 01:37 PM
Being a good job candidate is a lot about having great research ideas. It is easier to gain an advantage in this when you are surrounded by people who are coming up with ideas that will be in AER 4 years down the road, as opposed to everybody else who has to wait for a working paper at a conference. Also, second rate ideas that don't get pursued by professors at Harvard and MIT are still first rate ideas for a job candidate.

Programs with worse placement may try to make up for their lack of great ideas that students are exposed to (I am talking relatively here!) by giving their students advantages in other areas, like technical training.

reactor
03-03-2008, 01:35 AM
Why do you think the places with the best placements do not have (following this thread) the most advanced math in first year sequences? I'm taking about MIT and Harvard.

Perhaps because the students who go there either:
1) already know this stuff
2) can/will learn it themselves and do not need a course


(i.e., in supplementing MWG; the text is good, but nowhere near the standards of a real math text)

MWG is an economics book, not even mathematics for economists! I would say lets see which programs teach "Mathematical Methods and Models for Economists" by Angel de la Fuente which is one of the most advanced and comprehensive mathematics books for economists. Contents: Amazon.ca: Books: Mathematical Methods and Models for Economists (http://www.amazon.ca/gp/reader/0521585295/ref=sib_dp_bod_toc/702-4345689-7740809?ie=UTF8&p=S006#reader-link)

darcie
03-03-2008, 01:58 AM
I think SL might be the most difficult book in Macro area, compared to Sargent's or Romer's books. But I know someone who can manipulate different models very well but could not publish any papers(Maybe he just submitted to top 5 Journals). And I have also seen many famous professors dealing with very simple model but excellent ideas in it. So math or modelling ability might be grasped more easily relatively than having something interesting to model and write.


I wonder, are there any schools that make a systematic attempt to cover a significant portion of Stokey and Lucas's dynamic programming book during first year? It seems like at many places professors of macroeconomics just say: "Here is how to work with a dynamic program analytically and numerically. However, if you want to convince yourself that this actually works then read Stokey and Lucas's book, but we're not going to focus on it much in this course."

I mean, that's a tough book. If there is a school that covers the first say 5-6 chapters rigorously, then I would say that that program is more mathematical than almost all other schools out there (at least if you look at the first year coursework).

Karina 07
03-03-2008, 02:53 AM
MWG is an economics book, not even mathematics for economists! I would say lets see which programs teach "Mathematical Methods and Models for Economists" by Angel de la Fuente which is one of the most advanced and comprehensive mathematics books for economists. Contents: Amazon.ca: Books: Mathematical Methods and Models for Economists (http://www.amazon.ca/gp/reader/0521585295/ref=sib_dp_bod_toc/702-4345689-7740809?ie=UTF8&p=S006#reader-link)

YEA!!! Best book ever! We used it for math camp and it still sits by my side for whenever a piece of math is assumed knowledge. That book explains what you could spend a few hours looking for elsewhere in like 3 pages. Huge fan of that book. It's quite possibly the best book I've ever seen in my whole life for anything.

bgg
03-03-2008, 02:58 AM
"Mathematical Methods and Models for Economists" by Angel de la Fuente completely agree.. I am a big fan of this book as well

C152dude
03-03-2008, 03:05 AM
"Mathematical Methods and Models for Economists" by Angel de la Fuente completely agree.. I am a big fan of this book as well

I love this book. Nothing was better after a long day of New Orleans volunteering than a delve into de la Fuente.

Mathematical Methods and Models for Economists is the best coffee table book ever.

polkaparty
03-03-2008, 03:14 AM
Ok I wasn't going to say anything but with so many people piling up on de La Fuente's side, I must provide a counterargument. I don't like the book--well actually I'm neutral. Primarily, it's typesetting is so hideous that it's barely readable. It just hurts my eyes too much. It seems like the book was written in Word, which is a joke.

The best `math for econ' text is Efe Ok's book, hands down. Comparing de La Fuente to Ok is like comparing a patrol boat to an aircraft carrier.

Another high quality underground text is the two volume work by James Moore, Mathematical Methods in Economic Theory.

Here is how my opinion evolved: The first `math for econ' text I saw was Simon & Blume, which resembles a calculus text. Then I saw de La Fuente, and I was quite excited because it is a huge step up. Then I saw Moore's texts, which were another huge step up. And finally, I got Efe Ok's book in hardcopy and I was blown away.

Anyway...all the texts have a purpose, I just wanted to mention these other fantastic texts.

BTW c152: Loved the comment about the coffee table! Hahaha....

C152dude
03-03-2008, 03:22 AM
Ehh... you get what you pay for. Not everyone has an unlimited budget for books. :hmm: You made me broke back in January... stop with the book recommendations.

bgg
03-03-2008, 03:29 AM
polkaparty: I am not sure why you like Efe's book. It's an analysis book which doesn't cover a lot of the things that La Fuente covers and why not just go through Rudy's books which are good enough.

Also I don't see how Moore's book is better either. Yeah maybe La Fuente's book could be more compact but the beauty of it is that it could be used both by people who had courses on most of the topics covered in the book and by those who didn't!

Karina 07
03-03-2008, 03:33 AM
Here is how my opinion evolved: The first `math for econ' text I saw was Simon & Blume, which resembles a calculus text. Then I saw de La Fuente, and I was quite excited because it is a huge step up. Then I saw Moore's texts, which were another huge step up. And finally, I got Efe Ok's book in hardcopy and I was blown away.

I will have to check these out, seeing as how de Fuente is my god. Will report back. That being said, I'm still a little skeptical that anything can be as good as de Fuente, just because I love it so much. It's so concise and exact! Ahh :).

But speaking of bad typesetting... I can't stand Ruud's metrics text, for some reason. I'm kind of torn because I don't want to spend money getting something else that covers exactly the same thing, but man, that thing hurts my eyes. Plus, in the 2nd half of it he chooses such poor notation sometimes....

jahizbarlas
03-03-2008, 08:35 AM
Minnesota students use it almost everyday during their PhDs. Also they use it as a pillow at night.

god, thats so true. its everyday reading just before going to bed, just like the christians read the bible. we did all of deterministic dynamic optimization theory and all the proofs on a saturday. the stochastics stuff of dynamic optimization which is chaps 7-14 or something in SLP were done in a couple of lectures by pastor chari.
northwestern and minnesota are prob the most rigorous.
upenn is rigorous, but not as much as the former two i think. plus, upenn is changing things with their macro sequence which, if i heard correctly, i dont like at all..

reactor
03-03-2008, 09:50 AM
The best `math for econ' text is Efe Ok's book, hands down. Comparing de La Fuente to Ok is like comparing a patrol boat to an aircraft carrier.

"Hints to Selected Exercises" (Efe Ok's book) vs. "Complete solutions included in the book to all problems"; and I rest my case.
(no I don't! I continue...)
Who can produce a math book with a good selection of problems and include their complete solutions at the end of the book? That is a book I was looking for: I want to know the final/complete solution without depending on others (professor, classmates etc because there may not even be a class!)
Now, do I have to say how important solving problems is in maths?
[especially "prove/show" types = problems (as opposed to exercises where you just calculate something)]
(Of course the best book is the one that offers you first a hint and then the solution.)

tangsiuje
03-03-2008, 11:51 AM
Who can produce a math book with a good selection of problems and include their complete solutions at the end of the book?My maths professors usually don't give solutions to exercises anyway: most as simply of the opinion that "if you did it right, you will know in your heart". I would imagine textbook authors are similar.

Then, of course, there is the time efficiency aspect as well, which the reasoning above does not take into account. Learning without solutions may not be particularly time efficient at all. However, I don't think that I would personally sweat for hours or days over a proof I knew I could find at the back of my back, so I'd doubt I would develop the same skills if it was there. But then, this might just be because I'm a bit lazy.

The real reason - I believe - is that most maths people find the propositions they give their students to prove so blatantly obvious that they simply cannot be bothered to write the proofs out. ;)

econphilomath
03-03-2008, 12:42 PM
god, thats so true. its everyday reading just before going to bed, just like the christians read the bible. we did all of deterministic dynamic optimization theory and all the proofs on a saturday. the stochastics stuff of dynamic optimization which is chaps 7-14 or something in SLP were done in a couple of lectures by pastor chari.
northwestern and minnesota are prob the most rigorous.
upenn is rigorous, but not as much as the former two i think. plus, upenn is changing things with their macro sequence which, if i heard correctly, i dont like at all..


Could you please elaborate on what you know of Macro changes at Penn????

Also, do you think macro at Minnesota is comparable to NWU? If not (my presumption is no) by what magnitude ?

reactor
03-03-2008, 12:52 PM
However, I don't think that I would personally sweat for hours or days over a proof I knew I could find at the back of my back, so I'd doubt I would develop the same skills if it was there. But then, this might just be because I'm a bit lazy.

But can we base the book writting on such self-discipline issues? Of course one can look the solution immediatelly but lets say that books with solutions are good for selfstudy which requires that ones knows that she should honestly try first and then look at the solution (and even then try to understand the mechanisms in the solution). :)


The real reason - I believe - is that most maths people find the propositions they give their students to prove so blatantly obvious that they simply cannot be bothered to write the proofs out.

I cannot see how someone could consider something trivial to be taught explicitly but important to be examined. (unless you assume that maths teachers are not consistent on this; so "anything goes" = we can assume whatever we want)
:)

math2009
03-03-2008, 02:20 PM
Perhaps because the students who go there either:
1) already know this stuff
2) can/will learn it themselves and do not need a course



MWG is an economics book, not even mathematics for economists! I would say lets see which programs teach "Mathematical Methods and Models for Economists" by Angel de la Fuente which is one of the most advanced and comprehensive mathematics books for economists. Contents: Amazon.ca: Books: Mathematical Methods and Models for Economists (http://www.amazon.ca/gp/reader/0521585295/ref=sib_dp_bod_toc/702-4345689-7740809?ie=UTF8&p=S006#reader-link)


The most advanced book for economics is infinite dimensional analysis:a hitchhiker's guide.
And it looks very comprehensive. I didn't read it so not sure if it's easy to read.

But if you're serious about theories I would recommand "Real Analysis: Modern Techniques and Their Applications by Folland" which is a very good book. If you're sometimes lost then Royden's real analysis would be very helpful.