求助 数学课选课 和 专业区别问题

jianghahaUID: 3590121

先修概率统计 有机会最好再修一下(intro) analysis

cjyNelUID: 3444522

李纸 发表于 2016-1-12 00:36
so Introduction To Mathematical Statistics 1&2 are necessary for master application and others may ...

Introduction To Mathematical Statistics I&II are a must for Econ students to get prepared for a serious econometrics course, and you will definitely need to work hard on it if you want to go to a master in Econ. Do not waste time on the 1-semester "statistical analysis". That one is mainly for techiniques and doesn't provide enough theoretical background usually.

Meanwhile, you need to be exposed to more mathematical reasoning (proof), which is typically learned through taking a course like the Intro Analysis you mentioned.

Linear algebra is also important. I see you list an introductory course. But, I doubt whether that will be sufficient. You probably also need an upper-level theoretical linear algebra course, if your U has one.

cheesechanUID: 3505689

cjyNel 发表于 2016-1-12 09:24

Linear algebra is also important. I see you list an introductory course. But, I doubt whether that will be sufficient. You probably also need an upper-level theoretical linear algebra course, if your U has one.

Would like to ask what is expected in an advanced level theortical linear algebra course,?

Normally i see a junior level linear akgebra covering various topic related to metirc space and etc,  but at senior level,  normally i only see course in algebra I and algebra II or similar but not linear one....did i miss something here...?

cjyNelUID: 3444522

cheesechan 发表于 2016-1-12 09:48
Would like to ask what is expected in an advanced level theortical linear algebra course,?

No ...

At many U, the math department provides both a lower-level linear algebra (course number 2XXX) and an upper-level linear algebra (course number 3XXX or 4XXX). The former one is mainly about basic definition and computation, things like how to do row reduction, calculate inverse/determinant of a matrix, and find eigenvalues and eigenvectors, but no proof. (typically this course talks more in terms of systems of linear equations)

The upper-level one I mentioned works with vector space and things like linear transformation from a more general perspective and goes through more theorems and proofs. The classical text is Friedberg et al., Linear algebra. I believe this course is also a good chance to get familiar with mathematical reasoning.

For example, in the 4XXX course, something almost definitely will be covered is how to prove eigenvectors with different eigenvalues must be linearly independent. But, this kind of theorems&proofs are not even mentioned in a 2XXX course.

cheesechanUID: 3505689

cjyNel 发表于 2016-1-12 10:46
At many U, the math department provides both a lower-level linear algebra (course number 2XXX) a ...

umum........get what you mean then. then of course a proof-based version is very important too.
why mathematics course are important for graduate school is mainly because the experience in proofing indeed.

what is known to me before is that both version of this of 2XX, where the non-math student (e.g. stat, QFin) do a version with less proof, while the math major student do the one with more proof.

OP: given OP's university even have the intro to linear algebra as a 3XX course, and no further course in linear algebra are available for bachelor student (1XX - 4XX), you can basically know what this difference means in #32, and forget about the advise.

李纸UID: 3611673

jianghaha 发表于 2016-1-12 06:10
先修概率统计 有机会最好再修一下(intro) analysis

谢谢～

李纸UID: 3611673

cheesechan 发表于 2016-1-12 17:25
umum........get what you mean then. then of course a proof-based version is very important too.
...

so i have to take Introduction To Mathematical Statistics I&II to satisfy basic requirement first.
i will try to catch up in math courses as much as possible and reconsider my plan.
thanks again for your help.

李纸UID: 3611673

cjyNel 发表于 2016-1-12 09:24
Introduction To Mathematical Statistics I&II are a must for Econ students to get prepared for a se ...

there are many pre courses requirements in my school, even that statistic analysis is the pre course of Introduction To Mathematical Statistics I&II, maybe I need to take both rather than choose the upper or the lower type. do you univ. has similar requirements in pre course of such classes?
thank you for advising.

cjyNelUID: 3444522

李纸 发表于 2016-1-13 14:01
there are many pre courses requirements in my school, even that statistic analysis is the pre cour ...

At my U the pre is only multivariate calculus.

I suggest you contact the instructor for a permission to enter the course directly and explain why you need this course so much.

cheesechanUID: 3505689

李纸 发表于 2016-1-13 14:01
there are many pre courses requirements in my school, even that statistic analysis is the pre cour ...

I will say normally NO.
I guess the reason why the maths course in your university has that much level of pre-req is because the mathematics background of the student are not strong enough, as we all know the common maths level of US student........especially the top one are not considered.
and as a result, the university need to have a couple of junior course, which is kind of revising some maths that should had been already coved in high-school,
and don't have enough time for the stuffs covered in junior level math/stat in other top university,
and thus then they also delayed some of the junior sequences to their senior year.....
and here why some unnecessary pre-req appears.


P.S. as far as I know, the common sequence is like this:
calculus I, II, III (which include multivariate calculus), which only depends on high-school maths
linear algebra is parallel with calculus
and (probability then statistics) sequence (calculus-based) require multivariate calculus
while regression rely on statistics and linear algebra.
other advanced statistics course like time series depends on regression.
while stochastic processes depends on probability.