Do I have enough math courses?

[Fancyfan10]

Hi everyone!

I am a junior student and will go to UCL as a exchange student. I want to apply statistics PhD program for 2021 fall. I am posting this to want to know whether I have enough math courses for application.

Have taken:

Calculus 1-3

Mathematical Analysis 

Linear algebra 1-2

Probability

Mathematical statistics 

Numerical analysis

Real analysis(measure theory)

I got all A or A- except for linear algebra so I will retake honorary linear algebra at UCL.

Currently taking:

Complex analysis

Functional Analysis

Stochastic process 

 

Will take at UCL:

Probability (based on measure theory graduate course)

Honorary algebra

 

Any suggestions and comments are appreciated. Thanks!

 

 

 

 

[BL250604]

Plenty of courses! It's always good to see (in my eyes) some extra high level math classes to show your understanding and ability to succeed in high level proof classes. There's certainly nothing you need. Only thing I can think of is grad school level courses. Something like a measure theoretic probability or linear models. These are certainly not expected and would be very impressive if you did well in them. There's nothing you need but if you do well in high level, high powered statistics courses, your application will be that much stronger. 

Hope that helps.

[Fancyfan10]

13 minutes ago, BL250604 said:

Plenty of courses! It's always good to see (in my eyes) some extra high level math classes to show your understanding and ability to succeed in high level proof classes. There's certainly nothing you need. Only thing I can think of is grad school level courses. Something like a measure theoretic probability or linear models. These are certainly not expected and would be very impressive if you did well in them. There's nothing you need but if you do well in high level, high powered statistics courses, your application will be that much stronger. 

Hope that helps.

Thanks for your reply!  Do you think I should take abstract algebra or some other algebra courses? Because I didn’t do well in linear algebra in my freshman year, really afraid of being suspected by committees about my math ability. BTW, I am an international student.

[BL250604]

50 minutes ago, Fancyfan10 said:

Thanks for your reply!  Do you think I should take abstract algebra or some other algebra courses? Because I didn’t do well in linear algebra in my freshman year, really afraid of being suspected by committees about my math ability. BTW, I am an international student.

It certainly can't hurt. I did the same thing. I did okay in linear algebra, and then got an A in both abstract algebra and group theory. It definitely helped alleviate concerns. Additionally, I personally think that seeing more math helps. Thinking of things algebraically does help make certain topics more intuitive. It also helps you understand and reinforce concepts like bijections (for isomorphisms) properties of matrices (non commutative, i.e. non abelian), etc. which will surely come up in graduate school, albeit in a different way of thinking.

[Fancyfan10]

50 minutes ago, BL250604 said:

It certainly can't hurt. I did the same thing. I did okay in linear algebra, and then got an A in both abstract algebra and group theory. It definitely helped alleviate concerns. Additionally, I personally think that seeing more math helps. Thinking of things algebraically does help make certain topics more intuitive. It also helps you understand and reinforce concepts like bijections (for isomorphisms) properties of matrices (non commutative, i.e. non abelian), etc. which will surely come up in graduate school, albeit in a different way of thinking.

Thank you so much for your kind input! I will fully consider my future course selection at UCL!

[DanielWarlock]

7 hours ago, Fancyfan10 said:

Thanks for your reply!  Do you think I should take abstract algebra or some other algebra courses? Because I didn’t do well in linear algebra in my freshman year, really afraid of being suspected by committees about my math ability. BTW, I am an international student.

I would caution any foray into abstract algebra for stats people. First of all, it is useless for most stats. Second of all, it can get out of hand, especially for "honour" abstract algebra unless you already had a formal training in pure math--a solid first two-years in analysis and algebra. From the look of the courses you have taken, I don't think you do. I was stupid enough to take honour abstract algebra in college with pure math people who had real training. The class was taught by an actual expert (Fiona Murnaghan) and I was destroyed. Class was 100+ people and by the time of midterm there was like 20 left. I got 31% on midterm. Granted, the average was 30% but I worked my ass off doing that stupid class and I was technically only taking 2 classes that semester. Some of those homework problems are extremely difficult to do with my math ability at the time. I ended up dropping that class. I took a non-honour version of that at another school last year and got 100% on every thing with minimum effort. So don't take the honour version. 

[BL250604]

14 minutes ago, DanielWarlock said:

I would caution any foray into abstract algebra for stats people. First of all, it is useless for most stats. Second of all, it can get out of hand, especially for "honour" abstract algebra unless you already had a formal training in pure math--a solid first two-years in analysis and algebra. From the look of the courses you have taken, I don't think you do. I was stupid enough to take honour abstract algebra in college with pure math people who had real training. The class was taught by an actual expert (Fiona Murnaghan) and I was destroyed. Class was 100+ people and by the time of midterm there was like 20 left. I got 31% on midterm. Granted, the average was 30% but I worked my ass off doing that stupid class and I was technically only taking 2 classes that semester. Some of those homework problems are extremely difficult to do with my math ability at the time. I ended up dropping that class. I took a non-honour version of that at another school last year and got 100% on every thing with minimum effort. So don't take the honour version. 

the experience is different for everyone. I understood algebra intuitively, and did have a very solid background in pure math. the mathematical rigor comes solely from the "theorem, proof" style in which most texts are outlined. the concept of a binary operation and a collection upon which you're working is not too difficult. 

[DanielWarlock]

2 hours ago, BL250604 said:

the experience is different for everyone. I understood algebra intuitively, and did have a very solid background in pure math. the mathematical rigor comes solely from the "theorem, proof" style in which most texts are outlined. the concept of a binary operation and a collection upon which you're working is not too difficult. 

I'm not know how good you are with math. But your last sentence is very naive. Understanding definition does not make things easy. For example see this exercise:

World-class mathematicians specializes in group theory, you know. It is not easy. Have heard any mathematician specialize in adding two numbers together? No because adding two numbers together is easy. Even if you are leading expert in group theory, you don't get to make that kind of claim considering that (i) you have studied group theory for at least 5 years to be world-class expert as you are and that is just like a few topics not entire field of group theory (ii) if it is not too difficult, why are there still open problems? shouldn't have you solved all of them already, given that they are so easy? 

Edited October 30, 2019 by DanielWarlock

[bayessays]

51 minutes ago, DanielWarlock said:

I'm not know how good you are with math. But your last sentence is very naive. 

Daniel, this forum is to help people with advice for getting into graduate school.  Some of your comments are veering a little far from the purpose and are unnecessarily hostile (like insulting the person's English).  Please keep the comments on topic and polite or they will be removed. 

[DanielWarlock]

3 minutes ago, bayessays said:

Daniel, this forum is to help people with advice for getting into graduate school.  Some of your comments are veering a little far from the purpose and are unnecessarily hostile (like insulting the person's English).  Please keep the comments on topic and polite or they will be removed. 

I never intend to initiate any hostile personal attacks. I give my personal opinions on people's profiles and comments made.

In this case, I give my reasons why I disagree with the commentator's claim regarding abstract algebra. It is not responsible to encourage someone ("why not") with stats background to take honour abstract algebra classes because "it is just binary operations and not too difficult". I myself made this mistake in college and was almost not able to graduate on time to attend my master program. 

In the other instance you mentioned, I observed that there are issues with the person's written English and cautioned him about not finding a proof-reader. This advice is based on my personal experience as a non-native speaker. It is also in the context of his unusual GRE verbal score. It is supposed to be a reminder and not a hostile attack. 

But there seems to be some misunderstanding on my part, too. I did post a lot more than I should and some of those comments are heavily opinion-based. I apologize and will refrain from posting comments henceforth. Thank you.

[Fancyfan10]

Just to be clear,

I am actually thinking to take some more algebra courses to alleviate the concerns from committees towards my math ability. Abstract algebra and honor linear algebra will be two possible choices. Honor linear algebra will include some introductions to group and go deep into eigenvalue, eigenvector, etc. I am not clear about the content of abstract algebra.

[statfan]

You have more than sufficient math background to apply for statistics PhD. It's always good to know more math, and this will help for any quantitative disciplines. Much of the statistics theory is related to real analysis/measure theory, but this doesn't mean that algebra is not or will not be useful. Indeed, algebra is starting to gain its popularity in statistics and there is an emerging area called algebraic statistics. That being said, if you are interested in these courses and have the time, you can take both. However, these are not required for admission to statistics PhD.

[Fancyfan10]

33 minutes ago, statfan said:

You have more than sufficient math background to apply for statistics PhD. It's always good to know more math, and this will help for any quantitative disciplines. Much of the statistics theory is related to real analysis/measure theory, but this doesn't mean that algebra is not or will not be useful. Indeed, algebra is starting to gain its popularity in statistics and there is an emerging area called algebraic statistics. That being said, if you are interested in these courses and have the time, you can take both. However, these are not required for admission to statistics PhD.

Thanks for your encouraging reply! Yeah, I totally agree with you. Before entering into PhD program, it is always good to learn more math from different sub tracks including analysis, algebra even geometry.

[BL250604]

12 hours ago, Fancyfan10 said:

Thanks for your encouraging reply! Yeah, I totally agree with you. Before entering into PhD program, it is always good to learn more math from different sub tracks including analysis, algebra even geometry.

Absolutely, imo the more you see the better off you'll be. Best of luck and keep us posted!