Math or Competitions: Which Path Should You Choose for Success?

[set]

Hello everyone. I am an international student who wishes to pursue a bachelors degree in mathematics or statistics. I am doing quite well in my senior year (90+% or 7 in IB HL Maths), although I do realize that high school grades do not matter much in studying the 'real' mathematics. I have been told that university and advanced level mathematics is quite different from that of in high school, but I'd like to know how different is it exactly. I know that university maths focus on proofs, but do they heavily depend on 'technical skills' or 'neat tricks' that are often used in contests like IMO? Or is it rather like philosophy?

Next, does it matter where I get my bachelor's degree from? Having been accepted to two different universites, I am having a dilema of which one to attend. Univ.A. is an internationally renowned university especially for mathematics, but because of its reputation, competitions will most likely be fierce. On the other hand, although Univ.B. might not be the top-tier university for mathematics, it seems like they do have a quite decent faculty and a smaller class size (around 75).

Lastly, staticians or applied mathematicians (especially for those who focus on differential equations) being replaced by computers, is it likely to happen in the future?

Any insight will greatly be appreciated.

Best Regards,

 

[victor.raum]

I know this doesn't answer your question, but I'm curious to hear which two universities are hiding behind the blackout expressions "Univ.A." and "Univ.B."

 

[set]

I know this doesn't answer your question, but I'm curious to hear which two universities are hiding behind the blackout expressions "Univ.A." and "Univ.B."

University of Waterloo and McMaster University for Univ.A. and Univ.B., respectively.

 

[chiro]

Hello everyone. I am an international student who wishes to pursue a bachelors degree in mathematics or statistics. I am doing quite well in my senior year (90+% or 7 in IB HL Maths), although I do realize that high school grades do not matter much in studying the 'real' mathematics. I have been told that university and advanced level mathematics is quite different from that of in high school, but I'd like to know how different is it exactly. I know that university maths focus on proofs, but do they heavily depend on 'technical skills' or 'neat tricks' that are often used in contests like IMO? Or is it rather like philosophy?

Next, does it matter where I get my bachelor's degree from? Having been accepted to two different universites, I am having a dilema of which one to attend. Univ.A. is an internationally renowned university especially for mathematics, but because of its reputation, competitions will most likely be fierce. On the other hand, although Univ.B. might not be the top-tier university for mathematics, it seems like they do have a quite decent faculty and a smaller class size (around 75).

Lastly, staticians or applied mathematicians (especially for those who focus on differential equations) being replaced by computers, is it likely to happen in the future?

Any insight will greatly be appreciated.

Best Regards,

Hey set and welcome to the forums.

The mathematics is different for a variety of reasons.

If I had to sum it up I would say that the thinking is a lot different. Things are a lot more general (think more abstract) and it's a lot more conceptual: in other words you have to deal with ideas and work on problems where you have to know how to apply a more general concept to a problem that in some ways might not seem connected or seem hard because it is not obvious how to connect that concept.

Different 'tricks' are used no doubt in the various subjects, but the big thing is understanding the concepts. The concepts are usually understood by looking at the constraints (think assumptions) and what these mean in the context of what you are analyzing and trying to make sense of: this is the shortest way I can describe this kind of thing.

I don't know about which university is 'better' but I can say that if you work hard in any university that has a decent course offering and make the most of it both learning wise and grade wise then you'll be ok. From the sounds of it, both universities should have good course offerings in terms of the content (I don't know this but after studying I have come to the conclusion that many undergraduate institutions teach the same things in general from my experiences and conversations with others as well as reading posts on here).

With regard to being 'replaced by computers', the answer is at least for the short term an emphatic no. Computers need to be programmed and you need to understand that these algorithms have their own assumptions and when these assumptions aren't good enough, theory needs to come into find ways of dealing with this.

The algorithmic side of mathematics although being a large part, does not represent what mathematics is all about. At the moment, we generate the algorithms for the computers and not the other way around. Even for something like machine learning, this is still the case (even though machines learn through these algorithms and display learning characteristics, they do not create new algorithms).

As you mentioned with the 'tricks', think about all the different kinds of 'tricks' that have been used to prove results, get good approximations (like say Stirlings Formula for the factorial if you want an example) and do all kinds of things. Computers can do very powerful algebraic simplifications and even find proofs computationally, but the one thing they really lack is the language skills that are in humans and until that bridge is crossed, computers will not even come close to doing what we currently do.

 

[set]

University of Waterloo and McMaster University for Univ.A. and Univ.B., respectively.

My dilemma is

Waterloo
Pros
-internationally renowned university
-excellent Putnam competition performance
Cons
-too competitive => less research opportunity and possible mental breakdown

McMaster
Pros
-better research opportunity, in fact, McMaster offers a senior research project course
-easier to maintain high GPA
-small class size
Cons
-global reputation

McMaster does have a decent faculty members (Ph.D. from Harvard, Princeton, Cambridge and etc...) but the sole reason I were to choose Waterloo over McMaster is because of the reputation issue. However, one of my acquintances advised me that, since I am definitely going to pursue graduate studies, the reputation of where I do my undergrduate studies won't matter as much as my research experience and GPA.

So which one should I choose?

Any insight or advice regarding this issue will be greatly appreciated.

 

[set]

Hi again.

How important is undergrad research experience when applying to grad schools for a master's, not for a PhD? Of course it is important if I were to apply to top schools like Princeton, but will a decent GPA and GRE score be enough to apply for all Canadian universities? Is there an advantage in admission if I apply to grad school where I did my undergrad stidies?

If I go to UWaterloo, I doubt that I will be able to secure a RA position so I am really concerned about this matter.

 

[micromass]

Doing research is quite important. Even if you just do it for yourself. The thing is: how do you know you will even like grad school?? Not everybody seems to like research. So doing research in your undergrad tells you whether research might or might not be something for you.

 

[set]

But only top few students get to get research position. I don't think I will be in the group of top students. I won't know how to do research on my own. In fact, I won't be able to understand a single paper that is being submitted to research journals. Does it mean only the top few students, who have assistance from supervisors, get to go to grad schools? (I mean, grad schools in general, not top grad schools)

I believe an undergrad is not expected to carry a research or discover new stuff on her/his own. So what kind of research they do?