A Query: On Math, Physics, Fear and Natural Aptitude
Hi there. First off, nice to meet you! This is indeed my first post and I look forward to getting to know you all. I came to you with the gravest of burdens on my mind so let's jump right in, shall we? We have a lot to cover!
This September I am starting my Honours Mathematics program at the University of Waterloo here in Canada. It is without a doubt our best concentration of math and computer science talent and has often been referred to as the MIT of the North. I like it but I was wondering how important an undergraduate education at a prestigious school (which means the States or UK) is to admissions at a prestigious graduate school. I don't think Waterloo is very well known (how many of you have even heard of it?) but I believe I will get the best math education in the country thereof course this doesn't amount to much if MIT or Cambridge, etc. doesn't consider me. Plaese assuage my fears and tell me all that matters is marks and research experience! More seriously, at the end of 1st year I have to choose a specialization (major) and I am torn between Mathematical Physics and Pure Mathematics. I have time to decide but knowing in advance would help me to put the focus on the appropriate things in 1st year. I took physics to ensure I meet the requirements for the Math Phys program, so there's no problem there, but I am having trouble weighing the merits of each. I like Mathematical Physics because it would let me apply the math (and see the impacts of my efforts with any hope) and the job prospects seem better to meI have connections to the Perimeter Institute for Theoretical Physicsand for more reasons that will become clear in a moment. I don't like it because I am afraid the program will be more procedural rather than conceptual and I really firmly believe in the bottom of my soul that while a functional command of a topic is imperative to learn it, a conceptual understanding of it is essential in order to innovate and actually accomplish anything new... with the exception perhaps of some monsters. As for pure math, I like it because I think math is beautiful and I like just the culture that is associated with academia and mathematics in particular. My one big deterrent is that sometimes I doubt whether I am smart enough to do this. I come from a small high school where things like AP or IB, etc. weren't offered and there was no math club or participation in many contests. Thus, when I meet the kids from the big cities with so much more experience in universitylevel maths who have the parents and money to back them I really feel like ****, like I am at a huge disadvantage that only a tremendous natural aptitude for the subject can negateaptitude that I really don't know if I have. Don't get me wrong, I graduated with High Honours (+90% CAV) and have a huge passion and entusiasm for both math and theoretical physics (math more) but I'm not sure if I can cut it at the most competitive levels when the time comes. I mean, pure math... I know there are pressures to publish and stuff (publish or perish, right?) but I sit here and think, "how the hell am I suppose to come up with new math? Stuff not only original but insightful? I can't even understand half the books I buy in a pathetic attempt to catch up with the more priveleged students." For this reason, I lean towards math phys because it seems easier to me. NOTE: Am I right in believing that Math Phys is the same as theoretical physics? Sort of a physics degree where you skip the labs and focus more on the math and concepts? That's my impression of it... a direct route to the theoretical side of physics in undergrad. I've always thought that the more theoretical it gets, the harder it gets because I can do experiments and get paid for it even if I'm only really making a minor contribution but with the theoretical side of the coin you need to think up new things and if you can't, you,re done. I just don't want to get in over my head. I know that to do well in something you need to be honest with yourself and first judge if you are actually good at it. I'm sure if I ever got to the forefront of research in math or math phys that I would be better equipped and that would make me more confident but I ask myself whether I will do something majorly important or throw in my $0.02 and then fade away. The big problem is that I know for certain that if I did something easier like chem or bio I could have big acheivements. But I guess while many in the math and physics world might be more succesful in 'easier' or less rigourous fields, they do it not only because they love it, but because they are the only ones who can. tl;dr  do you have to be a monster brain to not only survive in the world of grad school and beyond but make meaningful contributions? Also, with a PhD in just pure old math, can you still work with physicists and work on making new math for physics, etc. or is this really the realm of mathematical physics? (Please, I know it is probably possible, but is it likely or is it really hard?) Thoughts, please. And sorry if this was disjointed, I needed to vent! 
Re: A Query: On Math, Physics, Fear and Natural Aptitude
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Re: A Query: On Math, Physics, Fear and Natural Aptitude
First off, thanks for the reply!
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Re: A Query: On Math, Physics, Fear and Natural Aptitude
As a note, I know a great deal of mathematicians who have a degree in pure math but do most of their research in mathematical physics; similarly, I know many mathematicians with a degree in mathematical physics who do pure math.
Mathematical physics is not quite theoretical physics; it's definitely a lot more formal, and, well, more mathematical / formal. But in an undergraduate setting, I doubt there would be much difference between, say, a degree in mathematical physics, a degree in pure maths with lots of physics electives, or a degree in physics with lots of math electives. Ultimately, look at what courses you feel that you should take during your undergraduate education, and see which program will give you a degree for those. I don't quite want to keep the university competition thing going, but about UW being the best in math in Canada, you've gotta be careful. Math has many subfields, and no one university can be at the top in every one of them, and my perception is that UW is not at all the best in Canada in many of the math fields which relate strongly to theoretical physics (pure algebra, lie theory, representation theory...although they do have a number of mathematicians working on things many would consider theoretical physics, which is nice), since the main interest is computer science. That being said, you're an undergrad and need not care about such things provided that you're able to get research opportunities (and that's something that most would agree UW is indeed the best in the country), and UW can help you a lot into getting Perimeter. In the end, there's no need to really care too much about how others view your university: get good grades and research experience. That formula will always get you in a good grad school. 
Re: A Query: On Math, Physics, Fear and Natural Aptitude
Hmmm. Thanks for the insight. What you say makes senseespecially about the topics available as research interests being more likely CSoriented then physics oriented. I'll have to take that into consideration.

Re: A Query: On Math, Physics, Fear and Natural Aptitude
Although, I think there's a lot of interesting stuff going on at the border of CS and Physics (of course, most broadly quantum computing) and if you're interested in that area there aren't too many places in the world better than Waterloo.

Re: A Query: On Math, Physics, Fear and Natural Aptitude
Ya the PI and IQC are doing a lot of neat stuff together with UW. It's always an option and to each, their own!

Re: A Query: On Math, Physics, Fear and Natural Aptitude
First of all, calm down. Second, congratulations to being an undergrad in such a prestigious school.
Now lets get down to business shall we? Do not ever compare yourself to others. Especially not more experienced rich kids. Try to use their experience to learn things you haven't learned yet. Try to ease into the whole universitything, not by drinking, partying and whatnot, but by study, by maxing your studytechnique, by feeling and acting upon your conviction. And believe me when I say that a technical/mathematical education in the universitylevel is everything but easy. It is rewarding, because it's very often like ramming your head into a wall until you draw first blood. but after one or two years, you start to acclimate to your new surroundings and begin to understand what has to be done. If you got selfesteem issues, go see someone about this, otherwise it will greatly affect your studies in a bad way. Otherwise, I wish you luck. besides, I've often wanted to use the tl;dr here, but felt it's a bit out of context/place ;) 
Re: A Query: On Math, Physics, Fear and Natural Aptitude
Thanks for the encouragement. It is not so much a selfesteem issue as it is uncertainty (or ignorance, if you will). Having just graduated high school, I can't very well know what it will be like (and I am bracing for the worst) and I suppose I am putting it on a pedestal. With all the talent flowing into these kinds of institutions, you start to question yourself and wonder just how smart one should be. Thanks to all of your kind words, I can rest assured that once I get there it probably won't seem so impossible as I initially feared, I'm just anxious that's all. Gotta do my part.
I have to admit going from a small school with few opportunities to a huge one with some of the best will be crazy! I am very excited and quite understandably nervous. 
Re: A Query: On Math, Physics, Fear and Natural Aptitude
A nonapocryphal parable:
One of the top students at my high school got into a very prestigious university  where he found out he (along with 50% of the rest of the student body) was below average. His self esteem crushed, he fell into a downward spiral... But no one remembered to tell him that the people who are below average at a prestigious school are still brighter and more likely to succeed than the vast majority of the general population. It's culture shock, for sure. One gets used to being the best, and then is immediately forced to compare themselves only to the best! I think the very best advice given so far is to not compare yourself to others. You already are good enough for Waterloo, that should be all the confidence you need. You have nothing but opportunity in front of you  you'll have to work your butt off like the rest of us  but take it! 
Re: A Query: On Math, Physics, Fear and Natural Aptitude
Thanks, I will try!

Re: A Query: On Math, Physics, Fear and Natural Aptitude
Hehe, those who have it coming easy are always the first to crack. :devil:
The only way to really brace for impact is getting the first literature and read it through like a novel. Then you know what you are up against. Besides, a hard work ethic outflanks high quality any day. 
Re: A Query: On Math, Physics, Fear and Natural Aptitude
Good to know it's like that in the academic world as well as the work one.
EDIT: I'll try extra hard in uni because I actually know what the work world is like. So terrible... 
Re: A Query: On Math, Physics, Fear and Natural Aptitude
How's it going? what is the progress? getting the books and curriculums?

Re: A Query: On Math, Physics, Fear and Natural Aptitude
Some additional advice:
1. You seem overly fixated on the "prestige" of a school. What really matters are the courses available in the program, the quality of teaching, and how well you do in them. Jackson is still Jackson (advanced E&M) whether you study it Ivy League Central or Joe Blow's College of Knuckledraggers. 2. Quote:
3. Getting a Ph.D. in one subfield does not confine you to forever doing research in that arena. I think a lot of people are hurt by subscribing to this belief. With getting an education, no matter how high you go, your goal should be to acquire as many skills as you can so that you can apply them to the problems you want to solve. And you also have to keep in mind that the "hot" problems when you finish your Ph.D. will not be the same as the "hot" problems of today. 
Re: A Query: On Math, Physics, Fear and Natural Aptitude
Xs1t0ry, it's too early for you to be worrying about graduate school. Your interests will most probably change as you progress through your undergraduate career. Try to sample different courses and such before committing yourself to anything. Your ideas of what "pure math" and "mathematical physics" are may be naive and incorrect.
Since you said you're going to Waterloo, have you considered taking the advanced sections of the first year core courses (i.e. Math 145, 147, etc.)? Depending on whose teaching these, they will probably carry a very healthy load of pure math. [I see that Forrest is teaching 147 next term  he is a great teacher. I took first year calculus with him, and we did some really interesting stuff (pointset topology on the real line, some talk of Lebesgue measure, some very elementary functional analysis  e.g. we proved that C[a,b] is a Banach space, and so on). You should really take this course if you have the slightest interest in pure math. As for 145, you'll be getting Menezes. I personally haven't had him, but his 400level crypto course is very popular. I'm willing to bet he will do a great job teaching 145 too  he'll probably go crazy with the cryptography and finite field stuff towards the end.] To add to what others have said previous, the statement "X is the best in math" is very broad and will probably be wrong. Each school has its own strengths and weaknesses, and Waterloo is no different. For instance, in the pure math category, Waterloo is strong in number theory and analysis and weak in algebra. But these things don't matter very much at the undergraduate level, so you'll probably get a strong undergraduate education at any of the better Canadian schools. Just make sure you take advantage of the opportunities you have. Take good courses and do well in them, get to know your professors, take graduate courses in your later terms, try to get a research assistantship (this is possible, and many undergrads do it), etc. Most importantly don't stress out too much and have a good time. [By the way, the good Waterloo pure math grads do get into the 'brandname' American schools. For example, I know of recent grads who are currently doing their PhDs at Berkeley, MIT, Chicago, Harvard and Stanford. So going to Waterloo at least won't be a hindrance. But you really shouldn't concern yourself too much with stuff anyway.] 
Re: A Query: On Math, Physics, Fear and Natural Aptitude
Thanks, that is good advice. Especially about the skills... another thing I need watch out for... opportunities to get them.
@ Fearless: I'm going by sometime next week to pick up books, student card, etc. Got an email yesterday reminding me that in 4 weeks I will be in my "first" lecture taking notes. lol. I checked out the curriculum and they use Spivak for the first year advanced calculus course... I'm in the regular physicsbased calculus now. I want to switch so I need to talk to the instructor of that course. So stupid... I'm not in the adv. one of the bat because I didn't write a specific math contetst (the Euclid). Guess the other ones I did don't count for much. But aside from that, I've been reading up on topics listed it the course descriptions of what I am taking 1st term. 
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