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 there--of 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 me--I have connections to the Perimeter Institute for Theoretical Physics--and 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 university-level 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 negate--aptitude 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!
So what does that make the University of Toronto? You want a conceptual understanding and are contemplating pure math? Mathematical physics is not exactly theoretical physics. There is a lot of overlap, and the two are only subjective terms. Mathematical physics is more of dealing with the mathematical methods used to describe physics and finding new ways to reformulate physics. Theoretical physicists are the ones making the theories. In any case, if you intend on being a theoretical phycist mathematical physics is an ideal preparation. Not to survive grad school. As for making meaningful contributions? Honestly... I don't know. Mathematical physics. If you get a PhD in pure math, thats what you wil be doing.
First off, thanks for the reply! UofT is undoubtedly the best university in Canada for a number of reasons. However Waterloo is subjectively a better school for both math and cs. All of their money goes into those programs and as a result their other programs--arts for example--are pretty poor (but that doesn't concern me). To cite an overly-cited fact, Microsoft hires more grads from waterloo than any other university in the world (ya, the whole world). This doesn't have much to do with math per se, but does lend credit to the idea that it is a prestigious technical school, like MIT. This along with their close proximity to RIM, the Institute for Quantum Computing (both of which are directly adjacent to the campus), the Perimeter Institute for Theoretical Physics and one of Canada's largest up and coming technical industry and business parks helps to make this clear. Plus they administer many important tests such as the Euclid, etc. So what that makes UofT, Howers, is second best at math and cs. I will say that UofT is better for physics and theoretical physics, though. Of that there is no question. They have better funding and great staff like Amanda Peet (a very nice lady, btw). But then again, I never said they weren't so I don't know why you got all defensive. Maybe you go there or are an alumni. Isn't that the most logical? What better way to understand the math than to focus on nothing but the math? How does it compare to actual pure physics in terms of preperation? That's a reasonable answer... though define 'survive.' (Sorry, I forgot that part the 1st time around) Granted, but if you choose to focus on areas relevant to modern physics in your research then there is bound to be some overlap. It's not as if you are forbidden contact with mathematical physicists or even theoretical or experimental ones, right?
Oh don't get me wrong, I'm not getting all defensive. I just thought UT was more renown for math. All I know about Waterloo is computer sci and engineering. I'm a student here (UT) I guess I am using an informal definition of "conceptual". When textbooks use a conceptual approach, they often emphasize things like visuals and applications focusing on the bigger picture rather than the details. Pure math focuses on the details, and the bigger picture may not be immediately apparent. Well, in undergrad the only real distinction is not doing many labs but taking all the pure versions of math. This means you will likely be required to take real analysis and topology over say modern and electronic labs. In graduate school, this gap widens because in a lot of cases the physics courses of mathematical physics are offered by the math department, with their own spin. Not fail? You don't need to be a genius to do grad school. But the school you get into may be another story. Being top of the class may be another issue. That depends. In general, its unlikely that a mathemetician will be doing a physicists work if that is not what he specialized in - even if they sit 10 feet from each other. Sure there may be projects with you and physicists, but you won't be doing the physics. If you are concerned with reformulating physics then you should study physics, and pick up the math you need as you need it. Math will give you a deeper picture of its structure, but not neccessarily one that will help you with physics. If you are interested in inventing new math all together, then you know what department you should be in.
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.
Hmmm. Thanks for the insight. What you say makes sense--especially about the topics available as research interests being more likely CS-oriented then physics oriented. I'll have to take that into consideration.
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.
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!
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 university-thing, 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 university-level 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 self-esteem 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 ;)
Thanks for the encouragement. It is not so much a self-esteem 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.
A non-apocryphal 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!
Hehe, those who have it coming easy are always the first to crack. 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.
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...
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. Not necessarliy. There are lots of "theorists" who hit the run button on someone else's software, and there are lots of experimentalists who need to be extremely resourceful to get their experiments to work. 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.
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 (point-set 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 400-level 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 'brand-name' 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.]
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 physics-based 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.
Thanks, Morphism. You are not just probably right, you are right. The only real tough decision facing me in the near future is picking my major. I'm sure first year will sort that out. I am going to try to get into 145/147, but I didn't write the Euclid (I thought my teacher was administering it--he wasn't) so now it's time for begging to do things I've done before.
You'd do well to read books on the foundations of mathematics on your own before you take the advanced sections. Not because they're hard classes, they're not, they're just more sophisticated than high school classes, which is not saying much anyways. But because of how incredibly lame those classes are in that area. You'll get through these classes and you even won't be able to tell what a number is.