Shouldn't your course supervisor or someone in a similar role be the better person to ask? The likelihood of someone on this forum understanding enough about your timetable and course to be able to give better information and advice is slim.
I'm in my last year of Mathematical Physics, I've taken 5 courses/semester every year so far, and I'm registered in 5 each for my last two semesters as well. It really varies from school to school, and even program to program.
But do you want to know the subject more deeply? If so, 3 is max for me too. After that, is just to keep up with the system and a constant fight to go above the mediocre level. and I'm not talking about marks for which I can't complain. Just look at it this way: you went through high school, but if you pick up any decent problem solving book with basic maths, you will be scared to see that what you know is nothing.
well i agre it all depends on how much time you want to sopend on them, but to me spending so little time on each makes it not worth doing them, unkless they are for plkay, like art appreciation.
even in undergrad school, some of us began with grad courses, i enrolled in ym first one as a firsts emester freshman, and my more advanced colleagues took them for several years as undergrads.
so for advanced science students, it is often advised to take grad rstehr than udnergrad courses, and then they would be facing the same time demands as grad stduents, onlky without the commitment.
i.e. a successful undergrad career at the high level, often involves taking grad courses, and one needs to do well in them.
anyway i do not agree that rgad courses are so much harder for the grad student than undergrad courses are for the undergrad. i just do not believe there are many undergrads out there who can profitably take honors calculus ala spivak, and honors physics ala feynman, honors chemistry, plus honors writing, maybe a language like russian or german, and also a demanding philosophy course which reads a book or more a week like the illiad or republic.
these were the kinds of courses we took as freshmen at harvard, and i think we were taking too many of them at 4 1/2, much less 6. i gues it is my turn of mind but i like to think about what i am taking, not just listen to surveys, and never get into it.
i.e. to me learning is about understanding, not just exposure. and i think for most undergrads, the last two years are also about deep investigation, maybe writing a thesis. 6 courses at that time seems silly to me.
in fact i question how much oppenheimer got out of his vaunted 7 harvard courses. i tried unsuccessfully to see a list of what he took last night. but apprently he was a voracious reader who did little else but study.
in my day too, there were a few people who entered the library in the morning and left only at night when it closed, every day. this may even be thought unhealthy, and i worry abiut some of our young members here who speak of nothing but study.
oh and the notes for my "grad" course in algebra will reveal that it is considered undergrad material at many schools. e.g. at brandeis in the 1960's such material was taught to honors sophomores, out of bourbaki. also the book by chi han sah which i often recommend, was written as notes for a sophomore course at harvard in about 1963.
I don't understand why undergrads take grad level courses. If they take grad level courses after they've completed all their undergrad courses, why not just graduate early and go to grad school?
Or do they take grad level courses in place of their equivalent undergrad courses? for example, instead of taking undergrad real analysis, do they take graduate level instead? and in the process skip alot of undergrad courses. if so, wouldnt that be extremely difficult?
to get an undergraduate degree requires a certain number of hours. these hours may be taken from graduate courses if one is qualified.
you cannot stop and receive an undergraduate degree just because you are advanced enough to take grad courses. also undergrad school is more fun than grad school and it is prudent to spend all 4 years there among friends and girls, and extracurricular activities.
yes it is difficult, but that is what top people do at top places. it was fairly standard for the better math majors at harvard to take graduate reals and complex and algebra and algebraic topology, as juniors and seniors.
if you look at the content of the grad courses now given at harvard in these topics you may see that their grad courses now assume one has already had what are considered grad courses at other places. e.g. at other places grad comple teaches cauchys theorem, residue theory and elementary matters like that, and at harvard they may do sheaf cohomology, oka's theorem and nevanlinna theory.
so to even aspire to admission at a top grad school, one may need to arrive knowing hat is called graduate material at ones own school.
i once had a high school student who was also enrolled at uga in my graduate algebra course. he was the ebst in there, and graduated somehow simultaneously from high school and uga undergrad, and went straight to UCLA grad school at 17, without ever actually enrolling as an undergrad on campus.
i thought this a serious mistake, as he lost a lot of fun time from his life, indeed is probably the most fun most people ever have. they are pon campus with thousands of other kids, young and energetic, amonf=g stimuaklting people, and with ideally none of the responsibilities of adults.
I must say if they cut out the gen ed courses my life would be alot easier, taking things like grad courses would become much more feasible, but as it is now students come in as freshman and can only take calc 1 and physics 1 their first year, it slows the entire learning process down as you are distracted by things you never once cared about.
not to say that I don't enjoy learning about philosohpy and such, its just that I woud rather learn it from another philosohpy major over a beer and a cigar then in a classroom.
I agree Mathwonk very much. I went from a regular state school to Rutgers. I am sure this is not as demanding as Harvard. But it is much better to start the race at the front position than catching up later. It just won't happen if you want to wait until you get into top grad school. I know a friend who is doing algebraic topology 2, commutativity algebra, category etc in MIT as a second year in undergrad while I graduated my undergrad without knowing what topolgy really does. I am sure he would much better change to get into top grad school than I do.