Which Harvard course should I take?

[TheLastMagician]

Hi, apologies if I'm on the wrong website or anything. I'll be starting math at Harvard next year but am at a loss as to which course I should start with. I have a good background in competition math (so I know the essentials of most elementary math topics), finished working through Apostol's two calculus volumes a few months ago and have been dabbling into things like linear and abstract algebra but with no clear direction. I would say I'm fairly strong at proofs but I will probably end up taking math 101* at some point.

To summarize, I know high school math well and have studied calculus using Apostol's two calculus volumes.

Would you say math 25* is a good choice? I heard it's pretty tough-going...

Thanks

*The courses I'm referring to: http://www.math.harvard.edu/pamphlets/beyond.html

 

[BiGyElLoWhAt]

25 sounds like fun, depending on how proof heavy it is. I haven't really had intensive proof classes, but I'm about to take one here next semester or so; it's required for a maths degree. So that really seems like the big difference between 23 and 25 to me. Also, the maximum allotment for the homework is the same for both classes (15 hours/week).

My opinion, if you're into math, and are going for a math degree, go for gold. If you think you're capable of it, then you probably are. Sign up, and do it.

 

[radium]

You should attend all of the courses you are considering for the first week to get a better idea of what you want to do. It would also be very informative to look at the q scores as this will give you a very good idea of the workload.

 

[IGU]

To summarize, I know high school math well and have studied calculus using Apostol's two calculus volumes.

Would you say math 25* is a good choice? I heard it's pretty tough-going...

You say where you are coming from but not where you're going. What classes you ought to take depends almost entirely on your goals. If you have done all the problems in Apostol I & II, and understood the proofs, and preferably can work them out yourself now that you understand them, then you should find Math 25 to be mostly straightforward. The advice http://www.math.harvard.edu/pamphlets/freshmenguide.html is quite good.

But it's a matter of time management. There are many other things to do at Harvard. What else do you want to do? There's time for only so much.

Incidentally, the page you reference says "Those who are taking or have taken Math 23, 25, or 55 should not take 101." Why do you think you'll want to take 101? If, after Apostol, you feel unsure of your ability to deal with proofs properly, then something is wrong. But regardless, things are set up for you to try the level of course you want and then drop back to something easier after a couple of weeks if you think you made a poor choice.

 

[radium]

You should try to meet with the math undergrad chair to help you decide. Harvard has a very long time you can add courses and an even longer drop period so just attend the classes you are interested in and you will be fine.

 

[mathwonk]

have you read this page?

http://www.math.harvard.edu/pamphlets/freshmenguide.html

It gives explicit criteria for choosing among those courses.

I am a little puzzled by your description of your background since you say you have read apostol but mention only beginning to dabble in linear algebra. apostol devotes some 150 pages to linear algebra in volume 2, and has already treated a lot of it in volume 1, which is repeated in volume 2. and when you say you have worked through apostol do you mean you have done most of the problem sets?

 

[mathwonk]

in my view, much depends on who is teaching which course. the harder courses often have excellent professors. I gather from online viewing that Benedict Gross e.g. is quite good, and he apparently often teaches some of these courses.