Academic advice for fall semester?

[The_ArtofScience]

Hi PF members,

I've been thinking about taking Modern Algebra I and Real Analysis I in the same semester, but I'm having doubts if this is a realistic schedule. A semester is only four and a half months long and I don't believe that I can fully comprehend the subjects I'm studying for that short of time. As for my background, I had done math well up until Exploration and Proofs where I earned a B-, so you can see why I'm a bit shaky in signing up for two proofs-intensive classes. On the sidenote, I'm a double major in history and mathematics for teaching which explains my hesitation in taking more challenging courses. I've been going over this in my head for a few times now, not sure what path to go. I would like some advice from people experienced in taking these type of math courses or have been in a similar situation such as I've described.

Thanks

 

[snipez90]

From a logical point of view, there is no reason to take either of those courses. If you plan on teaching K-12 mathematics (up to and including calculus), knowing about groups, rings, vector spaces in abstract algebra or epsilon-delta arguments in analysis is simply unnecessary. While it might provide added insight if you learn the material well, odds are the insights won't be directly useful. I can see how real analysis might be useful if you wanted to teach a not so watered down calculus course (meaning with some proofs of the more well-known theorems), but even that's a stretch. As for modern algebra, even the very basics demonstrate the power and value of generalization, which I feel is too explicit for people learning elementary mathematics for the first time.

Finally, both of these courses form the core of any math major's education, and while I wouldn't necessarily say you need to do exceptional in your proof course, you might need to brush up some skills to catch up with those who did very well. I would strongly advise against taking both simultaneously (probably a lot of stress for most people), and you have my thoughts on taking even just one.

 

[The_ArtofScience]

Thanks for taking the time in relating your thoughts about the subjects. I wanted to get through all the hard courses this junior year and then have an easier senior year, but I guess that would be rushing and not learning.