The Most Common Errors in Undergraduate Mathematics (2009)
math.vanderbilt.edu
The Most Common Errors in Undergraduate Mathematics (2009)
1–10 of 161 posts
Re: The Most Common Errors in Undergraduate Mathematics (2009)
#2[deleted]
Re: The Most Common Errors in Undergraduate Mathematics (2009)
#3When I was in undergrad, I declared a math minor quite late - just before my junior year. This led to me taking up to 9 hours of math credits in a semester. The reason I declared my math minor was because I was interested in going for a PhD in economics and my econ professors all recommended that I try to take as many math classes as possible to prepare. Reader, I was not a 'numbers person' at all.
However, in all of my math classes, I asked questions all. the. time. when I didn't understand. I would go to office hours and the teachers were seriously so helpful. This was the only way I survived. I learned that you don't have to be a 'numbers person' at all to be good at math. You just have to understand what's going on under the hood, and this may require lots of questions and outside help. But most importantly, you just have to practice. I ended up graduating with nearly a 4.0 for my math minor.
Re: The Most Common Errors in Undergraduate Mathematics (2009)
#4When I was in undergrad, I declared a math minor quite late - just before my junior year. This led to me taking up to 9 hours of math credits in a semester. The reason I declared my math minor was because I was interested in going for a PhD in economics and my econ professors all recommended that I try to take as many math classes as possible to prepare. Reader, I was not a 'numbers person' at all. However, in all of…
> I would go to office hours and the teachers were seriously so helpful.
As a grad student that taught undergrads I always encouraged students to attend office hours. Most instructors do want you to succeed and one-on-one time is one of the best ways to learn. Definitely take advantage of your instructors' office hours; ask questions about anything that you aren't 100% sure about!
Re: The Most Common Errors in Undergraduate Mathematics (2009)
#5Bad handwriting.
At age 40 I started taking a masters in stats and had situations where I had exponents on exponents. This lead me to buy a higher resolution tablet for reading pdf's with tiny math.
I also bought a finer point pen and this helped me improve my handwriting a lot. Closing loops on "o's" or backtracing the upward line of a cursive "t" to not make a loop. With the finer point, I was able to see my imprecision and improve it.
I used to rewrite my finished work in undergrad and now my writing was improved to the point where the first draft was entirely legible.
Re: The Most Common Errors in Undergraduate Mathematics (2009)
#6The "working backwards" one was what I always noticed students doing. It's super frustrating as a teacher since they're simultaneously so close to being right (when they manage to avoid an irreversible step) and yet also have completely misunderstood a basic idea in what it means to even attempt to prove something.
Re: The Most Common Errors in Undergraduate Mathematics (2009)
#7The "working backwards" one was what I always noticed students doing. It's super frustrating as a teacher since they're simultaneously so close to being right (when they manage to avoid an irreversible step) and yet also have completely misunderstood a basic idea in what it means to even attempt to prove something.
Do you factor that into the teaching now?
Re: The Most Common Errors in Undergraduate Mathematics (2009)
#8Bad handwriting. At age 40 I started taking a masters in stats and had situations where I had exponents on exponents. This lead me to buy a higher resolution tablet for reading pdf's with tiny math. I also bought a finer point pen and this helped me improve my handwriting a lot . Closing loops on "o's" or backtracing the upward line of a cursive "t" to not make a loop. With the finer point, I was able to see my impre…
I stopped handwriting math to turn in my freshman year of college, LaTex was just too good looking.
Re: The Most Common Errors in Undergraduate Mathematics (2009)
#9The "working backwards" one was what I always noticed students doing. It's super frustrating as a teacher since they're simultaneously so close to being right (when they manage to avoid an irreversible step) and yet also have completely misunderstood a basic idea in what it means to even attempt to prove something.
Do you factor that into the teaching now?
I no longer teach. I'm also skeptical of how useful this page is except as therapy for teachers - students have to make mistakes to learn from them. Though it could be a good reference to point to after the fact instead of explaining the problem from scratch.
Re: The Most Common Errors in Undergraduate Mathematics (2009)
#10Mathematical notation is terrible.
I don't mean this in the usual "we need to invent new symbols to make it clearer" way.
I mean it in the way that it has implicit typing that gets coerced constantly. Using Haskell types D :: (R -> R) -> (R -> R). Yet it gets used on things like D 2 = 0 which implies D :: (R -> R).
What you've actually done is an implicit conversion of 2 :: R to 2(x) = 2 :: R -> R and 0 is not 0::R it is 0(x) = 0 :: R -> R.
The Q_0 system described in [0] is a good start for a mathematical system that is both sane and as expressive as the one we have now. With term rewriting you can even keep the ridiculous notation we have today if you love it so much. Though I have grown incredibly fond of typing out extended typed lambda calculus using scheme notation in Emacs with a home grown automated theorem proving mode that was trivial to implement.