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The Most Common Errors in Undergraduate Mathematics (2009)

math.vanderbilt.edu

21–30 of 161 posts

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#21
My biggest problems as a math major at the undergraduate level were proofs. I could muddle my way through abstract algebra proofs but real analysis just didn't click.

The oddity is that I could read proofs for both subjects: the reasoning made sense. But I couldn't develop a proof.

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#22
post #11

Earlier quoted context omitted.

I stopped handwriting math to turn in my freshman year of college, LaTex was just too good looking.

that seems like a ton of work, especially for problem sets

You get very fast at it, especially if you start early in college - I actually live tex'd the lectures I went to starting sophomore year.

Nowadays I mostly use markdown with inline latex as formatting with latex can be a pain.

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#23
post #12

Earlier quoted context omitted.

I stopped handwriting math to turn in my freshman year of college, LaTex was just too good looking.

Extra fine Japanese fountain pens are the solution to all your problems.

They're great...just not for math. Use a decent pencil instead, like a Graphgear 1000 and some HB lead.

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#24
post #21

My biggest problems as a math major at the undergraduate level were proofs. I could muddle my way through abstract algebra proofs but real analysis just didn't click. The oddity is that I could read proofs for both subjects: the reasoning made sense. But I couldn't develop a proof.

Highly recommend the book "How to Prove It" by Velleman.

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#25
post #11

Earlier quoted context omitted.

I stopped handwriting math to turn in my freshman year of college, LaTex was just too good looking.

that seems like a ton of work, especially for problem sets

It’s a matter of practice. My kid takes lecture notes live using LaTeX. Of course that reflects a ton of practice on PSets and papers over the years.

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#27
My undergrad math classes were in lecture halls with a couple hundred students. The labs taught by grad students were better but would have been more helpful without the exponential confusion added by the lectures that had required attendance. That ended the pursuit of an engineering degree. Thanks George Mason. The economics courses and professors were amazing however.

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#29
post #5

Bad 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 went from something like 0.5 to 0.4 and then 0.2. Now I'm finding 0.3 pens ideal.

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#30
post #21

My biggest problems as a math major at the undergraduate level were proofs. I could muddle my way through abstract algebra proofs but real analysis just didn't click. The oddity is that I could read proofs for both subjects: the reasoning made sense. But I couldn't develop a proof.

I had a similar experience doing my math minor. All the way through Caluclus classes and Diff EQ and up until the first half of Linear Algebra, everything is plug and chug. After the first half of Linear Algebra when proofs started making an appearance, I came to the realization that proofs are another type of mental activity entirely. Survey of Algebra, Basic Real Analysis, and even the dedicated proof writing course I took were all exponentially harder to pass.
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