Community college and the lack or teaching proofs

[RadiationX]

community college and the lack of teaching proofs

I'm in calculus II and to this date i have never had to write one proof! when i look through the forums i commonly come across postings about how to prove things, even from high school kids. why are community colleges less rigorous than 4 year universitys? this lack of rigour has me worried about future classes. how am i going to match up with people who have more mathematical tools than i have? any comments are welcome

 

[MathStudent]

not even in geometry?

I figure the reason that some Junior College classes are less rigorous is because those classes have to cater to the majority of students that enroll. As I am sure your aware, a large number of those students aren't to advanced or don't care to learn the theory behind math. This is not a put down to JC students, in fact there are many bright students who go to JC's for many reasons ( $$ ) other than brains (or a lack thereof ), who then transfer to prominent universities.

Unfortunately most intro calc classes (1,2,3) focus more on the calculational side of calculus rather than theory. This is true even in most universities, the exceptions are the honours courses. However, your prof should at least go over some of the proofs in class, but usually won't actually ask you to provide a proof to a theorem. If you eventually take Linear Algebra, then you should be exposed to proofs and will be asked to find proofs yourself, no matter where you take it. For the majority of students, this seems to be the natural course of things.

Here are some suggestions to help you prepare for the future. When reading your book, read carefully and make sure you understand every derivation and theorem. Some JC's offer courses that give an intro to logic and proofs. One course I know of called Discrete Structures (or something of that nature ) allows you to sample set theory, logic, combinatorics, probability, graph theory, etc... all in one semester. A course like that is useful for almost any math class, and can also provide a good foundation.

There are also resources available to you outside of your school ( too many to list ). Try getting ahold of a copy of some of the more advance texts on calculus such as Spivak, Apostol, or Courant. There is also a whole bunch of goodies available to you at the "open-coursware" section of the MIT website:
http://ocw.mit.edu/OcwWeb/Mathematics/index.htm
There you can find entire courses on video ( such as Lin Algebra and DE ), Professors lecture notes, etc..
And of course, there are the archives here at PF! You'll find a world of knowledge here, and better yet, tons of people with an impressive breadth of knowledge who are more than happy to provide guidance as well as assist you with your homework (for FREE!).

Another thought, most students that go on to upper devision math are the ones that don't just rely on what's taught in their classes. They're the ones that go out and learn for themselves, and when they don't understand a concept, they refer to another text on the subject. They start reading the textbook before any class begins. So IMO, even those students that just learn the "tools" from their classes are still behind.

Good luck,
-MS

 

[mathwonk]

ask about it in your school. thery may have advanced classes that teach proofs. here at UGA we only teach proof writing to juniors too. but we have advanced honors classes that doa bit mroe for top freshmen and sophomores.

read some on your opwn. get a used copy of spivak or apostol calculus and study proofs yourself. I did it in high school and learned enough to get a beginning.

you are in a college. there is a library there, do you ever go there? do not be dependent on what some professor asks you to read. read some good stuff yourself. take more responsibility, as you are doing now, by asking what to do.

My apologies mathstudent, you already said it better, but i did not read it.;

 

[bfd]

I'm in calculus II and to this date i have never had to write one proof! when i look through the forums i commonly come across postings about how to prove things, even from high school kids. why are community colleges less rigorous than 4 year universitys? this lack of rigour has me worried about future classes. how am i going to match up with people who have more mathematical tools than i have? any comments are welcome

I wouldn't worry to much about matching up with people who have more math tools than you do. I've read from math professors/textbook authors that it is a common problem that many students in upper division math courses are not properly equipped to handle proofs. What one professor, I believe Peter Hilton, says, "One must agree with Dr. Solow that, in this country, students begin to grapple with ideas of mathematical proof far too late in their student careers - the appropriate stage to be initiated into these ideas is, in the judgement of many, no later than eighth grade"

I had this problem (as did many of my classmates) too in my methods of analysis class back at school. If you want to get a head start (depending on whose view you look at) I might suggest finding books on how to write proofs (I started the thread somewhere here though I can't remember off hand). Its unfortunate that I didn't do this myself when I had the class. I would have probably walked away with a better grade.

 

[jai6638]

Im a high school sophomore and i learned proofs in geometry in 8th and 9th grade although i wasnt great at it .. Should i spend time improving my skills in these proofs or should i just let it go and try improve my skills at calculus proofs later?

 

[RadiationX]

try to do both if you can, it will improve your analytical skills

 

[learningphysics]

I'm in calculus II and to this date i have never had to write one proof! when i look through the forums i commonly come across postings about how to prove things, even from high school kids. why are community colleges less rigorous than 4 year universitys? this lack of rigour has me worried about future classes. how am i going to match up with people who have more mathematical tools than i have? any comments are welcome

Yes, I agree with Mathwonk. Do not depend on professors... even in higher university level classes there can be a lack of rigour. Find the books, and go through the proofs on your own. If you have questions post them, and I'm sure somebody on PF will be able to help.

Also, do searches on the internet to find proofs... It's amazing the stuff you can find.

Your questions and posts show great initiative. Use that initiative and try to learn on your own. This website is certainly a great place to clarify any doubts you have during your self-study and readings.