
Understanding Calculus and Higher Mathematics without Geometry?
Posted:
Jul 9, 2008 5:13 AM


Question: How can a sentient being understand the rigours of modern Calculus without geometry?
I'm an engineering student who decided to take calculus last Winter at my current institution, and for all intensive purposes I thought I was prepared. I had taken all necessary prerequisites (making up for an appalling high school education), including Algebra I, II, Intermediate Algebra, College Algebra and Analytic Trigonometry (Elementary Functions I & II).
I received an A in all 5. (I had great instructors) I was in my Jr. Year. Upon switching institutions I took calculus and was thrust into a new world. A wonderful world. However, my instructor, being an older gentleman, saw fit to assume all the students in class were well versed in geometry.
I sadly did not have the opportunity in high school, and seeing most colleges, especially community colleges these days, do not provide coursework in the subject, I was not. My previous instructor at my previous institution was great about realizing the students you get, especially those in a community college environment, may not have all the necessary prerequisites. As such, you cannot just assume they know everything.
This was a problem for me.
So I have a question for all the mathematicians out there.
Can you adequately learn and comprehend higher mathematics without understanding the fundamentals of geometry? And, I'd like to make the added suggestion, we need a comprehensive system for people who were not able to study it in HS. Perhaps a comprehensive compilation of videos, texts, exercises. Something that can help out students like myself who have to scrounge the entire internet for much of their summer trying to find what little is out there.
I have only the option of studying old textbooks. I admit, perhaps I am just a spoiled fool, but I tend to learn a lot more from a lecture, simply because my mind is more audio/visual than just visual/linguistic. I need math humor and analogies to keep me alert and cognizant.
Currently I am making up for my high school deficiencies, ironically after I thought I had already done so, but this is life and it often throws you a curve ball.
I guess this is half a plea, and half a question to mathematicians out there to realize, many of your undergraduate students who enter, especially those who come from the community college sector, can be deficient in geometry. Why? Because our college system does not consider it an important venture.
All I'm asking is if I can understand ideas like cords, lines of tangent and sine effectively without understanding the fundamentals of geometry, and if not, what can I do to foster my understanding.
I live in the Seattle Metro area, and there is not a single institution teaching the subject besides a high school. (I don't think the district would like a college student crashing a math class...It would be interesting though.)
I'm studying a few books, and in general they are low level texts on geometry. One more advanced college text went missing with my copy of the Elements after I moved, I think it's in a box somewhere...
Besides reading that copy of the Elements, and what few texts have been recommended out there, do you all have any suggestions?
I have acquired some videos on geometry from the teaching company on HS geometry, but besides that, is there anything else out there? Lectures on geometry that really give the subject a full and intuitive look. Something of classical rigour that we lack today. I really want to walk back into my calculus class when I transfer to Berkeley and be able to take whatever geometric problem they throw at me. I can't have these cases of needing to understand the relationships of geometric objects I've never looked into.
Advanced studies on trigonometry. All the fun stuff I wasn't able to cover because of time restraints in my Elementary Functions II class. (We were on a Quarter System)
Please, if anyone has any suggestions I'd truly appreciate it. Sorry if this post is so long, but I've been struggling with this for over three terms.
Chris
Message was edited by: Christopher M. VanderwallBrown
Message was edited by: Christopher M. VanderwallBrown

