Clearly, this proves that I'm stupid
January 31, 2013 8:35 PM Subscribe
I can't seem to wrap my mind around the language of higher level math. Definitions, theorems, and proofs make me fall asleep, but I really do want to understand. Do you know of any good resources that can help me out?
posted by lucia_engel to education (19 answers total) 16 users marked this as a favorite
Back in high school (Canadian) I was a math whiz. I had no trouble with any of the concepts, including calculus in Gr 12. I can "do the math" and am good at problem solving. However when I got to university and started taking Number Theories, Abstract Algebra, etc., my logic suddenly disappeared on seemingly simple concepts. I've obtained my degree in CS already, somehow memorizing or handwaving my way through on my assignments and exams, but now I actually need to understand higher math for my current job.
For example, these are excerpts from one of my textbooks (A Concrete Introduction to Higher Algebra by Lindsay Childs):
[on real numbers] "The real numbers form a complete Archimedean ordered field...Archimedean means that for every positive real number r there is a natural number n with n > r."
[division theorem] "Given nonnegative integers a > 0 and b, there exist integers q> 0 and r with 0 <= r < a such that b = aq +r
I thought I understood real numbers and division until I read these definitions and was also asked to prove them. First of all, my brain have difficulty just parsing out what's written; it's like a foreign language to me. Secondly I never know how to begin when proving things. I can somewhat follow along if there's an example in the textbook, but on my own I would be completely lost.
I'm not looking to take any classes in math or hire a tutor. Books or online resources would be good. At minimum I'm hoping to at least be able to read through a math textbook and actually understand the explanation.