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Jan6-06, 05:35 PM
P: 29
Introductory Real Analysis - check answers please! 4 Questions

Quote Quote by CarlB
I had no idea that this is how mathematics is being taught today, but I have to say that it is a considerable improvement from 30 years ago. Back then it was clear that a lot of students just weren't picking up the ideas but this sort of first week's assignments makes it very clear exactly what the problem is. You can't imagine how much more difficult the later problems in this class will be, in terms of interpreting the English correctly. They're doing you a big favor by bringing this up so early in the class. When I took classes like this they sucked the students in with easy stuff and then hit them hard by the end.
It is this fundamental mathematics that I consider to be part of a transition course. Such a course should also include all the nitty gritty about functions, relations, and a few other things as well as how to write a proof. Unfortunately, all too many schools still don't insure students know this stuff before they let them take higher math courses. I was unable to get the hang of higher math until I figured out on my own that this was what I was missing.

Ideally, this should be taught in freshman calculus. Limits would have been so much easier to understand. But, since freshman calculus courses are mostly populated by future engineers and engineers have a propensity to only want to know how to calculate things, perhaps professors don't try anymore. At least, this was my attitude when I was in my engineering phase.

"Analysis with an Introduction to Proof" by Steven Lay is a great book to have whether you know this transition material or not. I studied undergraduate analysis out of Rudin's book and Lay's book was an essential companion.