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Real analysis was my first proofs-based math class and it really felt like being thrown into the deep end with no clue what was going on half the time. I did q
by opencl 9y ago
Real analysis was my first proofs-based math class and it really felt like being thrown into the deep end with no clue what was going on half the time.
I did quite like Bartle's "Introduction to Real Analysis" and "Elements of Real Analysis" books, kind of surprised that nobody else has brought them up. I think they strike an excellent balance between rigor and actually being comprehensible and approachable to people that aren't already familiar with proofs.
- tzs 9y agoI think we make this harder than it has to be, by not doing proof-based math earlier. Real analysis is often the first class in a math bachelor's program where things really get far from intuition and much harder to wrap your head around than the material from earlier classes. Making that the first proof-based class is just piling one hard thing on top of another. I think we'd be better off if we made basic calculus proof-based, at least for people such as math majors who are going to need to learn to follow and do proof-based math at some point. For those going into fields where they will not need to read and do proves, have a separate "practical calculus" track. You can start out with more informal proofs at the start of basic calculus, and slowly step up the level of rigor throughout the year.