Real numbers and set theory Mark Sioen. This demands Analysis I as prerequisite:
Elementary set theory with attention to quotient, products and factorization of functions
Cauchy construction of R
Algebraic properties of R
Order properties of R
Q as subfield of R
Basics of metric and normed...
Can a good analysis curriculum begin without calculus, meaning starting by a book on proofs which I ordered, and then step into real analysis. I think yes. From a prof in Brussels, I could follow her 2nd years analysis course If I first had mastered the basic material on sets, proofs...
I have download copies of those as well.
Are you keen on :
Advanced Calculus (A Transition to Analysis) - Joseph B. Dence and Thomas P. Dance
Having to bridge 30 years, which approach would you take ?
Were these just video lectures without studymaterial ?
Were the videos readable (some use blackboard on youtube and totally unreadable)?
If there is no studymaterial ? What about exercises ? How to capture the theory on your mac or pc, to have at least a copy.
Just videolectures is for math...
I'd like to start learning at home real analysis.
Now, in order to start there was an older book Techniques of mathematical analysis by Tanter which looks good as preparation.
I also saw that another user SanjeevGupta studied the same one, and found it good.
I'd like to see some comments on...