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inthenickoftime

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Do you think a first course in analysis should focus entirely on inequalities and leave set-theoretic topology for another occasion? Should this depend on whether or not the student had a first rigorous calculus course first? If I'm not mistaken, Victor Bryant (Yet Another Introduction to Analysis) and Arthur Mattuck (Introduction to Analysis) authored analysis books in the language of inequalities. Has anyone had previous experience with these two? Did it alleviate topological proofs in later courses? Is topology even required for the level I'm aiming at? Let's say my main concern is grasping the calculus of variations (much needed in mechanics). At what point do you absolutely need to incorporate topology in your analysis?

edit: I'd like to add that David Bressoud's A Radical Approach to Analysis also does this.

edit: I'd like to add that David Bressoud's A Radical Approach to Analysis also does this.

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