So I am taking an analysis class in my university and I want a problem book for it.
The topics included in the teaching plan are
Real Numbers: Introduction to the real number field, supremum, infimum, completeness axiom, basic properties of real numbers, decimal expansion, construction of real numbers.
Sequences and Series: Convergence of a sequence, Cauchy sequences and subsequences, absolute and conditional convergence of an infinite series, Riemann's theorem, various tests of convergence.
Point-set Topology of: : Open and closed sets; interior, boundary and closure of a set; Bolzano-Weierstrass theorem; sequential definition of compactness and the Heine-Borel theorem.
Limit of a Function: Limit of a function, elementary properties of limits.
Continuity: Continuous functions, elementary properties of continuous functions, intermediate value theorem, uniform continuity, properties of continuous functions defined on compact sets, set of discontinuities.
I am already following up Michael J. Schramm's Introduction to Real Analysis for my theory
But a problem book with varied questions on the concepts would help me a lot.
Please recommend some problem books.
P.S : I have already asked my professor to recommend some books but he always recommends baby Rudin and also doesn't provide a lot of assignments. I am not compatible with Rudin's book. Also his tests are very tough as he wants us to cook up counter examples and I am very poor in that. So I need a good problem book to master real analysis.