I'm a physics major interested in taking some upper level math classes such as topology, differential geometry, and group theory but these classes are only taught in the math department and are heavy on the proofs. Analysis are recommended and preferred prerequisites but are apparently not necessary. Should physics majors need to know analysis, especially before learning topology and differently geometry? If so, are there any good books you'd recommend on analysis for non-pure math majors and getting introduced to proofs? Thanks in advance.