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I'm taking a number theory course and don't know whether it's worth it. I currently can't understand algebra and real analysis and decided to take # theory to see whether this would help me prove and understand set theory and cardinality and sequences and the prerequisites for analysis and galois theory. Should I expect to get better at proving after this course?

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closed as too broad by Mike Pierce, Adam, Xander Henderson, user52817, Joonas Ilmavirta Mar 3 '18 at 11:31

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ A good answer to your question would depend on so many subtle details of what you're doing in the course and details about you, that I don't think anyone here can really answer it. If your interested is improving you ability to write proofs though, that really just comes from practice. Any practice. Prove lots of things. $\endgroup$ – Mike Pierce Feb 28 '18 at 15:46
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At the very least, elementary number theory (e.g., the notion of "congruence", the notion of "prime", rings of integers-mod-$n$, Fermat's Little Theorem, Wilson's Theorem, and so on) gives a very tangible practice scenario for reading and writing proofs. At the same time, most of the elementary number theory results are indeed prototypes and examples for various basic results in abstract algebra (group theory, commutative rings).

Arguably, the logical complexity of assertions and proofs in elementary number theory is less than that of basic rigorous analysis, where the nesting of quantifiers is just slightly deeper in many cases.

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