Note: I am not sure if this is the correct place to ask these types of questions, so please let me know if I should remove my question.
I'm taking Real Analysis 1 this semester, and was thinking of taking the second part next semester, but I have heard that it is probably the hardest undergraduate math course. Is it that much harder than the first course?
Also, would it be a good idea to take Real Analysis 2 and Elementary Number Theory in one semester?
Here are the course descriptions:
Real Analysis 1:
Properties of the real number system; point set theory for the real line including the Bolzano-Weierstrass theorem; sequences, functions of one variable: limits and continuity, differentiability, Riemann integrability.
Real Analysis 2:
Includes the rigorous study of functions of two and more variables, partial differentiation and multiple integration. Special topics include: Taylor Series, Implicit Function Theorem, Weierstrass Approximation Theorem, Arzela-Ascoli Theorem.
Elementary Number Theory:
Properties of the integers, the division algorithm, Euclid's algorithm, Fermat's theorems, unique factorization of integers into primes, congruences, arithmetic functions, Diophantine equations, continued fractions, quadratic reciprocity.