My school offers three undergraduate courses (which are substitutes for one another) in real analysis, and I was wondering if taking one of the more difficult courses in real analysis would significantly help me getting into a top statistics graduate program?
The three courses offered are:
Math 444 - Elementary Real Analysis
Description: Careful treatment of the theoretical aspects of the calculus of functions of a real variable; topics include the real number system, limits, continuity, derivatives, and the Riemann integral. 4 hours of credit requires approval of the instructor and department with completion of additional work of substance. Credit is not given for both MATH 444 and MATH 447.
Math 447 - Real Variables
Description: Careful development of elementary real analysis including such topics as completeness property of the real number system; basic topological properties of n-dimensional space; convergence of numerical sequences and series of functions; properties of continuous functions; and basic theorems concerning differentiation and Riemann integration. Credit is not given for both MATH 444 and MATH 447.
Math 424 - Honors Real Analysis
Description: A rigorous treatment of basic real analysis via metric spaces. Metric space topics include continuity, compactness, completeness, connectedness and uniform convergence. Analysis topics include the theory of differentiation, Riemann-Darboux integration, sequences and series of functions, and interchange of limiting operations. As part of the honors sequence, this course will be rigorous and abstract.
The elementary real analysis course is offered over the summer, which helps a lot since I'm completing all my my classes for a math major in 2 years (changed major), but I could take one of the other courses if it would really help my grad school chances. I'm also an honors student that meets the requirements for taking the honors class. Alternatively, I could take the elementary class this summer and the honors class in the fall.
Thanks
Edit: Math 444 uses Bartle, Math 447 uses Ross, Math 424 uses Rosenlicht