Hello, I am a mechanical engineering student that loves mathematics and fluid mechanics. My school offers three different analysis courses and I’m not sure which to take. I took honors Fundamental of Mathematics, where we covered Abstract Linear Algebra, Set theory (along with rings and fields), morphisms, construction of the reals, and analysis up to Heine Borel and Bolzano Weirstrass. I also want to be challenged and push my thinking. Which of the below courses will challenge me, but not be overwhelming? Or how much harder is one versus the other, just from the list of topics of course. Math 424: Honors Analysis A rigorous treatment of basic real analysis via metric spaces recommended for those who intend to pursue programs heavily dependent upon graduate level Mathematics. 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. Math 447: Real Variables (http://www.math.uiuc.edu/Bourbaki/Syllabi/syl447.html) Careful development of elementary real analysis for those who intend to take graduate courses in Mathematics. Topics include 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. I would like to take the more rigorous one if possible, but I don’t want it to take away from the classes in my major. I will also be taking a lab course, doing research, and taking a graduate level fluids course. What would you all recommend for me?