KGZotU

As a former math major at UCSD who took these course equivalents, I think you're going to need some proofs background in order to tackle these courses. Honestly, algebra and analysis--presented fully, as you'll be taking them--are probably the most painful courses a university can offer. I might be wrong about the particulars at UCLA, but I'd talk to the major advisor before trying this out.

Good luck,
Joe

Edit: Taking a look at the course descriptions, I might be wrong. The analysis course says that students learn to write clear arguments in the course. *shrugs* Weird.

Edit2: I'd suggest considering yourself up for _either_. Typically, students will find themselves more suited towards one of algebra or analysis. Most people, and you're likely most people, will find themselves in a world of hurt taking both. So, if you want to sign up for both, try them out for a few weeks and don't consider it a shame to drop one.