This brings up, not surpisingly, an old trope in mathematics: "what use is abstract mathematics?" Some of the philosophy is disccussed well in Michael Harris's new book Mathematics without Apologies: Portrait of a Problematic Vocation [http:/
Often courses like analysis and topology seem awfully abstract, but become much more useful when combined with other topics like linear algebra and group theory to build up other abstract topics like Lie groups and Lie algebras which have more specific problem applications. A few years ago I was shocked to see a Birkhauser/Springer text entitled Stochastic Models, Information Theory, and Lie Groups [http:/
I might suggest you sit back and enjoy the abstract portions of the ride for a bit while keeping your eyes out for applied areas for application. You'll find enough applied math as you go along. In general, you may find that many applied areas will become more comprehensible to you because you better understand the abstract math which underpins them.
One bright light at the end of the tunnel for analysis is that it builds up things for measure theory which underpins probability theory.
For resources, you might find Francis Su's (he's the current president of the MAA) online lectures to be interesting/useful. They can be found via http:/
There are also a wealth of materials via India's IIT http:/