What are some UC schools that specialize in mathematics and/or various types of engineering?

Well all the UC's have the same tuition. It is just a matter of the amount of financial aid you get, which over the past few years has also gone down. Most of the UC's have all those majors. Berkeley has the best civil engineering department in the nation. Architectural engineering is not a popular major because it is more of a subfield of civil/mechanical dedicated to buildings. You could do so much more with a degree in civil or mechanical. The only school in CA that offers architectural engineering as a major is Cal Poly SLO. It never hurts to apply and you might get lucky and end up at Berkeley or UCLA!