You are not alone. Here is a quotation from John Stillwell that I put in a FAQ for parents about mathematics education:
"What should every aspiring mathematician know? The answer for most of the 20th century has been: calculus. . . . Mathematics today is . . . much more than calculus; and the calculus now taught is, sadly, much less than it used to be. Little by little, calculus has been deprived of the algebra, geometry, and logic it needs to sustain it, until many institutions have had to put it on high-tech life-support systems. A subject struggling to survive is hardly a good introduction to the vigor of real mathematics.
". . . . In the current situation, we need to revive not only calculus, but also algebra, geometry, and the whole idea that mathematics is a rigorous, cumulative discipline in which each mathematician stands on the shoulders of giants.
"The best way to teach real mathematics, I believe, is to start deeper down, with the elementary ideas of number and space. Everyone concedes that these are fundamental, but they have been scandalously neglected, perhaps in the naive belief that anyone learning calculus has outgrown them. In fact, arithmetic, algebra, and geometry can never be outgrown, and the most rewarding path to higher mathematics sustains their development alongside the 'advanced' branches such as calculus. Also, by maintaining ties between these disciplines, it is possible to present a more unified view of mathematics, yet at the same time to include more spice and variety."
That's from the preface to his book Numbers and Geometry (New York: Springer-Verlag, 1998), which is a delight to read and full of thought-provoking problems.
http://www.amazon.com/Everything-More-Compact-Infinity-Disco...
The sad truth is that you have a very limited view of what math is if you think of logical syntax and parsing as something other than math.
Frankly, I'm a little tired of the position calculus holds, where it is the pons asinorum for everyone who wants to do the more advanced (that is, non-arithmetic non-trivial-algebra) math regardless of what their true focus is. I think proof construction should be its own class and CS folk should take that and discrete math in order to move up the ladder. Engineers-in-training could take proof construction if they want a math minor and, yes, calculus their little brains out because calculus is what physics uses for a language.