You must learn C but you might be better off with that not being your first language
I am core C programmers for a decade now so i might be biased. I think - Learning C is a MUST. It forces you to closest to hardware programming (even if you are no long doing assembly). For example, it really make you think in terms of how computer uses memory, heap and stack. And of course, it will be hell on earth if you happen to try understanding Assembly before you try to learn C.
Stealing comment from @TikhonJelvis
I think not having any low-level courses would be a shame. –
However, having said that- understanding how machines work is still not everything. How to program is rather elementary thing you should learn before getting deep into how machines will interpret that - so in general, whenever C was being used as a first language. So using higher level language, something which gets you started more quickly and avoid some initial hickups might make you learn some other aspects
Also, after learning to do problem solving with programming, one can reasonably delve in to design and modeling aspect again C isn't really the most important language there. I think there is a great upswing in use of Perl, Python in many machine learning, web/data mining, information retrieval, bioinformatics class of applications (the top current research areas for CS folks over say topics like networking) where you are conceptually very higher up. They are replacing languages like Fortran rather than C.