Importance of undergraduate institution in grad-school admissions (math) I am a applied math major, and very much want to enter graduate school for applied math.  I spent my freshman year of undergrad at a very highly ranked (top 10 or 15 depending on ranking) university, with an equally good applied math program.  I unfortunately had to transfer out due to financial circumstances, and I am now attending a large state school, although it is research 1 and has an equally ranked (top 10/15) applied math program.  

At this new institution I will be able to concurrently get a BS and MS in applied math with a minor in computer science, which is more than I would have been able to achieve at the original institution I was attending.  With that said, I am worried that upon my transfer to a generally lower ranked university I severely damaged my chances of getting into a good graduate school for applied math.  

Is it generally the case that graduate school admissions committees will give more attention to applicants applying from better institutions?  The applied math program I am currently in at the state school sends students to grad schools in the ivy league every year (and as mentioned is highly ranked), however I am wondering if it is significantly more difficult to gain acceptance into such grad schools coming from a generally lower ranked school.
I predict that you will be fine. The admission to a grad/doctoral program depends much (much) more on what you do than on the ranking of the institution you attend. Rankings can be deceiving and no one sorts candidates by the rankings of, for example, news magazines. 

If you do well and impress people so that you get good letters of recommendation then you will be in contention. 

That said, the competition for slots in top programs is very fierce. 

The effect of mere college rankings would be small. But the effect of good grades in hard courses with good letters is large. 

In particular, an A student from a state school (almost any of them) would be in better shape than a C student from a school in anyone's top five. 

Work hard. Take advantage of opportunities. Work closely with a few professors.