What does the field of mathematical biology study? I like math and bio and I want to study both. There is a subject called mathematical biology. What is it? What does a mathematical biologist do? What institutions have good mathematical biology programs?

Mathematical biology asks many different questions.  An intro course will look at things like population genetics (the study of the dynamics of gene propagation in populations) and basic bioinformatics.  But any use of mathematical models in biology is in this field, and it can get fairly deeply mathematical.  René Thom's classic "Structural Stability and Morphogenesis" applies algebraic topology and catastrophe theory to the modelling of biological structure.  Knot theory is found in the study of DNA recombination and the action of enzymes like topoisomerase.  Physiology and pharmacological dynamics all study rate equations over complex metabolic graphs.  Nonequilibrium thermodynamics and dissipative structures are studied in the realm of biogenesis.  Autocatalytic sets, fitness landscapes, etc. are modelled in basic information evolution studies.
The field is really as it sounds - it is the application of mathematics to biology.
