Erey, Nursel2015-08-132015-08-132015http://hdl.handle.net/10222/59856In this thesis, we investigate the relation between invariants of minimal free resolutions of monomial ideals and combinatorial properties of simplicial complexes. We provide a sufficient combinatorial condition for monomial ideals to have nonzero Betti numbers and show that such a condition completely characterizes Betti numbers of facet ideals of simplicial forests. We also present a new approach to computing Betti numbers of path ideals of certain graph classes.enMonomial idealsMinimal free resolutionsBetti numbersSimplicial complexesThesis