Zhu, Yifei2013-09-102013-09-102013-06https://hdl.handle.net/11299/156552University of Minnesota Ph.D. dissertation. June 2013. Major: Mathematics. Advisor: Tyler Lawson. 1 computer file (PDF); ii, 102 pages, appendices A.Dyer-Lashof theories organize power operations in cohomology. We give an overview of the structure of the Dyer-Lashof theories associated to Morava E-theories. When the E-theory is an elliptic cohomology theory, this structure enables us to compute power operations by doing calculations with elliptic curves. We give explicit computations of the Dyer-Lashof theory for a specific E-theory spectrum and its K(1)-localization.en-USThesis or Dissertation