So I've been given the opportunity to create my own undergraduate honours program. I can take whatever courses from whatever faculty I want at almost any university (although I'm keeping it local). I can create from scratch courses that do not yet exist immediately prior to taking them. I am to write a thesis before graduation, and have access to researchers at the Institute for Quantum Computing and the Perimeter Institute for Theoretical Physics. The program is extremely research-intensive, both in studies and in "field work". My interests are in the philosophy of physical theory, mathematical physics, quantum information, and emergence in physical theories and models. In particular, I am interested in modeling quantum mechanical molecular systems and interactions using algebraic and geometric methods. I am looking to set up a preliminary curriculum to give the academic advisors an idea of where I'm looking to go before I step foot in the door. Of course, as I traverse the ocean, I must sway with the seas, but as yet even my preliminary course is not mapped. I want to emphasize lateral thinking (whatever that means). Currently, I am considering the following split: I - Information and Computation, e.g.: probability theory statistics information theory theory and models of computation II - Analysis and Algebra, e.g.: abstract algebra (e.g group theory) multilinear algebra complex analysis / Hilbert Spaces III - Geometry, e.g.: metric spaces forms/vector analysis/multivariable calculus topology manifolds IV - Physics, e.g.: mechanics statistical mechanics quantum theory quantum information and computation V - Computational Modeling and Approximation Theory I am thinking of doing my thesis on the application of geometric methods to quantum mechanical systems. There are likely many factors I haven't considered, and so I am wondering if the kind people of this forum could help me think about this! Thanks in advance!