So I Have Summer Filled With Nothing to Do Help Me Fix That(Math Plan)

  • Thread starter Neohuman
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Need Advice On Which Math(s) to Learn & Which Order to Learn Them In

So my major is in theoretical physics and I am interested in quantum computing. Will be completing single variable this term and thought "hmm why not get ahead". So I am going to use this summer to get as far ahead as possible. Problem is I am not sure the path. Here is my general thoughts...
  1. Multivariable
  2. Differential Equations/Matrix Theory
After that I am unsure what is the order I learn things. I know I need to learn real and complex analysis but should I learn topology first? Where does ODEs,PODEs, differential geometry, or differential topology come in? Many thanks to anyone that replies.
EDIT:
This is what I have come up with before but it is probably very wrong...
  1. Real Analysis
  2. Complex Analysis
  3. Abstract Algebra
  4. General Topology
  5. Algebraic Topology
 
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