Recommended program: Numerical analysis

Ken Bube, Ioana Dumitriu

First Year: 
554  555  556  (Linear Analysis) 
534  535  536  (Complex Analysis) 
AMath 584  AMath 585  AMath 586  (Applied Linear Algebra and Introductory Numerical Methods) 
Second Year: 
524  525  526  (Real Analysis) 
544      (Manifolds) 
  AMath 568    (Analysis in Engineering and Science) 
    AMath 569  (Partial Differential Equations) 
594  595  596  (Special Topics in Numerical Analysis) 
Third Year:
(Possibilities) 
557  558  559  (Introduction to Partial Differential Equations) 
527  528  529  (Functional Analysis) 
Of the core courses, linear analysis is the one we think should definitely be taken. Which other core courses are taken and which year depend on the interests of the students and the direction they plan to go in. Above we recommend taking Complex the first year and then starting both Real Variable and Manifolds the second year, and continuing with at least one of them through the year. Many variations are possible.

Some students might want to take optimization earlier, or take less PDE's, depending on interests. Functional analysis is recommended for students interested in theoretical aspects of numerical analysis. Other students might want to take courses in particular applications such as fluid mechanics.