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Feb 25th, 2021
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  1. Illinois Tech Interview Questions
  2. It took about 46 minutes.
  3.  
  4. [Functional Analysis]
  5. What is a Banach space?
  6. If ∫f_ndx converges to zero, then can we say that f_n converges to zero?
  7. What is the dominated convergence theorem?
  8.  
  9. [Probability Theory]
  10. Describe convergence of random variables.
  11. What is convergence in distribution?
  12. Does convergence in distribution imply convergence in probability?
  13. Does almost sure convergence imply convergence in probability?
  14.  
  15. [Linear Algebra]
  16. Define the rank of a matrix.
  17. Define the linear independence of vectors.
  18. Describe the Gaussian elimination.
  19.  
  20. [ODE Theory]
  21. Solve y'=5y, y(0)=1.
  22. Solve y'=5y+x, y(0)=1.
  23.  
  24. [Complex Analysis]
  25. Evaluate the integral of e^z on the unit circle.
  26.  
  27. [Discrehe Mathematics]
  28. What is the maximal number of edges in the graph of n vertices?
  29.  
  30. [Group Theory]
  31. {0,1,2,3,4} forms a group with addition x+y := x+y(mod 5).
  32. What is the inverse of 2?
  33.  
  34. ---
  35. After those questions, I got time to ask questions to the professor.
  36.  
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