Possible Set of Topics for the Course

The topics listed will not be presented in the listed order.

• Algorithms and Data Structures
  • Computational complexity (Oh notation)
    • Tractable vs intractable
  • Elementary data structures
    • Arrays
    • Linked lists
    • Trees
    • Graphs
  • Elementary algorithms
    • Sort
    • Search
    • Dynamic programming (divide-and-conquer)
    • Matrix algorithms
    • Graph algorithms
• Basics of programming
  • Compilers vs interpreters
  • Programming in R (Lab)
    • Data visualization
  • Programming in C (Lecture/Lab)
  • Basic syntax
  • Functions
  • Loops and control flow
  • Arrays
  • Strings
  • Pointers and memory management
  • Input/Output
  • Interfacing C with R
• Basic non-uniform random number generation
  • Transformation
  • Accept/reject
  • Monte Carlo sampling
  • Monte Carlo integration
  • Metropolis-Hastings and Gibbs sampling (time permitting)
• Optimization
  • Convexity
  • Graduate descent
  • Newton's method
  • Conjugate gradients
  • BFGS (time permitting)
• Statistical applications (not all may be covered)
  • Sampling
  • Basic linear algebra in C (dense and sparse vectors and matrices)
  • Linear regression
  • Logistic regression
  • Maximum likelihood estimation
    • Exponential families
    • Mixture models
      • Expectation-Maximization (EM)
  • Bayesian estimation
  • Non-parametric density estimation
    • Curse of dimensionality
  • k-means clustering
  • Rank statistics estimation
  • Hidden Markov models