Mathematical Methods for Computer Science Syllabus

1. Descriptive statistics(5h):
   • frequency tables & graphs
   • Central tendency & variability indexes
   • percentiles & correlation coefficient
2. Elementary probability(15h):
   • elements of combinatorics;
   • probability definitions;
   • conditional probability
   • independence
3. Discrete & absolutely continuous random variables(15h):
   • distributions
   • expected values & variances
   • Notable examples
4. Jointly distributed random variables(15h):
   • marginals & conditional distributions
   • Independence
   • correlation & conditional independence
   • notable multivariate distributions
5. Convergence in probability & in distribution(5h):
   • weak law of large numbers & central limit theorem
6. Statistical inference(10h):
   • sampling from a population
   • sampling statistics & their distribution;
   • parameter estimation
   • estimators & related properties
   • maximum likelihood estimators
   • pseudo-random numbers
   • examples of related generating alghoritms
7. Confidence intervals(10h):
   • confidence intervals for the mean & for proportions
   • asymptotic confidence intervals.
   • Basics of hypothesis testing

8. Multiple linear regression & least square estimation (5h).

9. Theory of distributions(8h):
   • definitions & basic operations
     • algebraic operations
     • translation
     • rescaling
     • derivatives
   • Dirac delta
   • $p.v.\left(\dfrac{1}{t}\right)$
   • Dirac comb;
   • Convolution of functions & distributions
10. Fourier & Laplace transforms of complex valued functions & of distributions(12h):
    • definitions & properties
    • inverse transforms
    • inversion formula
    • Notable transforms