1. Probability and Statistics:
- Counting (permutation and combinations),
- probability axioms,
- Sample space, events,
- independent events, mutually exclusive events,
- marginal, conditional and joint probability,
- Bayes Theorem,
- conditional expectation and variance,
- mean, median, mode and standard deviation,
- correlation, and covariance,
- random variables,
- discrete random variables and probability mass functions,
- uniform, Bernoulli, binomial distribution,
- Continuous random variables and probability distribution function,
- uniform, exponential, Poisson, normal, standard normal,
- t-distribution, chi-squared distributions,
- cumulative distribution function,
- Conditional PDF,
- Central limit theorem,
- confidence interval,
- z-test, t-test, chi-squared test.
2. Linear Algebra:
- Vector space,
- subspaces,
- linear dependence and independence of vectors,
- matrices,
- projection matrix,
- orthogonal matrix,
- idempotent matrix,
- partition matrix and their properties,
- quadratic forms,
- systems of linear equations and solutions;
- Gaussian elimination,
- eigenvalues and eigenvectors,
- determinant,
- rank,
- nullity,
- projections,
- LU decomposition,
- singular value decomposition.
3. Calculus and Optimization:
- Functions of a single variable,
- limit,
- continuity and differentiability,
- Taylor series,
- maxima and minima,
- optimization involving a single variable.
4. Programming, Data Structures and Algorithms:
- Programming in Python,
- Basic data structures: stacks, queues, linked lists, trees, hash tables;
- Search algorithms: linear search and binary search,
- Basic sorting algorithms: selection sort, bubble sort and insertion sort;
- Divide and conquer: merge sort, quicksort;
- Introduction to graph theory: Basic graph algorithms , traversals and shortest path.
5. Database Management and Warehousing:
ER-model,
relational model:
relational algebra, tuple calculus,
SQL,
integrity constraints,
normal form,
file organization,
indexing,
data types,
data transformation such as normalization, discretization, sampling, compression;
data
warehouse modelling:
schema for multidimensional data models, concept hierarchies,
measures: categorization and computations.
6. Machine Learning:
1. Supervised Learning:
regression and classification problems,
simple linear regression,
multiple linear regression,
ridge regression,
logistic regression,
k-nearest neighbor,
naive Bayes classifier,
linear discriminant analysis,
support vector machine,
decision trees,
bias-variance trade-off: cross-validation methods such as leave-one-out (LOO) cross-validation, k-folds cross-validation,
multi-layer perceptron,
feed-forward neural network;
2. Unsupervised Learning:
- clustering algorithms,
- k-means/k-medoid,
- hierarchical clustering,
- top-down,
- bottom-up: single-linkage, multiple-linkage
- dimensionality reduction, principal component analysis.
7. AI:
- Search:
- informed,
- uninformed,
- adversarial
- Logic:
- propositional,
- predicate;
- Reasoning under uncertainty topics:
- conditional independence representation,
- exact inference through variable elimination, and
- approximate inference through sampling.