DA Data Science and Artificial Intelligence
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.
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.
Calculus and Optimization: Functions of a single variable, limit, continuity and differentiability,
Taylor series, maxima and minima, optimization involving a single variable.
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:
mergesort, quicksort; introduction to graph theory; basic graph algorithms: traversals and shortest
path.
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.
Machine Learning: (i) Supervised Learning: regression and classification problems, simple linear
regression, multiple linear regression, ridge regression, logistic regression, k-nearest neighbour,
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; (ii) Unsupervised Learning:
clustering algorithms, k-means/k-medoid, hierarchical clustering, top-down, bottom-up: single-
linkage, multiple-linkage, dimensionality reduction, principal component analysis.
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.
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.
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.
Calculus and Optimization: Functions of a single variable, limit, continuity and differentiability,
Taylor series, maxima and minima, optimization involving a single variable.
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:
mergesort, quicksort; introduction to graph theory; basic graph algorithms: traversals and shortest
path.
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.
Machine Learning: (i) Supervised Learning: regression and classification problems, simple linear
regression, multiple linear regression, ridge regression, logistic regression, k-nearest neighbour,
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; (ii) Unsupervised Learning:
clustering algorithms, k-means/k-medoid, hierarchical clustering, top-down, bottom-up: single-
linkage, multiple-linkage, dimensionality reduction, principal component analysis.
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.
