| Topics (Section) | Sub-Topics |
|---|---|
| Probability and Statistics | Counting (permutation and combination) | probability axioms | sample space | Bayes Theorem | Discrete Random Variables and Probability Mass Theorems | Binomial Distribution | Central Limit Theorem | Chi-Squared Test |
| Linear Algebra | Vector space | Subspaces | Projection Matrix | Quadratic Forms | Orthogonal Matrix | Eigen Values and Eigen Vectors | 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 | Search Algorithms: Linear Search and Binary Search | Basic Sorting Algorithms | Basic Data Structures: Stacks, Queues, Linked Lists, Trees, Hash Tables | 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, File Organization, Indexing, Data Types, and Data Transformation, such as normalisation, discretisation, sampling, compression, etc. | Data Warehouse Modelling: Schema for Multidimensional Data Models, Concept Hierarchies, Measures: Categorisation and Computations |
| Machine Learning | Supervised Learning: Regression and Classification Problems | Simple Linear Regression | Support Vector Machine | Multi-Layer Perception | Feed-Forward Neural Network | Unsupervised Learning |
| Artificial Intelligence (AI) | Search: Informed and Uniformed | Adversarial: Logic, Propositional, Predicate | Reasoning under Uncertainty Topics – Conditional Independence Representation, Exact Inference Through Variable Elimination, and Approximate Inference Through Sampling |
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