Core Textbook Directories
Calculus and Optimization
Functions of a single variable, limit, continuity and differentiability, Taylor series, maxima and minima, optimization involving a single variable.
Matrices and Linear Algebra
Matrices and Determinants, System of Linear Equations, Eigenvalues and Eigenvectors, Special Matrices, Matrix Factorizations
Vectors Algebra
Vector Space, Subspaces, Projection, Orthogonality, Quadratic forms, singular Value Decomposition (SVD).
Probability and Statistics
Counting (permutation and combinations), probability axioms, marginal, conditional and joint probability, Bayes Theorem, conditional expectation and variance, Central limit theorem, confidence interval, z-test, t-test, chi-squared test.
Database Management Systems
ER-model, Relational Model: Relational Algebra, Tuple calculus, SQL, Normalization, File Organization, Indexing: B and B+ Trees.
Python Programming
Syntax, Control Structures, Functions, Recursion, Scope, and Built-in Collections for Algorithmic Problem Solving.
Data Structures & Algorithms
Stacks, Queues, Linked Lists, Trees, Hash Tables, Searching/Sorting, Divide & Conquer, and Graph Traversals.
ML: Supervised Learning
Linear/Logistic Regression, Ridge, KNN, Naive Bayes, LDA, SVMs, Decision Trees, Bias-Variance, Cross-Validation, & Neural Networks.
ML: Unsupervised Learning
K-Means, K-Medoids, Hierarchical Clustering (Single/Multiple Linkage), Dimensionality Reduction, and Principal Component Analysis (PCA).
Data Warehousing
Data types, Data Transformation, Normalization, Discretization, Sampling, Compression; Data Warehouse Modelling: Schema, MultidimensionalModels, Concept Hierarchies, Measures: Categorization and Computations.
Official GATE DA Syllabus Breakdown
Curriculum specification organized by subject section.
Section 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.
Section 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.
Section 3: Calculus and Optimization
Functions of a single variable, limit, continuity and differentiability, Taylor series, maxima and minima, optimization involving a single variable.
Section 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: mergesort, quicksort; introduction to graph theory; basic graph algorithms: traversals and shortest path.
Section 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.
Section 6: Machine Learning
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.
Unsupervised Learning: clustering algorithms, k-means/k-medoid, hierarchical clustering, top-down, bottom-up: single-linkage, multiple-linkage, dimensionality reduction, principal component analysis.
Section 7: Artificial Intelligence
Search: informed, uninformed, adversarial; logic, propositional, predicate; reasoning under uncertainty topics — conditional independence representation, exact inference through variable elimination, and approximate inference through sampling.