GATE Data Science and Artificial Intelligence (DA) Syllabus
GATE DA covers probability and statistics, linear algebra, calculus and optimisation, programming and data structures, database management, machine learning, and artificial intelligence, plus the common general aptitude section.
8 subjects · 57 topics · 363 subtopics
General Aptitude
Verbal Aptitude
- English Grammar (Tenses, Articles, Prepositions, Conjunctions)
- Verb-Noun Agreement & Parts of Speech
- Vocabulary (Words, Idioms, Phrases in Context)
- Reading Comprehension
- Narrative Sequencing
Quantitative Aptitude
- Data Interpretation (Bar, Pie, Graphs, Tables)
- Ratios, Percentages, Powers, Exponents & Logarithms
- Permutations & Combinations
- Series
- Mensuration & Geometry
- Elementary Statistics & Probability
- Simple & Compound Interest
- Alligation & Mixture
- Partnership
- Time & Work
Analytical Aptitude
- Deduction & Induction
- Analogy
- Numerical Relations & Reasoning
Spatial Aptitude
- Transformation of Shapes (Translation, Rotation, Scaling, Mirroring)
- Paper Folding, Cutting & Patterns
- 2D & 3D Patterns
Probability & Statistics
Counting
- Factorials
- Permutations
- Combinations
- Binomial Theorem
- Multinomial Theorem
- Inclusion-Exclusion (PIE)
- Seating Arrangements
- Circular Arrangements
- Derangements
Probability
- Sample Space & Events
- Probability Axioms
- Conditional Probability
- Multiplication Theorem
- Independent Events
- Mutually Exclusive Events
- Marginal Probability
- Joint Probability
- Total Probability
- Bayes' Theorem
Descriptive Statistics
- Mean
- Mode
- Median
- Skewness
- Kurtosis
- Range
- Interquartile Range
- Variance
- Standard Deviation
- Covariance
- Correlation
Discrete Random Variables
- PMF
- CDF (Discrete)
- Expectation (Discrete)
- Variance (Discrete)
- Conditional Distributions (Discrete)
- Conditional Expectation
- Conditional Variance
- Covariance of RVs
- Joint PMF
- Joint CDF (Discrete)
- Independent RVs (Discrete)
- Discrete Uniform
- Bernoulli
- Binomial
- Poisson
Continuous Random Variables
- CDF (Continuous)
- Expectation (Continuous)
- Variance (Continuous)
- Conditional PDF
- Conditional Distributions (Continuous)
- Conditional Expectation (Continuous)
- Conditional Variance (Continuous)
- Covariance (Continuous)
- Joint PDF
- Joint CDF (Continuous)
- Independent RVs (Continuous)
- Uniform (Continuous)
- Exponential
- Normal
- Standard Normal
- Standardization & z-Score
Statistical Inference
- Markov's Inequality
- Chebyshev's Inequality
- Central Limit Theorem
- Sample Mean
- Sample Variance
- Point Estimation
- Confidence Intervals
- Hypothesis Testing
- z-Test
- t-Test
- Chi-Square Test
- t-Distribution
- Chi-Squared Distribution
- Sampling Distributions
Calculus & Optimization
Functions
- Standard Functions
- Odd & Even Functions
- Types of Functions
- Inverse Functions
Limits
- Limits
- Standard Limits
- Limit Laws
Continuity & Differentiability
- Continuity
- Differentiability
- Limits, Continuity & Differentiability
- L'Hôpital's Rule
- Mean Value Theorem
- Differentiation
Taylor Series
- Taylor Series Theorem
- Taylor Series of Standard Functions
- Ratio Test
Maxima, Minima & Optimization
- Maxima & Minima
- Single Variable Optimization
Linear Algebra
Matrix Algebra
- Scalars, Vectors, Matrices & Tensors
- Types of Matrices
- Matrix Addition & Subtraction
- Scalar Multiplication
- Matrix Multiplication & Conformability
- Transpose
- Symmetric & Skew-Symmetric
- Idempotent, Involutory & Nilpotent
- Orthogonal & Partitioned Matrices
- Periodic Matrices
- Trace of a Matrix
Vector Algebra
- Vector Notation & Operations
- Dot Product
- Angle Between Vectors
- Orthogonality
- Norms (L1, L2, Lp, Max)
- Euclidean Distance & Metrics
- Projection of Vectors
- Projection Matrix
Vector Spaces, Basis & Dimensions
- Vector Spaces
- Subspaces
- Linear Combinations
- Span
- Linear Independence & Dependence
- Basis & Dimension
- Rank of a Matrix
Systems of Linear Equations
- Homogeneous Systems
- Non-Homogeneous Systems
- Nullity
- Rank-Nullity Theorem
- Gaussian Elimination
- Echelon Forms
- Gauss-Jordan Elimination
- Inverse of a Matrix
Orthogonality & Projections
- Orthogonal Subspaces
- Four Fundamental Subspaces
- Projections & Least Squares
- Gram-Schmidt Orthogonalization
- Orthogonal Matrices
- QR Decomposition
LU Decomposition & Determinants
- LU Decomposition
- Determinant Calculation
- Determinant Properties
- Vector & Matrix Transformations
- Matrix of a Linear Map
Eigenvalues & Eigenvectors
- Eigenvalue Computation
- Eigenvector Computation
- Diagonalization
- Defective Matrices
- Properties of Eigenspaces
- Symmetric Matrices
- Quadratic Forms
- Positive Definite Matrices
- Spectral Theorem
Singular Value Decomposition
- SVD Formulation
- Singular Values
- Low-Rank Approximation
- Applications of SVD
Programming, Data Structures & Algorithms
Python Syntax & I/O
- Tokens & Operators
- Data Types & Expressions
- Input & Output
- Variables & Memory Management
- Operator Precedence
Data Types & Control Statements
- Conditional Statements
- Loops (for, while)
- Strings
- Lists
- Tuples
- Sets
- Dictionaries
Functions, File & Error Handling
- Functions
- Recursion
- Lambda, Map & Filter
- Comprehensions (List, Dict, Set)
- Built-in Functions & Libraries
- File Handling
- Error & Exception Handling
Stacks & Queues
- Stack Operations & Applications
- Queue Operations & Applications
Linked Lists & Hashing
- Singly Linked Lists
- Doubly Linked Lists
- Circular Linked Lists
- Hashing & Hash Tables
- Collision Handling
Complexity Analysis
- Time Complexity
- Space Complexity
- Best, Average & Worst Case
Searching & Sorting
- Linear Search
- Binary Search
- Selection Sort
- Bubble Sort
- Insertion Sort
Divide & Conquer
- Divide & Conquer Strategy
- Merge Sort
- Quick Sort
- Recurrence of Merge & Quick Sort
Trees
- Tree Properties
- Binary Tree Traversals
- BST (Insert, Search, Delete)
- AVL Trees
Graphs
- Graph Terminology
- Graph Traversals (BFS, DFS)
- BFS Shortest Path
- Dijkstra's Algorithm
- Bellman-Ford Algorithm
- Topological Sort
- MST (Prim's, Kruskal's)
Machine Learning
Regression
- Simple Linear Regression
- Multiple Linear Regression
- Lasso Regression
- Ridge Regression
- Regression Error Metrics
Classification
- Confusion Matrix & Metrics
- Classification Error Metrics
- k-Nearest Neighbors (k-NN)
- Naive Bayes Classifier
- Logistic Regression
Decision Trees & Ensembling
- Gini Index
- Information Gain
- Decision Tree Construction
- Pruning
- Bagging
- Random Forests
- Boosting
Clustering
- k-Means Clustering
- k-Medoids Clustering
- Hierarchical Clustering
- Single & Multiple Linkage
- Agglomerative Clustering
- Divisive Clustering
- Clustering Evaluation
Model Evaluation & Validation
- Regularization & Over/Underfitting
- Bias-Variance Trade-off
- Holdout Validation
- Leave-One-Out CV
- k-Fold CV
- Stratified k-Fold CV
- Model Selection
- Nested Cross-Validation
Neural Networks
- Artificial Neural Networks
- Activation Functions
- Loss Functions
- Feed-Forward Networks
- Multi-Layer Perceptron
- Gradient Descent
- Backpropagation
Dimensionality Reduction
- Principal Component Analysis (PCA)
- Linear Discriminant Analysis (LDA)
- LDA for Classification
Support Vector Machines
- SVM Theory
- Soft Margin Classifier
- Kernel Methods
Database Management & Warehousing
ER Model
- ER Model Concepts
- Attributes
- Relationships
- Weak & Strong Entities
- ER Diagrams
Relational Model
- Relational Model Concepts
- Tuples
- Domain Constraints
- Key Constraints
- Integrity Constraints
- Entity Integrity
- Keys & Super Keys
ER to Relational Mapping
- Conversion Rules & Techniques
Normalization
- Functional Dependencies
- Candidate & Super Keys
- Minimal Cover
- Lossless Decomposition
- Dependency Preservation
- 1NF, 2NF, 3NF
- BCNF
Relational Algebra
- Selection & Projection
- Rename Operation
- Set Operations
- Join & Division
- Extended Operations
- Relational Calculus (TRC)
SQL
- CRUD Operations
- Views
- ALTER Command
- Arithmetic Operations
- Aggregate Functions
- Filtering, Grouping & Nested Queries
- Joins
File Organization & Indexing
- File Organization
- Records
- Primary Indexing
- Secondary Indexing
- Clustering Indexing
- B Trees
- B+ Trees
Data Mining
- Data Types
- Similarity Measures
- Data Preprocessing
- Data Normalization
- Discretization
- Lossless & Lossy Compression
- Sampling
Data Warehousing
- Warehouse Architecture
- Data Marts & Lakes
- Warehouse Modelling
- Data Cube
- Multidimensional Schemas
- Concept Hierarchies
- Measure Types
- Cube Measure Computation
- OLAP Operations
- OLAP Indexing
- Cube Storage
Artificial Intelligence
Uninformed Search
- Breadth-First Search (BFS)
- Depth-First Search (DFS)
- Depth-Limited Search
- Iterative Deepening
- Uniform Cost Search
- Bidirectional Search
Informed Search
- Best-First Search
- Greedy Best-First Search
- A* Search
- A* Admissibility & Consistency
- Iterative Deepening A*
- Weighted A*
- AND/OR Graph
- AO* Search
Local Search
- Hill Climbing
- Simulated Annealing
- Genetic Algorithms
Adversarial Search
- Game Theory
- Minimax Search
- Alpha-Beta Pruning
- Heuristic Alpha-Beta Search
- Monte Carlo Tree Search
Propositional Logic
- Logical Connectives
- Logical Equivalence
- Propositional Inference
- Propositional Resolution
Predicate Logic
- First-Order Predicate Logic
- Predicate Inference
- Unification
- Predicate Resolution
- Translations
Uncertainty
- Bayesian Networks
- Conditional Independence
- d-Separation
- Bayesian Network Inference
- Variable Elimination
- Approximate Inference
- Sampling-Based Inference
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