Article
DA — Data Science and Artificial Intelligence
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
- Binary search
- Basic sorting algorithms:
- Selection sort
- Bubble sort
- Insertion sort
- Divide and conquer:
- Mergesort
- Quicksort
- Introduction to graph theory
- Basic graph algorithms:
- Traversals
- 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
- 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: AI
- Search:
- Informed
- Uninformed
- Adversarial
- Logic:
- Propositional
- Predicate
- Reasoning under uncertainty topics:
- Conditional independence representation
- Exact inference through variable elimination
- Approximate inference through sampling
Source: GATE 2027 DA Syllabus — IIT Madras
CS Computer Science and Information Technology
Section 1: Engineering Mathematics
Discrete Mathematics
- Propositional and first order logic
- Sets
- Relations
- Functions
- Partial orders and lattices
- Monoids
- Groups
- Graphs:
- Connectivity
- Matching
- Colouring
- Combinatorics:
- Counting
- Recurrence relations
- Generating functions
Linear Algebra
- Matrices
- Determinants
- System of linear equations
- Eigenvalues and eigenvectors
- LU decomposition
Calculus
- Limits
- Continuity and differentiability
- Maxima and minima
- Mean value theorem
- Integration
Probability and Statistics
- Random variables
- Uniform, normal, exponential, Poisson and binomial distributions
- Mean, median, mode and standard deviation
- Conditional probability and Bayes theorem
Section 2: Digital Logic
- Boolean algebra and minimization:
- Algebraic technique
- Karnaugh map
- Tabular method
- Design of combinational and sequential circuits
- Number representation and arithmetic:
- Fixed point
- Floating point
Section 3: Computer Organization and Architecture
- Instruction set and addressing modes
- Design of arithmetic and logic unit (ALU)
- Design of control unit:
- Hardwired
- Microprogrammed
- Memory interfacing and hierarchy:
- Performance
- Cache memory mapping
- I/O interface:
- Interrupt
- DMA
- Instruction pipelining
- Pipeline hazards
Section 4: Programming and Data Structures
- Programming in C
- Recursion
- Arrays
- Stacks
- Queues
- Linked lists
- Trees
- Binary search trees
- Binary heaps
- Graphs
Section 5: Algorithms
- Searching
- Sorting
- Hashing
- Asymptotic worst case time and space complexity
- Algorithm design techniques:
- Greedy
- Dynamic programming
- Divide-and-conquer
- Graph traversals
- Minimum spanning trees
- Shortest paths
Section 6: Theory of Computation
- Regular expressions and finite automata
- Context-free grammars and push-down automata
- Regular and context-free languages
- Pumping lemma
- Turing machines
- Undecidability
Section 7: Compiler Design
- Lexical analysis
- Parsing
- Syntax-directed translation
- Runtime environments
- Intermediate code generation
- Local optimisation
- Data flow analyses:
- Constant propagation
- Liveness analysis
- Common sub expression elimination
Section 8: Operating System
- System calls
- Processes
- Threads
- Inter-process communication
- Concurrency and synchronization
- Deadlock
- CPU and I/O scheduling
- Memory management and virtual memory
- File systems
Section 9: Databases
- ER-model
- Relational model:
- Relational algebra
- Tuple calculus
- SQL
- Integrity constraints
- Normal forms
- File organization
- Indexing:
- B and B+ trees
- Transactions and concurrency control
Section 10: Computer Networks
- Principles of Layering
- Basics of switching:
- Circuit
- Packet
- Virtual circuit
- Performance metrics
- Data link layer:
- Error detection
- Medium Access Control
- Ethernet
- Distance vector and link state routing
- IPv4:
- Fragmentation
- CIDR Notation
- Network Address Translation
- TCP:
- Flow control
- Congestion control
- Socket API
- DNS
- HTTP