GATE CSE syllabus 2027

Discrete Mathematics

• Propositional and first-order logic
• Sets, relations, functions, partial orders and lattices
• Monoids and groups
• Graphs: connectivity, matching and colouring
• Combinatorics: counting, recurrence relations and generating functions

Linear Algebra

• Matrices and determinants
• Systems 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

• Boolean algebra
• Combinational and sequential circuits
• Minimization
• Number representations and computer arithmetic (fixed and floating point)

• Machine instructions and addressing modes
• ALU, data path and control unit
• Instruction pipelining and pipeline hazards
• Memory hierarchy: cache, main memory and secondary storage
• I/O interface: interrupt and DMA mode

• Programming in C
• Recursion
• Arrays, stacks, queues and linked lists
• Trees, binary search trees and binary heaps
• Graphs

• Searching, sorting and hashing
• Asymptotic worst-case time and space complexity
• Algorithm design techniques: greedy, dynamic programming and divide-and-conquer
• Graph traversals, minimum spanning trees and shortest paths

• Regular expressions and finite automata
• Context-free grammars and push-down automata
• Regular and context-free languages; pumping lemma
• Turing machines and undecidability

• Lexical analysis, parsing and syntax-directed translation
• Runtime environments
• Intermediate code generation
• Local optimisation
• Data flow analyses: constant propagation, liveness analysis and common subexpression elimination

• System calls, processes and threads
• Inter-process communication, concurrency and synchronization
• Deadlock
• CPU and I/O scheduling
• Memory management and virtual memory
• File systems

• ER model
• Relational model: relational algebra, tuple calculus and SQL
• Integrity constraints and normal forms
• File organization and indexing (e.g. B and B+ trees)
• Transactions and concurrency control

• Concept of layering: OSI and TCP/IP protocol stacks
• Basics of packet, circuit and virtual circuit switching
• Data link layer: framing, error detection, medium access control and Ethernet bridging
• Routing protocols: shortest path, flooding, distance vector and link state routing
• Fragmentation and IP addressing: IPv4 and CIDR notation
• IP support protocols (ARP, DHCP, ICMP) and network address translation (NAT)
• Transport layer: flow control and congestion control, UDP, TCP and sockets
• Application layer protocols: DNS, SMTP, HTTP, FTP and email

Verbal Aptitude

• Basic English grammar: tenses, articles, adjectives, prepositions, conjunctions, verb–noun agreement and other parts of speech
• Basic vocabulary: words, idioms and phrases in context
• Reading and comprehension
• Narrative sequencing

Quantitative Aptitude

• Data interpretation: bar graphs, pie charts and other graphs, 2- and 3-dimensional plots, maps and tables
• Numerical computation and estimation: ratios, percentages, powers, exponents and logarithms, permutations and combinations, and series
• Mensuration and geometry
• Elementary statistics and probability

Analytical Aptitude

• Logic: deduction and induction
• Analogy
• Numerical relations and reasoning

Spatial Aptitude

• Transformation of shapes: translation, rotation, scaling, mirroring, assembling and grouping
• Paper folding, cutting and patterns in 2 and 3 dimensions