GATE Computer Science (3 months)

Discrete Mathematics: Propositional and first-order logic, sets, relations, functions, partial orders, lattices, groups. Graphs: connectivity, matching, coloring. Combinatorics: counting, recurrence relations, generating functions.

Linear Algebra: Matrices, determinants, system of linear equations, eigenvalues, eigenvectors, LU decomposition.

Calculus: Limits, continuity, differentiability, maxima and minima, mean value theorem, integration.

Probability: Random variables, uniform, normal, exponential, Poisson, and binomial distributions. Measures of central tendency (mean, median, mode), standard deviation. Conditional probability, Bayes theorem.

Boolean algebra, combinational and sequential circuits, minimization techniques. Number systems, binary arithmetic (fixed-point and floating-point).

Machine instructions, addressing modes, ALU, data-path, control unit. Instruction pipelining, memory hierarchy (cache, main memory, secondary storage). I/O interface, interrupts, DMA.

Programming in C: Recursion, arrays, stacks, queues, linked lists, binary search trees, heaps, graphs. Algorithms for insertion, deletion, and traversal.

Searching, sorting, hashing. Algorithm design techniques: greedy, dynamic programming, divide-and-conquer. Graph algorithms: BFS, DFS, minimum spanning trees, shortest paths.

Regular expressions, finite automata, context-free grammars, pushdown automata. Regular and context-free languages, pumping lemma, Turing machines, undecidability.

Lexical analysis, parsing, syntax-directed translation, runtime environments, intermediate code generation, optimization techniques.

Processes, threads, inter-process communication, concurrency, synchronization, CPU scheduling. Memory management, virtual memory, deadlock handling, file systems.

ER-model, relational model (relational algebra, tuple calculus, SQL). Normal forms, integrity constraints, file organization, indexing (B/B+ trees). Transactions, concurrency control.

Layering concepts, LAN technologies (Ethernet), flow/error control, switching. IPv4/IPv6, routing algorithms (distance vector, link state), TCP/UDP, congestion control. Application layer protocols (DNS, SMTP, FTP, HTTP). Basics of Wi-Fi, network security (authentication, cryptography, firewalls).