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Discrete Mathematics[edit]

  • Propositional and first order logic.
  • Sets, relations, functions, partial orders and lattices. Groups.
  • Graphs: connectivity, matching, coloring.
  • Combinatorics: counting, recurrence relations, generating functions.

Linear Algebra[edit]

  • Matrices, determinants
  • System of linear equations
  • Eigenvalues and eigenvectors
  • LU decomposition

Calculus[edit]

  • Limits, continuity and differentiability.
  • Maxima and minima. Mean value theorem.
  • Integration.

Probability[edit]

  • 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. Combinational and sequential circuits. Minimization. Number representations and computer arithmetic (fixed and floating point). Section 3: Computer Organization and Architecture Machine instructions and addressing modes. ALU, data‐path and control unit. Instruction pipelining. Memory hierarchy: cache, main memory and secondary storage; I/O interface (interrupt and DMA mode). 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 and divide‐and‐conquer. Graph search, minimum spanning trees, shortest paths. Section 6: Theory of Computation Regular expressions and finite automata. Context-free grammars and push-down automata. Regular and contex-free languages, pumping lemma. Turing machines and undecidability. Section 7: Compiler Design Lexical analysis, parsing, syntax-directed translation. Runtime environments. Intermediate code generation. Section 8: Operating System Processes, threads, inter‐process communication, concurrency and synchronization. Deadlock. CPU 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 (e.g., B and B+ trees). Transactions and concurrency control. Section 10: Computer Networks Concept of layering. LAN technologies (Ethernet). Flow and error control techniques, switching. IPv4/IPv6, routers and routing algorithms (distance vector, link state). TCP/UDP and sockets, congestion control. Application layer protocols (DNS, SMTP, POP, FTP, HTTP). Basics of Wi-Fi. Network security: authentication, basics of public key and private key cryptography, digital signatures and certificates, firewalls.