Discrete Mathematics: Propositional and first-order logic. Sets, relations, functions, partial orders, and lattices. Groups. Graphs: connectivity, matching, and coloring. Combinatorics: counting, recurrence relations, generating functions.
Linear Algebra: Matrices, determinants, systems of linear equations, eigenvalues, and eigenvectors. LU decomposition.
Calculus: Limits, continuity, and differentiability. Maxima and minima. Mean value theorem. Integration.
Probability: 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 techniques. Number representations and computer arithmetic (fixed and floating point).
Section 3: Computer Organization & 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 & Data Structures
Programming in C. Recursion. Arrays, stacks, queues, linked lists, trees, binary search trees, binary heaps, and graphs.
Section 5: Algorithms
Searching, sorting, and hashing. Asymptotic worst-case time and space complexity. Algorithm design techniques: greedy, dynamic programming, and divide-and-conquer. Graph search, minimum spanning trees, and 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 and undecidability.
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, and 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, certificates, and firewalls.
