Engineering Mathematics | Discrete Mathematics | Propositional and first-order logic; Sets, relations, functions, partial orders, lattices; Monoids, Groups; Graphs: connectivity, matching, coloring; 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; Distributions: uniform, normal, exponential, Poisson, binomial; Mean, median, mode, standard deviation; Conditional probability, Bayes theorem. |
Digital Logic | Boolean Algebra | Combinational and sequential circuits; Minimization. |
| Number Representations | Fixed and floating-point arithmetic. |
Computer Organization and Architecture | Machine Instructions | Addressing modes, ALU, data-path and control unit. |
| Instruction Pipelining | Pipeline hazards. |
| Memory Hierarchy | Cache, main memory, secondary storage. |
| I/O Interface | Interrupt and DMA mode. |
Programming and Data Structures | Programming in C | Basics of C programming. |
| Data Structures | Recursion, arrays, stacks, queues, linked lists, trees, binary search trees, binary heaps, graphs. |
Algorithms | Algorithm Concepts | Searching, sorting, hashing. |
| Complexity | Asymptotic worst-case time and space complexity. |
| Design Techniques | Greedy, dynamic programming, divide-and-conquer. |
| Graph Algorithms | Graph traversals, minimum spanning trees, shortest paths. |
Theory of Computation | Finite Automata | Regular expressions, finite automata. |
| Context-Free Grammars | Push-down automata, context-free languages, pumping lemma. |
| Turing Machines | Undecidability. |
Compiler Design | Compiler Phases | Lexical analysis, parsing, syntax-directed translation. |
| Runtime Environments | Intermediate code generation. |
| Optimizations | Local optimization, data flow analyses: constant propagation, liveness analysis, common sub-expression elimination. |
Operating System | Processes | System calls, processes, threads, inter-process communication. |
| Concurrency and Synchronization | Deadlock, CPU and I/O scheduling. |
| Memory Management | Virtual memory, file systems. |
Databases | ER Model | Entity-relationship model. |
| Relational Model | Relational algebra, tuple calculus, SQL. |
| Normalization | Integrity constraints, normal forms. |
| File Organization and Indexing | B and B+ trees. |
| Transactions | Concurrency control. |
Computer Networks | Layering Concepts | OSI and TCP/IP Protocol Stacks. |
| Data Link Layer | Framing, error detection, Medium Access Control, Ethernet bridging. |
| Routing Protocols | Shortest path, flooding, distance vector, link-state routing. |
| IP Layer | Fragmentation, IP addressing (IPv4, CIDR), support protocols (ARP, DHCP, ICMP), NAT. |
| Transport Layer | Flow control, congestion control, UDP, TCP, sockets. |
| Application Layer Protocols | DNS, SMTP, HTTP, FTP, Email. |
