Section I – Engineering Mathematics
| Topics | Sub-Topics |
|---|---|
| Discrete Mathematics | Propositional and first-order logic | sets, relations, functions, partial orders and lattices | Monoids | Groups | Graphs: connectivity, matching, and colouring | 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 and Statistics | Random variables | Uniform, Normal, Exponential, Poisson and Binomial Distributions | Mean, median, mode and standard deviation | Conditional Probability and Baye’s Theorem |
Section II – Subject-Specific
| Section | Topics |
|---|---|
| Digital logic | Boolean Algebra | Combinational and Sequential Circuits | Minimization | Number Representations and Computer Arithmetic (fixed and floating point) |
| Computer Organization and Architecture | Machine Instructions and Addressing Modes | ALU | Data-Path and Control-Unit | Instruction Pipelining | Pipeline Hazards | Memory Hierarchy: Cache, Main Memory, and Secondary Storage | I/O interface (interrupt and DMA mode) |
| Programming and Data Structures | Programming in C | Recursion | Arrays | Stacks | Queues | Linked Lists | Trees | Binary Search Trees | Binary Heaps | Graphs |
| Algorithms | Searching | Sorting | Hashing | Asymptotic Worst Case Time and Space Complexity | Algorithm Design Techniques | Greedy, Dynamic Programming, and Divide-Conquer | Graph Traversals | Minimum Spanning Trees | Shortest Paths |
| Theory of Computation | Regular Expressions and Finite Automata | Context-Free Grammars and Push-Down Automata | Regular and Context-Free Languages | Pumping Lemma | Turning Machines and Undecidability |
| Compiler Design | Lexical Analysis, Parsing, Syntax-Directed Translation | Runtime Environments | Intermediate Code Generation | Local Optimisation | Data Flow Analyses: Constant Propagation, Liveness Analysis, Common Sub Expression Elimination |
| Operating System | System Calls, Processes, Threads, Inter-Process Communication, Concurrency and Synchronisation Deadlock | CPU and I/O Scheduling | Memory Management and Virtual Memory | File Systems |
| 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 |
| Computer Networks | 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 | Ethernet Bridging | Routing Protocols: Shortest Path, Flooding, Distance Vector, and Link State Routing | Fragmentation and IP Addressing | IPv4 | CIDR Rotation | Basics of IP Support Protocols (ARP, DHCP, and ICMP) | Network Address Translation (NAT) | Transport Layer: Flow Control and Congestion Control | UDP, TCP, Sockets | Application Layer Protocols: DNS, SMTP, HTTP, FTP, and Email |