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ENGINEERING MATHEMATICS (4 topics) Subject

Discrete Mathematics (5 subtopics) Topic

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 (3 subtopics) Topic

Matrices, determinants, system of linear equations

Eigenvalues and eigenvectors

LU decomposition

Calculus (5 subtopics) Topic

Limits, continuity, and differentiability

Maxima and minima

Mean value theorem

Integration

Definite and improper integrals

Probability and Statistics (4 subtopics) Topic

Random variables

Uniform, normal, exponential, poisson, and binomial distributions

Mean, median, mode, and standard deviation

Conditional probability and Bayes theorem

COMPUTER SCIENCE AND INFORMATION TECHNOLOGY (9 topics) Subject

Digital Logic (4 subtopics) Topic

Boolean algebra

Combinational and sequential circuits

Minimization of Boolean functions

Number representations and computer arithmetic (fixed and floating-point)

Computer Organization and Architecture (5 subtopics) Topic

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)

Programming and Data Structures (3 subtopics) Topic

Programming in C

Recursion

Arrays, stacks, queues, linked lists, trees, binary search trees, binary heaps, graphs

Algorithms (4 subtopics) Topic

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

Theory of Computation (4 subtopics) Topic

Regular expressions and finite automata

Context-free grammars and push-down automata

Regular and context-free languages, pumping lemma

Turing machines and undecidability

Compiler Design (4 subtopics) Topic

Lexical analysis, parsing, syntax-directed translation

Runtime environments

Intermediate code generation

Local optimisation, Data flow analyses: constant propagation, liveness analysis, common subexpression elimination

Operating System (5 subtopics) Topic

System calls, processes, threads, inter-process communication, concurrency, and synchronization

Deadlock

CPU scheduling

Memory management and virtual memory

File systems

Databases (5 subtopics) Topic

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 (8 subtopics) Topic

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 notation

Basics of IP support protocols (ARP, DHCP, ICMP), Network Address Translation (NAT)

Transport layer: flow control and congestion control, UDP, TCP, sockets

Application layer protocols: DNS, SMTP, HTTP, FTP, Email

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