ENGINEERING MATHEMATICS
Mathematical Logic: Propositional Logic; First Order Logic.
Probability: Conditional Probability; Mean, Median, Mode and
Standard Deviation; Random Variables; Distributions; uniform, normal,
exponential, Poisson, Binomial.
Set Theory & Algebra: Sets; Relations; Functions; Groups;
Partial Orders; Lattice; Boolean Algebra.
Combinatorics: Permutations; Combinations; Counting; Summation;
generating functions; recurrence relations; asymptotics.
Graph Theory: Connectivity; spanning trees; Cut vertices &
edges; covering; matching; independent sets; Colouring; Planarity; Isomorphism.
Linear Algebra: Algebra of matrices, determinants, systems of
linear equations, Eigen values and Eigen vectors.
Numerical Methods: LU decomposition for systems of linear
equations; numerical solutions of non-linear algebraic equations by Secant,
Bisection and Newton-Raphson Methods; Numerical integration by trapezoidal and
Simpson’s rules.
Calculus: Limit, Continuity & differentiability, Mean value
Theorems, Theorems of integral calculus, evaluation of definite & improper
integrals, Partial derivatives, Total derivatives, maxima & minima.
COMPUTER SCIENCE AND ENGINEERING
Theory of Computation: Regular languages and finite automata,
Context free languages and Push-down automata, Recursively enumerable sets and
Turing machines, Undecidability; NPcompleteness.
Digital Logic: Logic functions, Minimization, Design and
synthesis of combinational and sequential circuits; Number representation and
computer arithmetic (fixed and floating point).
Computer Organization and Architecture: Machine instructions
and addressing modes, ALU and data-path, CPU control design, Memory interface,
I/O interface (Interrupt and DMA mode), Instruction pipelining, Cache and main
memory, Secondary storage.
Programming and Data Structures: Programming in C; Functions,
Recursion, Parameter passing, Scope, Binding; Abstract data types, Arrays,
Stacks, Queues, Linked Lists, Trees, Binary search trees, Binary heaps.
Algorithms: Analysis, Asymptotic notation, Notions of space and
time complexity, Worst and average case analysis; Design: Greedy approach,
Dynamic programming, Divide-and-conquer; Tree and graph traversals, Connected
components, Spanning trees, Shortest paths; Hashing, Sorting, Searching.
Compiler Design: Lexical analysis, Parsing, Syntax directed
translation, Runtime environments, Intermediate and target code generation,
Basics of code optimization.
Operating System: Processes, Threads, Inter-process
communication, Concurrency, Synchronization, Deadlock, CPU scheduling, Memory
management and virtual memory, File systems, I/O systems, Protection and
security.
Databases: ER-model, Relational model (relational algebra,
tuple calculus), Database design (integrity constraints, normal forms), Query
languages (SQL), File structures (sequential files, indexing, B and B+ trees),
Transactions and concurrency control.
Computer Networks: ISO/OSI stack, LAN technologies (Ethernet,
Token ring), Flow and error control techniques, Routing algorithms, Congestion
control, TCP/UDP and sockets, IP(v4), Application layer protocols (icmp, dns,
smtp, pop, ftp, http); Basic concepts of hubs, switches, gateways, and routers.