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Limits, continuity and differentiability. Maxima and minima. Mean value theorem. Integration.

 Conditional Probability; Mean, Median, Mode and Standard Deviation; Random Variables; Distributions; uniform, normal, exponential, Poisson, Binomial. 

Sets; Relations; Functions; Groups; Partial Orders; Lattice; Boolean Algebra

 Permutations; Combinations; counting, recurrence relations, generating functions

This section contains tips useful for GATE preparation. Please watch these videos before starting the course. 

Algebra of matrices, determinants, systems of linear equations, Eigen values and Eigen vectors

Graphs: Connectivity , Matching , Colouring.

Links to Useful notes

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. Network security basic concepts of public key and private key cryptography, digital signature, firewalls.

Lexical analysis, Parsing, Syntax directed translation, Runtime environments, Intermediate and target code generation, Basics of code optimisation.

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. Asymptotic analysis (best, worst, average cases) of time and space, upper and lower bounds, Basic concepts of complexity classes P, NP, NP-hard, NP-complete.

Regular languages and finite automata, Context free languages and Push-down automata, Recursively enumerable sets and Turing machines, Undecidability.

Logic functions, Minimization, Design and synthesis of combinational and sequential circuits; Number representation and computer arithmetic (fixed and floating point).

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.

Processes, Threads, Inter-process communication, Concurrency, Synchronization, CPU Scheduling, Deadlock, Memory management and virtual memory, File systems, I/O systems, Protection and security.

 ER-model, Relational model (relational algebra, tuple calculus), Database design (integrity constraints, normal forms), Query languages (SQL), File structures (sequential files,  B and B+ trees), Transactions and concurrency control

 Programming in C; Functions, Recursion,  Abstract data types, Arrays, Stacks, Queues, Linked Lists, Trees, Binary search trees, Binary heaps.

Problems on IP addressing,Sliding window protocol,LAN technologies