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BASIC MATHEMATICS
Mathematical Logic:
Propositional Logic, First-order Logic -- Probability: Random variables and expectation, Conditional probability, Independent random variables, Distributions (Uniform, Normal, Exponential, Poisson, Binomial) --
Discrete Mathematics:
Sets, Relations, Functions, Groups, Lattice, Boolean algebra, Induction, Recurrence relations -- Combinatorics: Permutations, Combinations, Counting, Summation --
Elementary graph theory:
Basic properties, Connectivity, Covering and matching, Planarity -- Elementary concepts of Linear and Matrix Algebra -- Numerical methods: Classical algorithms for interpolation and root finding.
THEORY OF COMPUTATION
Formal Languages and Automata Theory:
Regular languages and finite automata, Context free languages and Push-down automata, Recursively enumerable sets and Turing machines, Un-decidability --
Analysis of Algorithms and Computational Complexity:
Asymptotic analysis (best, worst, average case) of time and space, Upper and lower bounds on the complexity of specific problems, NP-completeness.
COMPUTER HARDWARE
Digital Logic:
Logic functions, Minimization, Design and synthesis of Combinational and Sequential circuits -- Number representation and Computer Arithmetic (fixed and floating point) --
Computer Organization:
Machine instructions and addressing modes, ALU and Data-path, hardwired and micro-programmed control, Memory interface, I/O interface (Interrupt and DMA mode), Serial communication interface, Instruction pipelining, Cache, main and secondary storage.
SOFTWARE SYSTEMS
Data structures:
Notion of abstract data types, Stack, Queue, List, Set, String, Tree, Binary search tree, Heap, Graph -- Programming Methodology: C programming, Program control (iteration, recursion, Functions), Scope, Binding, Parameter passing, Elementary concepts of Object oriented, Functional and Logic Programming --
Algorithms for problem solving:
Tree and graph traversals, Connected components, Spanning trees, Shortest paths -- Hashing, Sorting, Searching -- Design techniques (Greedy, Dynamic Programming, Divide-and-conquer) --
Compiler Design:
Lexical analysis, Parsing, Syntax directed translation, Runtime environment, Code generation, Linking (static and dynamic) --
Operating Systems:
Classical concepts (concurrency, synchronization, deadlock), Processes, threads and Inter-process communication, CPU scheduling, Memory management, File systems, I/O systems, Protection and security.
Databases:
Relational model (ER-model, relational algebra, tuple calculus), Database design (integrity constraints, normal forms), Query languages (SQL), File structures (sequential files, indexing, B+ trees), Transactions and concurrency control --
Computer Networks:
ISO/OSI stack, sliding window protocol, LAN Technologies (Ethernet, Token ring), TCP/UDP, IP, Basic concepts of switches, gateways, and routers.
