Introduction to sets: Review only.

Logic : Propositions and logical operations, Truth tables, Equivalence and implication, Laws of logic, Mathematical induction and quantifiers.

Set theory : Method of proof for set, Venn diagram, set membership tables, definitions, Laws of set theory, Partition of sets.

Permutations, combinations and discrete probability : Introduction to permutations and combinations, Generation of permutation and combination, Discrete probability, Conditional probability.

Relations and Diagraphs : Relations and diagraphs., Paths and the relations and diagraphs, Properties of relations, Equivalence relations, Computer representation of relations and diagraphs, Manipulation of relations, Transitive closure, Warshall’s algorithm.

Function and pigeon hole principle : Definition, Types of functions: injective, surjective, bijective, Composition, identity and inverse, Pigeon hole principle. Graphs , Posets, Hasse Diagram, Lattices Finite Boolean Algebra, Groups & their Applications Introduction to Rings & Fields.

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· Introduction to object oriented programming, it’s need and requirements, general object oriented philosophy, software usability, code sharing, rapid prototyping, information hiding.

· Classes, attributes and methods, encapsulation, constructor, destuctors, iterator classes, class interface.

· Function overloading, inline, functi ons, operators & operator overloading, iterators.

· Inheritance base class, derived classes, friend class, static class, type checking, class scopes.

· Multiple inheritance & polymorphism, abstract classes, virtual function, virtual base class, static & dynamic binding, overloading, overriding type conversions.

· Object oriented design, class identification, defining inheritance, visibility & dependency coupling & cohesion.

· Case study of classes like ADT class, I/O class, string class, editor class.

· Language study: C++, object Pascal

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Probability and topics in Statistics: Statistical experiments with random outcomes, Sample space, probability defined on the basis of sample space and on the basis of events and their combinations. Theorem on probabilities, conditional probability. Bayes theorem. Random variable, probability distribution for discrete and continuous random variables. Density function and distribution functions. Expected values, variance , moments, moment generating functions, Bernoulli’s trials, Binomial , Poisson, normal distributions for detailed study with proof, Other common distributions, T , F, Beta, Gamma, X with indication of the applications(without proof) Central limit theorem, Bivariate probability and frequency distributions, Correlations, regression, lines of regression. Introduction to random samples, use of random numbers, stochastic processes, Time series , queuing theory.

Optimisation Techniques

· Problem formulation

· Simplex Method

· Revised Simplex Method

· Duality & Sensivity

· Unconstrained optimisation of several variables

· Numerical methods for unconstrained optimisation : Random search & Univariate method, Fletcher Reverse method, Newtons method

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· General organization of a digital computer, functional blocks, data representation, fixed and floating point decimal arithmetic, bit slice microprocessor (introduction), full adders, ripple carry adders, look ahead carry generators, multiplicationand division circuits, an arithmetic unit.

· Instruction cycle, instruction sequencing, formats and its interpretation, microprogram concepts and control unit design.

· Semiconductor memory and memory organization, virtual memory, segments, pages, paged segments, cache memory and interleaved memory.

· Concepts of I/O organization, data transfer methods, programmed I/O, DMA, interrupt-based transfer, I/O channels, I/O processors, serial transmission and synchronization.

· Introduction to assembly level programming – concepts of assemblers, macros, linkers, and loaders, linking loaders.

· Multiprogramming and time-sharing, introduction to advanced computer architecture (pipelining, array processors & multiprocessors).

· Introduction to operating systems. Case study (comparative) of DOS & UNIX.

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Introduction to Business Organization : Need , Structure and nature of Information Systems – data processing activities-Management Information Systems .Introduction to structured programming . Typical analysis of systems like –Inventory, Accounting, Payroll, Production, etc.

Introduction to Input / Output and Data Storage devices : their organisation and access methods .File concept,record layout. Organisation and access strategies of files.

Cobol programming : character set, words,data names, verbs, structure of a cobol program. Elementary and group data items,structuring of data ,picture clauses.

Arithmetic operations : Add, Subtract, Multiply, Divide and Compute statements, arithmetic expressions and operator precedence.

Data transfer statements: Move; editing and edit pictures .

Condition statements : relational and logical operators,simple and compound conditions .Control structure- IF,nested

IF,GOTO,GOTO depending on, PERFORM statements.

Array processing and table handling: OCCURS clause , single and multi-dimensional tables-their definition and usage .

PERFORM verb and tables- PERFORM . .TIMES, PERFORM . . UNTIL, PERFORM. . VARYING options.Index tables and index names , SET verb. Searching of tables –SEARCH verb.

Sequential file processing: fixed and variable record file, sorting and merging ,sequential file update operations , magnetic tape files.

Direct access files : index sequential while handling , update of indexed files ,relative files, relative file handling, key address transformations.

Introduction to report writer : report section , report group , description and procedure division statements.

Introduction to sub-routines , sub-programs, segmentation and overlay management. Introduction to system analysis and database management systems.

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· Features of C, ANSI C, structure of a C program.

· Character set, variable names, data types, constants and declarations, scope and lifetime of variables.

· Arithmetic, logical, relational, increment, bitwise, assignment operators and expressions, conditional expressions, precedence of order of evaluation and type conversion.

· Basic input and output, formatted input and output.

Control structures : Concept of a block statement. IF, IF-Else, Switch, Looping structures – FOR, DO, WHILE, Break and Continue statements, GOTO statement.

Functions : external variables, scope rules, nesting of functions, function of arrays.

Arrays : One dimensional, two dimensional and multi dimensional arrays, their initialisation and manipulation, String handling features.

Pointers : addresses, their initialisation, pointer arithmetic, pointers and functions, pointers and arrays, pointers to pointers, pointers to functions.

Structures and Unions. : Basics of structures, initialisation, structures and functions, structures and arrays, pointers to structures, structures within structures, unions and bit fields.

Dynamic Memory Management : malloc ( ) , calloc ( ) , free ( ), sizeof( ) functions.

File Management : Low level and high level file access. Sequential and random access files, error handling.

Pre processor : macro substitution, header file inclusion, study of standard libraries like stdio.h, ctype.h, string.h, math.h, stdlib.h, stdarg.h, dos.h

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Number systems and codes: Binary, Octal and Hexadecimal number systems. Conversion from any base to another base number system. Binary, BCD, Excess-3, Alphanumeric, EBCDIC, Hollerith, ASCII codes, code conversion, error detecting and correcting codes, parity and Hamming codes.

Binary Arithmetic: Basic rules for addition and multiplication. Sign magnitude notation, One’s complement notation. Two’s complement notation. Addition and multiplication using binary, octal and hexadecimal number systems.

Boolean Algebra and Logic Gates: Boolean algebra theorems, reduction of logic expressions using boolean algebra, truth tables, minterms, maxterms, SOP and POS forms. Standard SOP and POS forms. Basic and universal logic gates, control aspect of gates, enabling and disabling of gates. K map representation of logical functions, simplification of logic functions using K-maps upto 6 variables. Quine McCluskey method and Veitch diagrams used for logic function reduction.

Combinational Logic Circuits: Concepts of combinational and sequential logic circuits. Realisation of following circuits using gates.:

(a) Systems implementing combinational logic.

(b) Arithmetic circuits, half and full adders, subtractors, multipliers, code converters, parity generators, parity checkers, comparators.

(c) Multiplexers, demultiplexers, encoder, decoder.

(d) Concept of mode control

(e) Application of MSI devices for multiplexer, demultiplexer/decoder, parity generator/checker, concept of capacity expansion using gates. Use of MSI devices for adders, Sequential adder, BCD adder / subtractor, carry look ahead adder, multiplier, fast multipliers, Arithmetic Logic Unit

Sequential Circuits: Concept of Synchronous and Asynchronous operation.

(a) Flip Flops : Basic cell, SR , clocked SR, D, T , J-K, J-K with preset and clear, Master Slave J-K flip flops. Concept of level triggering and edge triggering , flip flop excitation tables, triggering and timing of flip flops.

(b) Registers: Shift registers, bi-directional, serial to parallel, parallel to serial conversion.

(c) Analysis of clocked sequential circuits.

(d) Asynchronous counters: up-down counters, modulo N counter, glitch problem.

(e) Synchronous counters: Use of K- maps for synchronous counters, ring counters, twisted ring counters, counters using shift registers, sequence generators using flip flops.

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Signals and their representations: Fourier series, Fourier transform, continuous spectra, frequency selective networks and transformers.

Basic Information Theory: Information , entropy of discrete systems, rate of transmission, redundancy, efficiency and channel capacity.

Amplitude Modulation: Frequency spectrum, power relations, basic requirements and description of various modulators, comparison. DSB, DSBSC, SSB, VSB, spectrum modulators and detectors.

Frequency Modulation: Frequency spectrum of FM, phase modulation, effect of noise, generation of FM and demodulators.

Pulse Modulation: Sampling theorem, low pass and band pass signals, elements of PAM, PWM, PPM, PCM and Delta Modulation. FDM,TDM.A.M. and FM radio transmitters and receivers. Characteristics, block diagrams.

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Low and High frequency analysis of BJT and FET amplifier circuits.

Analysis of: RC coupled amplifiers Cascode Amplifiers, Darlington pair and DC amplifiers. Design of two stage RC coupled amplifier.

Feedback Amplifiers: Introduction to negative and positive feedback, current, voltage, series and shunt feedback. Its effect on input impedance, output impedance, voltage gain, current gain and bandwidth.

Oscillators: Positive feedback, oscillators using feedback principle. Derivation for frequency of oscillation and conditions for maintenance of oscillations of ( i ) RC phase shift ( ii ) Wien Bridge ( iii ) Tuned collector / drain ( iv ) Tuned gate ( v ) Hartley / Colpitts ( vi ) Crystal Oscillators.

Analysis of Differential Amplifier: Discrete components, operational amplifiers ( ideal ), Basic Op-Amp circuits. Relaxation Oscillator and Linear Sweep Circuits. Analysis of large signal amplifiers: Class A, B, AB and C. Design of audio frequency power amplifiers of class A and class B type.

Special Devices: Photo sensitive devices, display devices and Schottky diode.

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Complex Variables: Regions and paths in the Z plane. Path/Line integral of a function. Inequality conditions for a path integral to be independent of the path joining two points. Contour Integral, Cauchy’s theorem for analytical functions with continuous derivatives. Cauchy Goursat theorem( statement only ) and its use for multiply connected regions. Cauchy’s integral formula and deductions. Morera’s theorem and maximum modulus theorem. Taylor’s and Laurent’s developments, Singularities, poles, residue at isolated singularity and its evaluation. Residue theorem – Application to evaluate real integrals.

Matrices: Brief revision of vectors over real field, inner product, normal, linear independence, orthogonality. Characteristic values and vectors, and their properties for Hermitian and real Symmetric matrices. Characteristic polynomial. Cayley Hamilton theorem, functions of a square matrix, minimal polynomial, diagonable matrix. Quadratic forms, orthogonal, congruent and Lagrange’s reduction of quadratic forms, rank, index, signature of a quadratic form, value class of a quadratic form. Statement of bilinear form.

Vector Calculus: Scalar and Vector point functions, directional derivative, level surfaces, gradient, surface and volume integrals, definition of curl, divergence. Use of operator. Conservative, irrotational, solenoidal fields. Green’s theorem for plane regions and properties of line integral in a plane, Statements of Stoke’s theorem, Gauss Divergence theorem, related identities, deductions, statement of Laplace’s differential equation in cartesian, spherical, polar and cylindrical co-ordinates.

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