FIRST YEAR COURSES

COMPUTER FUNDAMENTALS AND PROGRAMMING

UNIT-1: (i)  Introduction  to Computer System : Simple  model  of Computer,  CPU,  Memory, Basic concepts  of  Boolean algebra   and   their   electronic   implementation, Computer size, Storage media and I/O units, Software and Hardware. Booting process and DOS commands.
(ii) Number System : Data representation - binary, octal, hexadecimal, positive and negative numbers, integers and  real,  characters  and codes  -  BCD,ASCII  and EBCDIC coding.

UNIT-2:  Algorithms   and   Flowcharts   :   Problem    analysis, algorithms,   data  assignments,  flowcharts,   stepwise refining  sequencing alternation and Looping,  Searching (Linear, binary), Sorting (Exchange, bubble,  selection) and  merging, programming languages and problem  solving computers.

UNIT-3: Computer   Programming  (C++)  :  Representation   of integers,  real,  characters,  data  types,   constants, variable,     arithmatic    expression,     assignments, conditional  statement, control statements  (Sequencing, alteration and iteration), simple I/O.

UNIT-4: Arrays one and two dimensional, subprograms -  functions and procedures, parameter passing, concept of structured programming (control flow, top-down programming).

UNIT-5: Structured data types : Records- variant records,  sets, files  - sequential and random access,  Introduction  to  data structures (stacks, queues and trees)

COMPUTER ARCHITECTURE

UNIT-1: Number System : Introduction to Decimal, Binary, Octal, Hexadecimal and interconversion of all number systems. Complements : 1’s, 2’s, 9’s and 10’s, BCD, ASCII, EBSCIC Codes.
Boolean Arithmetic and Theorems, Binary Integer and Floating point arithmetic’s.
Logic Gates : AND, OR, NOT, NAND, NOR, XOR, XNOR.

UNIT-2: Digital Combinational Circuits : adder, subtractor, encoder, decoder, code converter,      multiplexer, demultiplexer.
Sequential Circuits : Flip-Flop (RS, JK, D, T and Master Slave), Shift Register,
Counters : Ring, Jhonson Counter’s, synchronous and Asynchronous Counter’s.

UNIT-3: IC Digital Logic Families : Bipolar Transister as current control switch, MOSFET as voltage  controlled  switch, RTL, DTL,  TTL, ECL, MOSFET and CMOS
Computer Organisation : Components of a Computer System, Memory, control, processing and I/O units, registers, CPU, ALU design.

UNIT-4: Instruction formats, instruction execution cycles,  machine instruction  types, concept of microprogramming, address techniques  : direct, indirect, absolute and relative addressing, zero-address, one-address and two-address computers.

UNIT-5: Memory  Technology : Memory device  Chracteristics, random access, sequential access, ROM, PROM, EPROM, Megnetic bubble memory.
I/O devices : Properties of simple I/O Devices, I/O controllers,   interfacing  I/O  devices   (Program Controlled and interrupt controlled) DMA,  interface, I/O channels.

NUMBER THEORY AND CO-ORDINATE GEOMETRY

UNIT-1: Divisibility in integers, prime and composite numbers, division algorithm, greatest common divisor, least common multiple, Euclidean Algorithm. Relatively prime integers, Gauss Theorem, Euclid Theorem. Fundamental theorem of arithmetic.

UNIT-2: Congruences- congruence relation in integers, theorems on congruences, residual classes, sum of residue classes, linear congruence, Fermat Theorem, Wilson Theorem.

UNIT-3: Complex numbers- Argand diagrams, geometrical representation of four fundamental operations, Demoivere’s theorem and its applications, separation of complex quantities ( circular, hyperbolic, logarithmic exponential, inverse circular)

UNIT-4: Parabola, Ellipse.

UNIT-5: Hyperbola, polar equation of a conic.

CALCULUS AND DIFFERENTIAL EQUATION

UNIT-1: Successive differentiation, leibnitz theorem. Polar tangent, normal, subtangent and subnormal. Derivative of an arc (Cartesian and polar), Pedal equations,
 
UNIT-2: Expansion of functions by Maclaurin’s and Taylors series. Intermediate forms.

UNIT-3: Integration and rational algebraic and trigonometrical functions. Definite integrals, properties of definite integrals

UNIT-4: Solution of differential equations of first order and first degree. Differential equations of first order and any degree. Singular solutions

UNIT-5: Linear differential equations with constant coefficients. Linear homogenous equations of any order.

MECHANICS-I

UNIT-1: Forces, velocity and acceleration (composition and resolution). Parallel forces, equilibrium of forces acting at a point (Lami’s theorem, theorem of triangle law of forces and its converse).
 
UNIT-2: Moments, simple problems on equilibrium of a body under the action of three forces.

UNIT-3: Rectilinear motion under uniform acceleration. Vertical motion and motion on inclined plane under gravity.

UNIT-4: Newton’s laws of motion. Motion of two particles connected by a string.

UNIT-5: Projectiles (horizontal plane). Direct impact of elastic bodies.

STATISTICAL METHODS

UNIT-1: Definition, scope and limitation of statistics, concept of statistical population, attributes and variables, types of data, collection of primary and secondary data, sample and census survey, their advantages and disadvantages, sampling errors.

UNIT-2: Classification and tabulation of data, construction of frequency table, frequency distribution, graphic and diagrammatic representation of data, measures of central tendency.

UNIT-3: Measures of dispersion, moments, measures of skewness and kurtosis, sheppared’s correction (without proof) for moments Charlier’s check.

UNIT-4: Theory of attributes: classes and class frequencies, consistency of data, independence of attributes, contingency table, association of attributes, measures of association, Yates correction, curve fitting by the principle of least squares, fitting of straight line, parabola, power curves and exponential curves.

UNIT-5: Bivariate distribution, correlation and regression, pearson’s correlation coefficient, lines of regression and regression coefficient, rank correlation and spearman’s rank correlation coefficient, partial and multiple correlation for three variables only.

PROBABILITY AND PROBABILITY DISTRIBUTIONS

UNIT-1: Random experiments, sample space, events, combination of two or more events, basic concept of probability, classical, empirical and axiomatic approach to probability, marginal joint and conditional probability, statistical independence of events, addition and multiplication theorems of probability, Baye’s theorem and its application.

UNIT-2: Random variable, discrete, continuous, univariate and bivariate, probability mass function and probability density function, distribution function, conditional and marginal distributions, independence of random variables

UNIT-3: Mathematical expectation: expectation of sum and product of random variables, variance and co-variance, conditional expectation, raw and central moments, moment generating functions, characteristic function (definition and statement of properties only), Cumulant generating function, relationships among raw moments, central moments and Cumulants.

UNIT-4: Theoretical univariate discrete distribution: uniform, binomial, Poisson, negative binomial, multinomial and hyper-geometric distribution with simple properties and applications, limiting cases of binomial and Poisson distributions, fitting of binomial and Poisson distribution.

UNIT-5: Theoretical univariate continuous distribution: rectangular, normal, exponential, gamma, beta, laplace and Cauchy distributions with simple properties and applications, fitting of normal distribution.

COMMUNICATION SKILLS

UNIT 1: Use of dictionary to find out the contextual meaning of words of having more than one meaning, Developing Vocabulary. Short and Essay types questions on Comprehension.

UNIT 2: Formation, synthesis and transformation of  Sentences, Translation. Reading stories, Plays and Tales of Adventures. Formal and Informal letter writing, Précis Writing. Expansion of given Idea.

UNIT 3: Listening: Listening to and understanding short speeches, passages  read about or dictated, Listening to and understanding conversation based  in familiar situations. Taking notes,  Reading : Reading newspapers and articles, short stories and two books to be selected by the  students in consultation  with the  teacher.

UNIT 4: Speaking:  Greeting and formulae of everyday conversation. Polite requests, questions, shorts questions, shorts answers. Short informal takes, Participations in Group discussions.  

UNIT 5: Writing: Writing paragraph on given topics, Writing stories, Reporting events, Expanding an Idea, Summarizing text, Formal and Informal letters. 

SECOND YEAR COURSES

DATA STRUCTURES AND PROGRAMMING METHODOLOGY

UNIT-1: (a) Concept  of  good  programming,   from  problems  to programs,  data types, data structures and  abstract data  types,  the  running time  of  a  program,  an efficient program.
(b) Basic data types, records, sets, files, pointers.

UNIT-2: C programming : basic constructs, functions, function as a  parameter, arrays and pointers,  address  arithmetic, pointer   to  functions,  structures  and  union,   file handling, command line arguments.

UNIT-3: Data   structures   :  stacks,   queues,   their   array implementations,   applications  of  stacks  &   queues, recursion stacks and recursive procedures.

UNIT-4: Linear Linked structures, the data types "list",  linked lists, doubly   &  circular   linked   lists,   linked representation    of   stacks   and    queues,    simple applications.

UNIT-5: Nonlinear structures : trees, basic terminology,  binary trees,  their  implementation, tree  traversal,  search, insertion  and  deletion, simple application  of  binary trees, Introduction to graphs and their representation.
Note  : Data structures to be implemented using C.                

COMPUTER ORIENTED NUMERICAL AND STATISTICAL METHODS

 SYSTEMS PROGRAMMING

UNIT-1: Components of system software, Evolution of system software, General machine structure (memory, register, data, instructions) machine language, problems in machine language programming using octal or hexadecimal, assembly language, its advantages and disadvantages, high level languages.

UNIT-2: General design of an assembler (one pass and two pass assembler), brief description of different phases of a compiler.
Software tools for program entry and testing, line and screen editors, debug monitors.

UNIT-3: Loaders : Compile & go, absolute, relocating, direct linking & subroutine linkage loader schemes, binders, linking loaders.
Structured Programming, Applications of structured programming techniques to construction of system software tools.

UNIT-4: Operating System : Types and basic functions of an operating system. Single user and multiuser operating system.
UNIX: Introduction, history, kernel and shell, file system, user management in UNIX, UNIX commands, security, background processing, editors on UNIX.

UNIT-5: Access to system services : ROM BIOS, DOS, Mouse and EMS function, keyboard and screen management, Introduction to terminal emulator, DOS device drivers, Types, structures and processing.

MICROPROCESSORS AND MICROCOMPUTER SYSTEMS

UNIT-1: Evolution of microprocessors, 8085 microprocessor architecture, concept of address, data & control bus, Internal operation, addressing modes, instruction formats & execution timings.

UNIT-2: 8085 Microprocessor instructions & programming : Data transfer, arithmetic, logical, shift, rotate, compare, jump.  Programming techniques, stack, subroutine, conditional call and return instructions.

UNIT-3: Interfacing output displays, interfacing input keyboards, memory interfacing, memory mapped I/O. Interfacing A/D and D/A converters.

UNIT 4: DMA data transfer, 8257 DMA controller chip, 8255 Programmable peripheral interface, interrupts - types & masking, 8259 programmable interrupt controller chip. Serial & Parallel communication : Synchronous, asynchronous, serial interface - RS-232 C.

UNIT-5: Internal organisation of 8086, Generating memory addresses, addressing modes, maximum & minimum modes, Brief introduction to 80286.

ALGEBRA

UNIT-1: Groups: definition and simple properties of groups and subgroups. Permutation groups, cyclic groups.
 
UNIT-2: Cosets, Lagrange’s theorem on the order of subgroup of a finite group. Morphisms of groups, Cayley’s theorem, normal subgroups and quotient groups, fundamental theorem of homomorphism of groups.

UNIT-3: Rings, definition and examples of ring, residue class ring, special classes of ring, integral domains, division rings (rings, fields). Simple properties of rings. Subrings and subfields. Ring Homomorphism and ring isomorphism. Field of quotients of integral domain.

UNIT-4: Ideals: ideals, principle ideals, principle ideal ring, quotient ring, prime ideal, maximum ideal, Euclidian ring and its properties. Unique factorization theorem, polynomial rings.

UNIT-5: Vector spaces: Definition and simple properties, subspaces, linear span, linear sum of two subspaces, linear dependence and linear dependence of two vectors, basis of a vector space, dimension of finitely generated vector space, dimension of a subspace, homomorphism of vector spaces, isomorphism of vector spaces. Quotient spaces, direct sum of spaces, dimension of direct sum.

CALCULUS

Differential Calculus
UNIT-1: Maxima and minima of one and two variables including method of undetermined multipliers. Curvature, partial derivatives including Euler’s theorem and its applications.
 
UNIT-2: Envelopes and evolutes, asymptotes, multiple points, curve tracing (Cartesian and polar co-ordinates

Integral Calculus

UNIT-3: Reduction formulae, integration as a limit of a sum.

UNIT-4: Quadrature rectification, volumes and surfaces of solids of revolution.

UNIT-5: Beta and Gamma functions, double and triple integrals, change of order of integration in double integrals

ANALYTICAL SOLID GEOMETRY AND VECTOR ANALYSIS

Analytical Solid Geometry
UNIT-1: Plane straight line.
 
UNIT-2: Equations of two skew lines in simplest forms, line intersecting of two lines, locus of a line, intersecting three given lines. Intersection of three planes, volume of a tetrahedron, sphere.

UNIT-3: Cone, Cylinder, Ellipsoid- standard equation, tangent plane, polar plane, enveloping cone, enveloping cylinder.

Vector Analysis

UNIT-4: Multiple product of vectors, application of vectors to geometry (centroid, straight line, plane, tetrahedron).

UNIT-5: Differentiation and integration of vector point functions, gradient, divergence and curve, application of Gauss, Stocks and Green’s theorems.

ENVIRONMENTAL STUDIES

UNIT 1: Environment: meaning, constituents, processes, elements, physical environment (land, water and air),
 
UNIT 2: Biological environment, formation of crust- internal and external processes, factors affecting environmental balance.

UNIT 3: Volcano: meaning and types, earthquake: meaning and factors affecting, greenhouse effect, cyclone and anticyclone, types of rain, distribution of rains in world.

UNIT 4:  Continents and oceans, soil erosion: concept, factors affecting, remedies,

UNIT 5: Population: distribution, factors affecting, global trends, pollution: means, types and hazards.

THIRD YEAR

DISCRETE MATHEMATICS

UNIT-1: Permutations,  Combinations,  selection with  &  without replacement;   Sets  and  multisets,   permutation   and combinations  of multisets, enumeration of  permutations and  combination   of  sets   &   multisets,   Discrete probability;  The rules of sum & product, generation  of permutation and combinations. Relations and functions-      properties  of binary relations, equivalence  relations, partial order relations, chains and antichains.

UNIT-2 & 3: Graph   theory  :-  Basic  concepts  of  graph   theory, & 3 multigraph   and weighted graphs, matrix  representation of  graphs, paths & circuits, shortest path in  weighted graph,  Adjacency  matrix, Eulerian path  and  circuits, Hamiltorian path and circuits, planar graphs.  Chromatic number,  edge colouring of  graphs,  Vizing's   theorem, K-connected and K-edge -connected graphs. Trees and  cut sets  -  Trees,  rooted trees, path  lengths  in  rooted trees, Spanning tree and cut set, minimum spanning tree. Flow in a graph, Max-flow min cut theorem.

UNIT-4: Pigeon    hole   Principle  :  Inclusion-Exclusion  principle.  Generating  functions and  Discrete  numeric functions - manipulation   of   numeric   functions. Asymptotic  behaviour  of numeric  function.  Recurrence relations,  Linear  recurrence  relation  with  constant coefficients and their solutions, Homogeneous  solution, particular  solution & total solutions. Solution by  the method of generating functions.

UNIT-5: Boolean   Algebra  ,  lattices  and  algebraic  systems, principle  of  duality.  basic  properties  of  algebric systems  defined  by  lattices  and  Boolean   Algebras. Uniqueness  of  finite  boolean  Lattices  and   Boolean functions   and   Boolean   expressions,   propositional Calculus.

OBJECT ORIENTED METHODOLOGY

UNIT-1: Introduction: Origin of object approach, procedural Vs object oriented languages, expectations of object  approach, object oriented programming, applications of loops, objects, links  between objects, classes and instances, graphs of classes, collections.

UNIT-2: Inheritance: Definition, single and multiple inheritance, polymorphism, type safety, accessing inherited methods/data members, reusability  of code through inheritance, overloaded  function, data encapsulation : definition, implementation of encapsulation.

UNIT-3: Implementation of object concept: abstract data type, object identity, generalization and inheritance, message passing, creation of objects, destruction of objects, how is an object  language  A  brief study of object oriented languages : ADA, SIMULA, OBJECT PASCAL, SMALL TALK, EIFFEL, JAVA, OBJECTIVE C, C++.

UNIT-4: Introduction to object oriented methods for design and development: motivation for new design  methods: evolution   for   business  applications, handling new technical applications, classical application development cycles, shortcomings of existing methods.
Different   classes of analysis and   design   methods: cartesian approach, systemic approach, object approach and its relation to two other approaches, models and techniques used by objects methods.

UNIT-5: Object oriented methodologies: OOD HOOD, OOA, OMT, OOSE, OOM Object databases: Introduction, aim of object databases, persistance of objects, object relational approach, architecture of object database system, basic techniques and tools.

DATA BASE MANAGEMENT SYSTEMS

UNIT-1: Data Base System architechture : Basic concepts, storage structure,  data strctures and corresponding  operators, aspects  of  file  organization  relating  to   physical allocation, performance issues.

UNIT-2 & 3: Classical data management : Modelling at user level, the & 3    process  of  data  base design, first  to  fifth  normal forms,  classical  data  models  including   relational, hierachical  and  networks;  example  models;  syste  R, codasyl  DBTG, IMS, detailed study of  relational  model including  querry  language and its  application,  forth generation languages.

UNIT-4: Approaches to data integrity and reliability, concurrent operations on data base, consistency, security,  privacy and authentication aspects in data bases.

UNIT-5: Distributed data base : Introduction, distributed system structure, reliable communications, data  fragmentation, homogeneous   VS   hetrogeneous   systems,   distributed concurrency control, management of deadlock and crashes, the optimistic approach.

REAL ANALYSIS

Analytical Solid Geometry
UNIT-1: Description of the real number system as a complete ordered field.  Bounded and unbounded sets of real numbers: supremum and infimum of a bounded set. Metric space, neighbourhood of a point. Limit point of abset, compactness, Heine-Borel theorem: Bolazano Weierstrass theorem: Lim supremum & Lim infimum.
 
UNIT-2: Real sequences and their convergence, Cauchy sequences; cauchy’s general principle of convergence; convergence of series; comparison test; ratio test; root test; Raabe’s test; Bertrand and D’ Morgan’s test for series of positive terms. Logarithmic test and integral test, alternating series, Leibnitz test.

UNIT-3: Real valued functions of a real variable-continous functions and their properties (theorems); characterization of continuity in terms of convergence sequence. Uniform continuity.

UNIT-4: Derviability, Rolle’s theorem; Lagranage’s mean value theorem, Taylor’s and Maclaurin’s theorem with Lagranges and Cauchy’s form of remainder, rigorous proof of power series, expansion of sinx, cosx, log(1+x) and (1+x)n.

UNIT-5: Riemanintegration of continous functions on closed and bounded intervals; properties of Reimann integrals; fundamental theorem of integral calculas for continous functions.

MATRICES AND LINEAR PROGRAMMING

Matrices
UNIT-1: Algebra of matrices, definition of various types of matrices. Symmetric and skew symmetric matrices. Matrices over the field of complex numbers, Hermitian and skew-Hermitian matrices. Determinants up to order four, elementary properties of determinants, product of determinants. Inverse of Matrix, inverse by polynomials, elementary matrices. Inverse of a matrix by E-Transformations. Partitioning of matrices.
 
UNIT-2: Rank of matrix, Equivalent matrices, invariance of rank through E-Transformations. Normal form of matrix. Linear equations, methods of solving simultaneous linear equations. Cramer’s rule. Inconsistency of linear equations, condition of consistency of linear equations. Homogenous equations.

UNIT-3: Vector spaces- Algebra of vectors, vector space over a field, linear dependence and independence of vectors, properties of linearly independent and independent set of vectors. Vector-space of vector space. Basic of subspace, matrix polynomials, characteristics of matrix polynomial, equation, root and vector. Cayley Hamilton Theorem, Relation between characteristic roots and characteristics vectors.

Linear Programming
UNIT-4: Introduction to linear programming problems; graphical method for the solution of a linear programming problem of two variables; convex set and their properties; the simplex method and its application to simple linear programming problems.

UNIT-5: Concept of duality in linear programming; forming of dual programmes, elementary theorems about duality.

MECHANICS-II

UNIT-1: Motion in plane-curve-velocity and acceleration ( radial, transverse, tangential and normal), relative velocity, simple harmonic motion, Hook’s law, motion of particle attached to elastic strings, motion under variable forces.
 
UNIT-2: Projectile and horizontal plane. Least velocity of projection, time of flight, projectiles on an inclined plane, work, power, energy, conservative forces, principle of conservation of energy, impulse, principle of conservation of linear momentum.

UNIT-3: Central orbits- Polar and pedal form of equations, Alpsa, Kepler’s law of planetary motion, motion in resisting medium: resistance varies as velocity and square of velocity.

UNIT-4: Constrained motion- motion along a smooth vertical circle, motion along a smooth vertical cycloid. Centre of gravity: Centre of gravity of continous distribution of matter (Arcs, Areas, Solids of Revolutions, Surfaces of Revolutions).

UNIT-5: Friction, Common Cetenary.

ENTREPRENEURSHIP

UNIT-1: Manager, entrepreneur and entrepreneurship, entrepreneurship and economic development, creativity, creative, personality and innovation, scanning of environment, introduction of promotional agencies.

UNIT-2: Entrepreneurial motivation training, motivation, self awareness or linking opportunities with “SELF”. (This part will be conducted through experimental learning in entrepreneurial motivation laboratory).

UNIT-3: Entrepreneurial traits and competencies, generating and gathering innovative ideas and using them interpersonal relationships, transactional analysis, Joe-Harry Window

UNIT-4: Project launching and resourcing, evaluation of potential opportunities, SWOT analysis, projects selection/formulation, project appraisal, financial analysis, collaboration procedure for application for foreign procedural requirements for establishing new enterprise, selecting type of business organization, registration and licensing, incentives and facilities available for small scale enterprise.

UNIT-5: Project Management: Basic concepts relating to financial, material, personnel, production, marketing and information management, problem solving: managing conflicts and social role, care of ecology and environment.