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Applied Mathematics V

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, Bernoullis 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

Linear optimisation
1.1 Problem formulation
1.2 Simplex Method
1.3 Revised Simplex Method
1.4 Duality & Sensivity

2.1 Unconstrained optimisation of several variables
2.2 Numerical methods for unconstrained optimisation : Random search & Univariate method, Fletcher Reverse method, Newtons method

COMPUTER ORGANIZATION

  1. 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.
  2. Instruction cycle, instruction sequencing, formats and its interpretation, microprogram concepts and control unit design.
  3. Semiconductor memory and memory organization, virtual memory, segments, pages, paged segments, cache memory and interleaved memory.
  4. 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.
  5. Introduction to assembly level programming - concepts of assemblers, macros, linkers, and loaders, linking loaders.
  6. Multiprogramming and time-sharing, introduction to advanced computer architecture (pipelining, array processors & multiprocessors).
  7. Introduction to operating systems. Case study (comparative) of DOS & UNIX.

 Recommended Books

  1. Computer organization and architecture: Hayes: - McGraw Hill.
  2. Computer organization: Hamacher, Zaky McGraw Hill.
  3. Structured computer organization: Tannenbaum.
  4. Computer organization and programming: William Gear.
  5. Introduction to systems software: D.M.Dhamdhare.
  6. Computer systems architecture: Morris Mano.

OBJECT ORIENTED PROGRAMMING METHODOLOGY

  1. Introduction to object oriented programming, it's need and requirements, general object oriented philosophy, software usability, code sharing, rapid prototyping, information hiding.
  2. Classes, attributes and methods, encapsulation, constructor, destuctors, iterator classes, class interface.
  3. Function overloading, inline, functions, operators & operator overloading, iterators.
  4. Inheritance base class, derived classes, friend class, static class, type checking, class scopes.
  5. Multiple inheritance & polymorphism, abstract classes, virtual function, virtual base class, static & dynamic binding, overloading, overriding type conversions.
  6. Object oriented design, class identification, defining inheritance, visibility & dependency coupling & cohesion.
  7. Case study of classes like ADT class, I/O class, string class, editor class.
  8. Language study: C++, object Pascal.

Books Recommended

  1. Introduction to Object Oriented Programming: Timothy Budd, Addison-Wesley.
  2. Programming language concepts & constructs: Ravi Sethi, Addison-Wesley.
  3. Object oriented programming with C++: E.Balguruswamy.
  4. The C++ programming language: Bjorne Strousstrup, Addison-Wesley.
  5. Object oriented programming in turbo C++: Robert Lafore, Galgotia.
  6. C++ and the paradigm: Bindu.R.Rao (McGraw).
  7. Learning C++: Eric Nagler (Jaico).

 Microprocessors I.

Introduction to microprocessors:

Features , Programmers model, external & internal organisation.

8085 Architecture:

8085 Architecture & organisation, Instruction cycles, machine cycles and

T-states, address decoding techniques, minimum system design, Memory interfacing with timing considerations, clock, reset & buffering circuits

8085 Instruction set

Instruction format, addressing modes, classification of instruction set.

8085 Programming:

Assembly language programming:- basic structure, data transfer, arithmetical, logical, transfer of control & miscellaneous instruction types.

Stack & subroutines:

Stack operations, limitations, subroutine concepts, parameter passing techniques, subroutine design, delay subroutine design & applications, Re-entrant & recursive subroutines, concept of counters and timers.

I/O data transfer techniques:

I/O interface concepts, speed considerations, program controlled I/O,

asynchronous & synchronous I/O techniques interrupt driven program controlled I/O, direct memory access data control techniques, handshake signals, concepts of serial communication, matrix keyboard & multiplexed display interface.

Interrupts:

Requirements, single level interrupt, multilevel interrupt & vector interrupt system, 8085 interrupt structure and its operation,8259A interrupt controller.

 

I/O controllers:

Features, organisation & operating modes of 8155 multifunction device,8255

Programmable peripheral interface, 8254 programmable timer,8237 programmable DMA

controller.

DISCRETE STRUCTURES

  1. Introduction to sets: Review only.
  2. Logic :

    2.1 Propositions and logical operations.

    2.2 Truth tables.

    2.3 Equivalence and implication.

    2.4 Laws of logic.

    2.5 Mathematical induction and quantifiers.

  3. Set theory :

    3.1 Method of proof for set, Venn diagram, set membership tables, definitions.

    3.2 Laws of set theory.

    3.3 Partition of sets.

  4. Permutations, combinations and discrete probability :

    4.1 Introduction to permutations and combinations.

    4.2 Generation of permutation and combination.

    4.3 Discrete probability.

    4.4 Conditional probability.

  5. Relations and Diagraphs :

    5.1 Relations and diagraphs.

    5.2 Paths and the relations and diagraphs.

    5.3 Properties of relations.

    5.4 Equivalence relations.

    5.5 Computer representation of relations and diagraphs.

    5.6 Manipulation of relations.

    5.7 Transitive closure, Warshall’s algorithm.

  6. Function and pigeon hole principle :

    6.1 Definition.

    6.2 Types of functions: injective, surjective, bijective.

    6.3 Composition, identity and inverse.

    6.4 Pigeon hole principle.

  7. Graphs.

COMPUTER GRAPHICS

  1. Introduction: Application areas, display devices and hard copy devices, interactive input devices, display processors, co-ordinate systems, vector generation.
  2. Raster Algorithms: Line drawing algorithms -- DDA and Bresenham's algorithm, and aliasing techniques, circle generation algorithm, ellipses and other curves generation, style primitives and display processor interface, area filling-scan line algo, boundary fill and flood fill techniques, text generation and display processor interface.
  3. Geometric transformations in 2D - basic transformations, world, NDC, device and homogeneous co-ordinate systems, composite transformations.
  4. Windowing and clipping: Windowing concepts, window view part transformation algorithms, line clipping algorithms like Cohen-Sutherland and Liang and Barsky, area chipping methods like Sutherland and Holgman.
  5. Segmentation: Segments, segment files, segmented display processor, segment attributes.
  6. Graphics hardware: Display controller, use of DAC and buffer organization.
  7. Introduction to 3-D: 3D co-ordinate system, 3D display techniques, and 3D transformations.
  8. Three-dimensional representations: Modeling polygon and curved surfaces, sweep representations, CSG and B- rep techniques.
  9. 3D viewing Projection methods, viewing transformations, chipping in 3D.
  10. Image synthesis: Hidden line and hidden surface removed techniques like back-face depth buffer method, scan line method, arc subdivision method, ochre methods.
  11. Light and shading: Illumination theory, reflections, textures and surface patterns, shadows, half toning surface shading methods, Gounand shading, Phang shading, Ray tracing.
  12. User interfaces: Interactive input techniques, physical device classification, interactive picture contraction techniques, positioning methods, constraints, grids and field input functions, event handle, design of user interface command language, mean design, output formats.

Text Books

  1. Computer graphics: Donald Hearn & M.Pauline Baker.
  2. Computer graphics: Steven Harrington.
  3. Theory and problems of computer graphics: Roy A.Plastock, Gordon Kelly, and Schaum. Series.

Reference Books

  1. Computer graphics software construction : John R.Ramkin
  2. Principles of interactive computer graphics: William M.Newman & Robert F. Sproull
  3. Mathematical elements of computer graphics: Rogers & Adams.
 
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