(Industrial Mathematics with Computer Application)
A three years duration course with total 150 credit points
FIRST YEAR
SEMESTER I
(All are compulsory and each course is of 5 credit points)
MIM 101 Linear Algebra
MIM 102 C-Programming
MIM 103 Operating Systems
MIM 104 Algebra
MIM 105 Numerical Analysis.
Total credits:25 points
SEMESTER II
(All are compulsory and each course is of 5 credit points)
MIM 201 Foundations of Analysis
MIM 202 Complex Analysis
MIM 203 Data Structures with C
MIM 204 Programming in C++
MIM 205 Differential Equations
Total credits: 25 points
SECOND YEAR
SEMESTER III
(All are compulsory and each course is of 5 credit points)
MIM 301 Web Programming
MIM 302 Discrete Mathematics
MIM 303 Theory of Computer Science
MIM 304 Design and Analysis of Algorithms
MIM 305 JAVA
Total credits: 25 points
1
SEMESTER IV
(Each course is of 5 credit points)
MIM 401 Field Theory / Optional Mathematics Course
MIM 402 Differential Geometry /Optional Mathematics Course
MIM 403 Data Base Management Systems I
MIM 404 MS.NET
MIM 405 Computer Networks.
Total credits: 25 points
THIRD YEAR
SEMESTER V
(Each course is of 5 credit points)
MIM 501 Coding Theory /Optional Mathematics Course
MIM 502 Probability Theory /Optional Mathematics Course
MIM 503 Data Base Management Systems II
MIM 504 Software Engineering
MIM 505 Advanced JAVA
Total credits: 25 points
SEMESTER VI
Industrial Training
Industrial Training has two projects:
(1) Minor project: During the vacation between 4 th semester and 5 th semester.
(5 credit points.)
(2) Major project: 6th semester.
(20 credit points.)
Total credits: 25 points.
2
MIM 101 : Linear Algebra
1. Prerequisites: Vector Spaces: Definition and Examples, Subspaces, Bases
and Dimensions, Linear Transformations, Quotient Spaces, Direct Sum,
The matrix of Linear Transformation, Duality.
2. Canonical Forms: Eigenvalues and Eigenvectors, The minimal Polynomial,
Diagonalisability, Triangular sable Operators, Jordan Forms, The
Rational Forms.
3. Inner Product Spaces: Inner Product Spaces, Orthogonally, The Adjoint
of Linear Transformation, Unitary operators, Self Adjoint and Normal
Operators, Polar and Singular Value Decomposition.
4. Bilinear Forms: Definition and Examples, The matrix of a Bilinear
Form, Orthogonality, Classification of Bilinear Forms.
5. Modules: Definition and Examples, Further notions and Results.
6. Free Modules: Linear Independence, Bases of Free Modules, Matrices
and Homeomorphisms.
Prescribed Books:
• Luthar and Passi, Modules (Narosa Publishing House).
• Vivek Sahai and Vikas Bist, Linear Algebra (Narosa Publishing House).
3
MIM 102 : C-Programming
1. Introductory Concepts: Introduction to computer, computer characteristics,
types of programming languages,introduction to C.
2. C Fundamentals: The character set, identifier and keywords, data types,
constants, variables and arrays, declarations, expressions, statements, symbolic
constants.
3. Operators and Expressions: Arithmetic operators, unary operators,
relational and logical operators, assignment operators, library functions.
4. Data Input and Outputs: Preliminaries, single character input-getchar()
function, single character output-putchar() function, entering input datascanf
function, writing output data- printf function, formatted inputoutput,
gets and puts functions.
5. Preparing and Running a Program: Planning and writing a C Program,
compiling and executing the program.
6. Control Statements: Preliminaries, the while statement, the do- while
statement, the for statement, nested loops, the if-else statement, the switch
statement, the break statement, the continue statement, the comma operator,
the goto statement.
7. Functions: A brief overview, defining a function, accessing a function,
passing arguments to a function, specifying argument data types, function
prototypes, recursion.
8. Program Structures: Storage classes, automatic variables, external
variables, static variables, multifile programs, more about library functions.
9. Arrays: Defining an array, processing an array, passing arrays to a function,
multidimensional arrays, arrays and strings.
10. Pointers: Fundamentals, pointer declarations, passing pointer to a function,
pointer and one dimensional arrays, operations on pointers, pointers
and multidimensional arrays, array of pointers, pointer to a function, passing
functions to other functions, more about pointer declarations.
11. Structures and Unions: Defining a structure, processing a structure,
user-defined data types (typedef), structures and pointers, passing structure
to a function, self-referential structures, unions.
12. Data Files: Opening and closing a data file, creating a data file, processing
a data file, unformatted data files.
4
Prescribed Books: 1. Byron S, Gottfried, Programming with C, Schaum’s
Outline series.
2. Yashwant Kanetkar, Let us C, BPB Publications.
Reference Book: Brian W, Kernighan, Dennis M, Ritchie, The C Programming
Language, Prentice Hall Publication.
5
MIM 103 : Operating Systems
1. Introduction to Operating Systems : Batch System, Time sharing
system, personal computer system, Parallel system, Distributed System,
Real Time System
2. File System : File Systems, File Concepts, Allocation Methods, Access
Methods, Directory Structure
3. Threads : Overview, Multithreading models, Threading Issues.
4. CPU Scheduling : Basics, Scheduling criteria, Scheduling Algorithms,
Multiple Processor Scheduling.
5. Disk and Drum Scheduling
6. Memory Management : Background, Swapping, Contiguous allocation,
Paging, Segmentation, Segmentation and paging- combined system,
virtual memory concept, Demand paging, Paging replacement algorithms.
7. Concurrent Processing and programming : Review of process concepts,
Hierarchy of processes, Problem and solution algorithm, Semaphores,
Overview of Concurrent programming, Modularization, Synchronization
in Windows 2000, Concurrent languages.
8. Deadlocks : System model, Deadlock characterization, methods of handling
Deadlocks, Deadlock Prevention, Deadlock Avoidence, Deadlock Detection,
Recovery from Deadlock.
Prescribed Book:
• Silberschatz, Operating System Concepts .
6
MIM 104 : Algebra
1. Prerequisites: Semigroups and groups, Homomorphisms, Subgroups and
cosets. Rings, Examples of rings, types of rings, subrings and characteristic
of a ring.
2. Cyclic groups, permutation groups, generators and relations.
3. Normal subgroups and quotient groups. Isomorphism theorems, automorphisms,
conjugacy and G-sets.
4. Normal series, Solvable groups, Nilpotent groups.
5. Group Homomorphisms, First Isomorphism Theorem, Fundamental Theorem
of Finite Abelian Groups.
6. Permutation Groups, Cyclic decomposition, Alternating group An, Simplicity
of An.
7. Structure of groups, Direct products, Finitely Generated Abelian Groups,
Invariants of a finite abelian group
8. Sylow Theorems, Groups of order p2, pq.
9. Ideals and homomorphisms, maximal and prime ideals, nilpotent and nil
ideals, Zorn’s lemma
10. . Unique Factorisation Domains, Principal Ideal Domains, Euclidean Domains.
Polynomials over UFD.
Prescribed Book:
• P. B. Bhattacharya, S. K. Jain and S. R. Nagpaul, Basic Abstract
Algebra (Second Ed.), Cambridge Univ. Press (Indian Ed. 1995).
Reference Book:
• Joseph A. Gallian,Contemporary Abstract Algebra (Fourth Ed.), Narosa,
1999.
• I. S. Luthar and I. B. S. Passi, Algebra-Vol. 1: Groups, Narosa, New
Delhi, 1996.
7
MIM : 105 Numerical Analysis
1. Iterative solutions of nonlinear equation: bisection method. Fixedpoint
interation, Newton’s method, secant method, acceleration of convergence,
Newton’s method for two non linear equations, polynomial equation
methods.
2. Polynomial interpolation: interpolation polynomial, divided difference
interpolation, Aitken’s formula, finite difference formulas, Hermite’s interpolation,
double interpolation.
3. Linear systems of Equations: Gauss Elimination, Gauss-Jordan method,
LU decomposition, iterative methods, and Gauss- Seidel iteration.
4. Numerical Calculus : Numerical differentiation, Errors in numerical
differentiation, Numerical Integration, Trapezoidal rule, Simpson’s 1/3 -
rule, Simpson’s 3/8 rule, error estimates for Trapezoidal rule and Simpson’s
rule.
5. Numerical Solution of Ordinary differential Equations : Solution
by Taylor series, Picard Method of successive approximations, Euler’s
Method, Modified Eular Method, Runge- Kutta Methods, Predicator-
Corrector Methods.
6. Eigenvalue Problem : Power method, Jacobi method, Householder
method.
7. Practicals with Scilab.
Prescribed Book:
• S. S. Sastry, Introduction Methods of Numerical Analysis ( 4th Edition)(
Prentice-Hall).
Refrence Book:
• K .E. Atkinson,: An Introduction to Numerical Analysis.
• J. I. Buchaman and P. R. Turner, Numerical Methods and Analysis..
8
SEMESTER II
MIM 201 : Foundations of Analysis
1. A Taste of Topology: Metric space concepts, Compactness, Connectedness,
Coverings, Cantor sets.
2. Functions of a Real Variable: Differentiation, Reimann integration,
Series.
3. Function Spaces: Uniform convergence and C0[a, b], Power series, Compactness
and equicontinuity in C0.
4. Multivariate Calculus: Derivatives, Higher derivatives, Smooothness
classses, Implicit and inverse functions.
5. Lebesgue Theory: Outer measure, Measurability, Regularity, Lebesgue
integrals.
Prescribed Book:
• C. C. Pugh, Real Mathematical Analysis, Springer, New Delhi, 2004.
(Ch. 2: Sec 1 to 5; Ch. 3, Ch. 4: Sec 1 to 5; Ch. 5: Sec 2 to 5; Ch. 6:
Sec 1 to 4.)
Reference Books:
• N. L. Carothers, Real analysis, Cambridge University Press India, 1999.
• H. Royden, Real Analysis, Third Edition, Prentice Hall of India, 1988.
9
MIM 202 : Complex Analysis
1. Pre-requisites:
(a) Topological and Analytical Preliminaries: Point sets in the
plane, sequences, compactness, stereographic projection, continuity.
(b) Elementary Functions: Exponential functions, mapping properties,
logarithmic function, complex exponents.
2. Analytic Functions: Cauchy-Riemann Equations, analyticity, harmonic
functions.
3. Power Series: Sequences, uniform convergence, Maclaurin and Taylor
series, operations on power series.
4. Complex Integration and Cauchy’s Theorem: Curves, parameterizations,
line integral, Cauchy’s Theorem.
5. Applications of Cauchy’s Theorem: Cauchy’s integral formula, Cauchy’s
inequality and applications, maximum modulus theorem.
6. Laurent Series and Residue Theorem: Laurent series, classification
of singularities, evaluation of real integrals, argument principle.
7. Bilinear Transformations and Mappings: Basic mappings, linear
fractional transformations, other mappings.
Prescribed Book: S. Ponnuswamy and Herb Silverman, Complex Variables
with Applications, Birkh¨auser.
Reference Book: J. B. Convey, Functions of one complex variables, Narosa
Publishing House.
10
MIM 203 : Data Structure with C
1. Basic Concepts : Overview,Pointers and Dynamic memory Allocation,
Algorithm Specification, Data Abstraction, Performance Analysis.
2. Arrays and Structures : Arrays, Dynamically allocated arrays, Structures
and Unions, Polynomials,Sparse Matrices, Representation of multidimensional
arrays, Strings.
3. Stack and Queues : Stacks, Stacks using Dynamic Arrays, Queues, Circular
Queues using Dynamic Arrays, Evaluation of Expressions, Multiple
Stacks and Queues.
4. Linked Lists : Singly Linked Lists and Chains, Representing Chains in
C, Linked Stacks and Queues, Polynomials, Additional List Operations,
Sparse Matrices, Doubly Linked Lists.
5. Trees : Introduction, Binary Trees, Binary Tree Traversals, Additional
Binary Tree Operations, Threaded Binary Trees, Heaps, Binary Search
Trees, Selection Trees, Forests, Counting Binary Trees.
6. Graphs : The Graph Abstract Data Type, Elementary Graph Operations,
Minimum Cost Spanning Trees, Stortest Paths and Transitive Closure,
Activity Networks.
7. Sorting : Motivation, Insertion Sort, Quick Sort, How fast we can sort?,
Merge Sort, Heap Sort, List and Table Sorts.
8. Hashing : Introduction, Static Hashing, Dynamic Hashing, Bloom Filters.
Prescribed Book :
• Horowitz, Sahni, Anderson-Freed, Fundamentals of Data Structures
in C, 2nd Edition (Universities Press)
Reference Books :
• Donald E. Knuth, The Art of Computer Programming, Volume 1,
Third Edition ( Pearson Education )
• Seymour Lipschutz, Data Structures (Tata McGrawHill).
• Aaron M. Tenenbaum, Data Structures Using C (Pearson Education).
11
MIM 204 : Progremming in C++
1. Introduction : Declarations, const declartions, Namaespaces, cin and
cout, Loops, Functions, references, Function Overloading, Function with
default parameters, passing arguments with reference and pointers, new
and delete operators.
2. Classes : Procedural and object-oriented programming, the class, public
and private, implementing class member functions, inline functions, constructor
and desructor, const memeber fuctions, static members, ”‘this”’
pointer an array of objects, class scope.
3. Working With Classes : class in class, initialiser list, operator overloading,
friend functions, automatic conversions, conversion fuctions, copy
constructor, assignment operator, classes and dynamic memeory.
4. Class Inheritance : Beginning with simple base, inheritance is a relation,
declaring derived classes, protected members, virtual funtions, pure
virtual functions, abstract classes, public, protected and private inheritance,
operators new and delete, virtual base, multiple inheritance.
5. Templates : Generic programming, template functions, defining a class
template, using a template class, using template with family of classes,
template versality, template specilization, inheritance.
6. Exception Handling : Exception, the exception mechanism, exception
versality, multiple try blocks, exception and classes, exception and inheritance,
the exception class.
7. Files and Streams : cin, cout cerr, clog streams, operators >> and
<<, formating output, manipulators, reading string and single character,
stream states, Files, ifstream, ofstream and fstream classes, file modes,
text and binary files, overloading << and >> operators for user defined
operators, user defined manipulators.
12
Prescribed Book:
• Stephen Prata, C++ Primer Plus (Tecmedia).
Reference Books:
• Bruce-Eckele, Thinking in C++ (vol-I and vol -II).
• B. Stoustroup, Programming Language C++ .
13
MIM 205 : Differential Equations
1. Prerequisites: Linear equations of the first order.
2. Linear equations with constant coefficients : Second order homogeneous
equations, Initial value problems, Linear dependence and independence,
Nonhomogeneous equations of n-th order, Algebra of constant
coefficients.
3. Linear equations with variable coefficients : Initial value problems,
Solutions of the homogeneous equation, Wronskian and linear independence,
Reduction of order, Nonhomogeneous equations, Legendre equation.
4. Linear Equations with regular singular points : Euler equation,
Second order equation with regular singular points, Exceptional cases,
Bessel equation.
5. Existence and uniqueness of solutions to first order equations:
Separation of variables, exact equations, Method of successive approximations,
Lipschitz condition, Approximation to and uniqueness of solutions.
6. Existence and uniqueness of solutions to systems and n-th order
equations: Complex n-dimensional space, Systems as vector equations,
Existence and uniqueness of solutions to systems, Existence, Uniqueness
for linear systems and equations of order n.
Prescribed Book:
• E. A. Coddington, An Introduction to Ordinary Differential Equations
(Prentice- Hall).
Reference Book: G. F. Simmons and S. G. Krantz, Differential Equations
(Tata McGraw-Hill).
14
SEMESTER III
MIM 301 : Web Programming
1. Web Programming HTML Programming CSS JavaScript DOM DHTML
2. Extensible markup Language (XML) The Purpose and Nature of
XML XML Syntax and Structure Rules XML Document Type Declaration
(DTD) XML Schema XSL Extensible Stylesheet Language XPath XQuery
XML Parsers Java and XML
3. AJAX Introduction to Ajax Ajax Architecture XMLHttpRequest Ajax
Framework and DOM Ajax using HTML,CSS,JavaScript
15
MIM 302 : Discrete Structures
1. Order Relations and Structures: Partially ordered set, Extremal Elements
of Partially ordered sets,Lattices, Finite boolean algebras, Functions
on boolean algebras, Circuit designs.
2. Trees: Trees,Labeled Trees, Tree Searching, Undirected Trees, Minimal
Spanning Trees
3. Topics in Graph Theory: Graph, Euler Paths and Circuits, Hamiltonian
Paths and Circuits, Tranport Networks, Matching Problems, Coloring
Graphs,
4. Combinatorics: Combination, Permutation, Generating Functions, Odinary
and Exponential Generating Functions, Recurrence Relation, Methods
of Solution of Recurrence Relatiion , Substitution Method, Characteristic
Method, Generating Function Method, Principle of Inclusion and
Exclusion.
Prescribed Book:
• Kolman, Busby, Ross, Discrete Mathematical Structures,Fifth
Edition (Pearson Education).
• Purna Chandra Biswal, Discrete Mathematics and Graph Theory,
Second Edition (PHI.).
Reference Book: Alan Tucker, Applied Combinatorics, Forth Edition
(John Willey).
16
MIM 303 : Theory of Computer Science
1. Propositions and Predicates: Propositions (or statements), Normal
Forms of Well-formed Formulas, Rules of Inference for Propositional Calculus
(Statement Calculus), Predicate Calculus, Rules of Inference for
Predicate Calculus.
2. Mathematical Preliminaries: Sets. Relations and Functions, Graphs
and Trees, String and Their Properties, Principal of Induction, Proof by
Contradiction, Supplementary Examples.
3. The Theory of Automata : Definition of an Automaton, Description
of a Finite Automaton, Transition Systems Properties of Transition Functions,
Acceptability Systems, Nondeterministic Finite Stare Machines,
The Equivalence of DFA and NDFA, Mealy and Moore Models, Minimization
of Finite Automata, Supplementary Examples
4. Formal Languages:Basic Definition and Examples, Chomsky Classification
of Language, Languages and Their Relation, Recursive and Recursively
Enumerable Set, Operations on Language, Language and Automata,
Supplementary Examples.
5. Regular Sets and Regular Grammars: Regular Expressions, Finite
Automata and Regular Expressions, Pumping Lemma for Regular Set,
Application of Pumping Lemma, Closure Properties of Regular Sets Regular
Sets and Regular Grammars.
6. Context Free Languages: Context-free Languages and Derivation Tree,
Ambiguity in Context-free Grammars Simplification of Context-free Grammars,
Normal Forms for Context-free Grammars, Pumping Lemma for
Context-free Languages, Decision Algorithms for Context-free Languages.
7. Pushdown Automata:Basic Definitions, Acceptance by pda, Pushdown
Automata and Context-free Languages, Parsing and Pushdown Automata,
Supplementary Examples.
8. Turing Machines and Linear Bounded Automata: Representation
of Turing Machine, Language Acceptability by Turing Machines, Design
of Turing Machines, Descriptions of Turing Machines.
Prescribed Book:
• K. L. P. Mishra and N. Chandasekaran, Theory of Computer Science
(PHI Learning Private Ltd).
17
MIM 304 : Design and Analysis of Algorithms
1. Mathematical Foundation: Growth Functions, Summations, Recurrences
Substitutions, Iterations, Master Methods, Counting and probability
.
2. Sorting :Heap Sort, Quick Sort, Merge Sort, Sorting in linear Time,
Medians and Order Statistics.
3. Dynamic Programming : Matrix chain Multiplication, longest common
subsequence, optimal polygon triangularisation.
4. Greedy Algorithm.
5. Graphs : Traversals, Topological sort, Minimum spanning trees, single
source shortest path, All pair shortest path, Maximum flow problems.
6. Sorting Networks : Comparision, bitonic sort and merge sort networks.
7. Parallel Algorithms : CRCW, EREW algorithms efficiency sorting linear
system problem, Matrix Operations, Strassens Algorithm and matrix
inversion.
8. FFT :Polynomials DFT, FFT.
9. Number Theoretic Algorithm : Rabin - Karp, KMP, Bower - Moore
algorithms.
10. Geometric Algorithms : Finding convex hall, closes pair of points,
linear programming problem.
11. NP Completeness : P and NP classes, NP completeness and reducibility.
12. Approximation Algorithms : Vertex cover problem, traveling salesman
problem, set covering and subset sum problems.
Prescribed Book:
• T. H Coreman, Leiserson, Rivest, Introduction to Algorithms .
18
MIM 305 : JAVA PROGRAMMING
1. Introduction to Java Programming - Overview, Java Tools, Java
Byte Code
2. Elementary Programming Concepts : Variables and Identifiers, Java
keywords, Data Types, Operators, Expression, Constants, Statements,
Arrays
3. Classes and Packages : Defining classes, Static Members, Using packages,
Access Specifiers, Constructors, Finalisers referencing objects
4. Inheritance, nested and inner class : Extending classes, Abstract
Class Interface, Super Keyword, Final classes, Constructors and Inheritance,
Dynamic Binding, Overriding methods
5. Exception and Input and Output : Byte streams, Character streams,
File i/o basics, Introduction to exception, Try and catch block and finally
block, Inbuilt Exception.
6. String Handling and Exploring Java.lang : String Operations, Character
Extractions, Data Conversions, Modifying strings.
7. Applet and Event Handling and Controls
8. Input and Output package : Object serialization, reader and writer
9. Swings : - Layout Manager Layout Manager swing Controls Components
Organizers, Jlish, Jtree, Jtables, Dialogue, File chooser, color chooser.
10. JDBC : The design of JDBC, JDBC programming concepts making the
connection, statement and result set class, Executing SQL commands,
Executing Queries.
11. Multithreading : Running multiple threads, The runnable interface
Threads priorities Daemon, Thread States, thread groups Synchronization
and Interthread Communication Deadlocks. Prescribed Book:
• Herbert Schildt, A Complete Reference Java 2.
19
MIM 401 : Field Theory
1. Prerequisites: Definitions and basic properties Rings and fields, Ideals
and homomorphisms, Characteristic of fields, Euclidean domains, Unique
factorization, Polynomials.
2. Field Extensions: The degree of an extension, Extensions and polynomials,
Polynomials and extensions.
3. Applications to Geometry: Ruler and compass construction, An algebraic
approach.
4. Splitting Fields.
5. Finite Fields.
6. The Galois Group: Monomorphisms between fields, Automorphisms,
Groups and subfields, Normal extensions, Separable extensions, The Galois
correspondence, The fundamental theorem, An example.
7. Equations and Groups: Solution by radicals of quadratics, cubics and
quartics. Cyclotomic polynomials, cyclic extensions.
8. Groups and Equations: Insoluble quintics, General polynomials.
9. Prescribed Book:
• J. M. Howie, Fields and Galois Theory, Springer Undergraduate
Mathematics Series, 2006.
(Chapters 1 to 8 and Chapter 10).
Reference Books:
• M. Artin, Algebra, Prentice-Hall, Englewood Cliffs, N.J., 1991.
• P. B. Bhattacharya, S. K. Jain and S. R. Nagpaul, Basic Abstract
Algebra, Second Ed., Cambridge University Press, Cambridge,
1995.
20
MIM 402 : Differential Geometry
1. Graphs and Level Sets
2. Vector Fields
3. The Tangent Space
4. Surfaces
5. Vector Fields on Surfaces;Orientation
6. The Gauss Map
7. Geodesics
8. Parallel Transport
9. The Weingarten Map
10. Curvature of Plane Curves
11. Arc Length and Line Integrals
12. Curvature of Surfaces
13. Parametrized Surfaces
14. Local Equivalence of Surfaces and Parametrized Surfaces
15. Surface Area and Volume
16. The Exponential Map
17. The Gauss-Bonnet Theorem
21
Prescribed Book:
• J. A. Thorpe, Elementary Topics in Differential Geometry, Springer,
Second Edition
(Chapters 1 to 12 and Chapter 14, 15, 17, 19, 22).
22
MIM 403 : Data Base Management Systems I
1. Database Concepts
2. Relational Algebra
3. Database Design Concepts
4. ER Diagrams and Normalization SQL
23
MIM 404 : MS.NET
1. Introducing .NET Platform: .NET and Windows DNA .NET Architecture
2. Features of .NET Platform: Multilanguage Support, Platform and
Processor Independence, Memory Management, Versioning, Deployment,
Interoperability with Unmanaged Code.
3. .NET Architecture: .NET Runtime, Managed/Unmanaged Code, Intermediate
Language, Common Language Specification/Common Type
System, .NET Base Class Library (BCL), Assemblies, Metadata, Assemblies
and Modules, Assembly Cache, Reflection, Just In Time Compilation,
Garbage Collection, Object Oriented in .NET.
4. Introducing C hash Programming: Data Types, Control Structures,
Properties and Indexers, Delegates and Events, Exception Handling, Basics
of Inheritance.
24
MIM 405 : Computer Networks
1. Introduction to Networking Hardware Architecture Topologies, Media,
Devices Transmission Techniques Twisted Pair, Coaxial Cable, Fiber
optics
2. The OSI Reference Model Protocol Layering, TCP/IP Model, OSI vs.
TCP/IP
3. Common Network Architecture Connection oriented N/Ws Connectionless
N/Ws Example of N/Ws-P2P, X, 25, ATM, Ethernet Wireless
LANs - 802.11, 802.11x, Gigabit Wireless Transmission Switching Circuit
Switching, Message Switching, Packet Switching
4. Local Area Networks Components and Technology, Transmission Protocol
and Media
5. IP Addressing Routing IP addresses Network part and Host Part
Network Masks, Network addresses and Broadcast addresses, Address
Classes, Loop back address, IP routing concepts,Routing Tables, Stream
and Packets TCP - a reliable pipe, TCP Connection IPV6: The next
generation Protocol.
6. Domain Network Services (DNS) Domain Names, Authoritative Hosts,
Delegating Authority, Resource Records, SOA records, DNS protocol,
DHCP and Scope Resolution
7. Network Applications Http, MIME, SMTP, POP
8. Network security Packet filtering, Encryption, Virtual Private network,
Digital signatures
• Prescribed Book :
• Andrew S. Tanenbaum , Computer Networks 4e, PHI, India.
Reference Books:
1. Douglas E. Comer, Computer Networks and Internets with Internet
Applications , Pearson Education, forth Edition
2. William R. Cheswick,, Firewalls and Internet Security 2nd Edition
Pearson Education.
25
SEMESTER V
MIM 501 : Coding Theory
1. Error detection: correction and decoding: Communication channels,
Maximum likelihood decoding,Hamming distance,Nearest neighbour
/ minimum distance decoding, Distance of a code.
2. Linear codes: Vector spaces over finite fields, Linear codes, Hamming
weight, Bases of linear codes, Generator matrix and parity check matrix,
Equivalence of linear codes, Encoding with a linear code,Decoding of linear
codes, Cosets, Nearest neighbour decoding for linear codes, Syndrom
decoding.
3. Cyclic codes: Definitions, Generator polynomials, Generator and parity
check matrices, Decoding of cyclic codes, Burst-error-correcting codes.
4. Some special cyclic codes: BCH codes, Definitions, Parameters of
BCH codes, Decoding of BCH codes.
Reference Books:
1. San Ling and Chaoing xing , Coding Theory- A First Course .
2. Lid and Pilz, Applied Abstract Algebra - 2nd Edition
26
MIM 502 : Probability Theory
1. Introduction to Discrete Probability : Intuitive concepts: probability
of an event as a measure between 0 and 1; random variable; probability
distribution; frequency interpretation of probability; random numbers;
coins, dice, and other games; simulations; odds; historical development of
probability; random walks.
2. Formal concepts: sample space, outcomes, and events; random variable;
discrete distribution functions and axioms of probability; unions,
intersections, and complements; properties of probabilities, principle of
inclusion and exclusion; tree diagrams; uniform distributions over finite
sets, symmetry; infinite sample spaces with discrete probabilities.
3. Introduction to Continuous Probability : The intuitive problems
with probabilities over space (line, plane, Rn in general). Monte Carlo
simulations, Buffon’s needle. Formal concepts: density function for a continuous
random variable; integration; cumulative distribution functions;
derivatives; exponential density function;
4. Conditional Probability : Intutive concept of conditional probability;
formal definition of conditional probability; Bayes’ formula for inverting
conditional probabilities; independent events; joint distribution functions;
independent random variables; independent trials. Conditional density
functions for continuous distributions; the beta distribution
5. Distributions and Densities : Uniform continuous distributions; geometric
distribution; Poisson distribution; exponential and gamma distributions;
introduction to queueing theory; normal (Gaussian) distribution;
Chi-squared distribution
6. Expected Value and Variance : Expected value for discrete random
variables, expectation; linearity of expectation; expectation of independent
random variables; conditional expectation; variance and standard
deviation; variance of various distributions. Expectation and variance for
continuous random variables.
7. Sums of Random Variables : Analysis of sums of independent random
variables with identical distributions, that is, independent trials.
8. Law of Large Numbers : Chebychev inequality, law of averages, law
of large numbers.
9. The Central Limit Theorem :The central limit theorem for Bernoulli
trials, binomial distributions again, the normal distribution, the general
central limit theorem.
Prescribed Book:
27
• Charles M. Grinstead and J. Laurie Snell, Introduction to
Probability, the American Mathematical Society, 1997.
(Chapters 1 to 8 and Chapter 10).
28
MIM 503 : Advanced Data Base Management Systems II
1. Advanced Database Concepts
2. Database Architecture
3. PL/SQL
29
MIM 504 : Software Engineering
1. Introduction To Software Engineering
Definition, System Concepts,
Types of System, Element of System
A generic view of Software Engineering
Characteristics of software
McCall’s Quality Factors
Software Process
Challenges Facing Software Engineering
2. Requirement Analysis
Definition of System Analysis
Fact Finding Techniques
Requirement Anticipation, Investigation
Feasibility Study
User Requirements
System Requirement Specification
Requirements Engineering
Requirements Validation
System Requirement Specifications (SRS)
3. Analysis and Design Tools
Decision Tree and Decision Tables
Data Flow Diagrams [Physical and Logical]
Data Dictionary
Input and Output Design
(Case Study: Minimum two case studies on each of the above topic should
be covered.)
4. Software Development Methodologies
System Development Life Cycle. - Classical Model
Waterfall Model
Spiral Model
Prototyping Approach
Agile Methods
Rapid Application Development
5. System Testing
Testing and Debugging Definition.
Verification and Validation
Testing Objectives and Principles.
30
Testing Strategies
- Black Box Testing.
- White Box Testing
- Performance Testing
- User Acceptance Testing
- Stress Testing
Test Case Design
Report Test Result
Test Automation
(Case Study: Minimum two case studies on test case design should be
covered.)
6. System Maintenance
Importance of Maintenance
Software Maintenance
Types of Maintenance
Maintenance Side Effects/Ripple Effects
Re-engineering
Reverse Engineering
Reference Books:
1. Ian Sommerville , Software Engineering , 7th/8th Edition [Pearson Education]
2. Roger S. Pressman, Software Engineering - A Practitioner’s Approach
7th Edition - [McGraw Hill International Edition]
3. James Senn, Analysis of Information Systems
4. Pathasarthy and Khalskar, System Analysis and Design.
Ch 1, -:Reference Book 1,2
Ch 2 -:Reference Book 1,2
Ch 3 -:Reference Book 1,3 (case studies from Ref Book 3)
Ch 4 -:Reference Book 2
Ch 5 -:Reference Book 2
Ch 6 -:Reference Book 4
31
MIM 505 : Advanced JAVA
1. JAVA Basic Reveiws
Java streaming - Networking - Event handling - Multithreading - Byte code
Interpretation - Customizing application - Data Structures - Collection
classes.
2. Distributed Computing
Custom sockets - Remote Method Invocation - Activation - Object serialization
-Distributed garbage collection - RMI - IIOP - Interface definition
language - CORBA - JINI overview.
3. JAVA Beans And Swing
Bean concepts - Events in bean box - Bean customization - Persistence -
Application - deployment using swing - Advanced swing techniques - JAR
file handling.
4. JAVA Enterprise Applications
JNI - Servlets - Java Server Pages - JDBC - Session beans - Entity beans
- Programming and deploying enterprise Java Beans - Java transactions.
5. Related JAVA Techniques
Java Media Frame work - 3D graphics - Internationalization - Case study
- Deploying n-tier application, E- commerce applications.
Reference Books:
1. Deitel and Deitel , Java How to program, Prentice Hall , 4 th Edition,
2000.
2. Gary Cornell and Cay S. Horstmann, Core Java Vol 1 and Vol 2 ,
Sun Microsystems Press, 1999.
3. Stephen Asbury, Scott R. Weiner, Wiley, Developing Java Enterprise
Applications, 1998.
32
SEMESTER VI
Industrial Training
33
A three years duration course with total 150 credit points
FIRST YEAR
SEMESTER I
(All are compulsory and each course is of 5 credit points)
MIM 101 Linear Algebra
MIM 102 C-Programming
MIM 103 Operating Systems
MIM 104 Algebra
MIM 105 Numerical Analysis.
Total credits:25 points
SEMESTER II
(All are compulsory and each course is of 5 credit points)
MIM 201 Foundations of Analysis
MIM 202 Complex Analysis
MIM 203 Data Structures with C
MIM 204 Programming in C++
MIM 205 Differential Equations
Total credits: 25 points
SECOND YEAR
SEMESTER III
(All are compulsory and each course is of 5 credit points)
MIM 301 Web Programming
MIM 302 Discrete Mathematics
MIM 303 Theory of Computer Science
MIM 304 Design and Analysis of Algorithms
MIM 305 JAVA
Total credits: 25 points
1
SEMESTER IV
(Each course is of 5 credit points)
MIM 401 Field Theory / Optional Mathematics Course
MIM 402 Differential Geometry /Optional Mathematics Course
MIM 403 Data Base Management Systems I
MIM 404 MS.NET
MIM 405 Computer Networks.
Total credits: 25 points
THIRD YEAR
SEMESTER V
(Each course is of 5 credit points)
MIM 501 Coding Theory /Optional Mathematics Course
MIM 502 Probability Theory /Optional Mathematics Course
MIM 503 Data Base Management Systems II
MIM 504 Software Engineering
MIM 505 Advanced JAVA
Total credits: 25 points
SEMESTER VI
Industrial Training
Industrial Training has two projects:
(1) Minor project: During the vacation between 4 th semester and 5 th semester.
(5 credit points.)
(2) Major project: 6th semester.
(20 credit points.)
Total credits: 25 points.
2
MIM 101 : Linear Algebra
1. Prerequisites: Vector Spaces: Definition and Examples, Subspaces, Bases
and Dimensions, Linear Transformations, Quotient Spaces, Direct Sum,
The matrix of Linear Transformation, Duality.
2. Canonical Forms: Eigenvalues and Eigenvectors, The minimal Polynomial,
Diagonalisability, Triangular sable Operators, Jordan Forms, The
Rational Forms.
3. Inner Product Spaces: Inner Product Spaces, Orthogonally, The Adjoint
of Linear Transformation, Unitary operators, Self Adjoint and Normal
Operators, Polar and Singular Value Decomposition.
4. Bilinear Forms: Definition and Examples, The matrix of a Bilinear
Form, Orthogonality, Classification of Bilinear Forms.
5. Modules: Definition and Examples, Further notions and Results.
6. Free Modules: Linear Independence, Bases of Free Modules, Matrices
and Homeomorphisms.
Prescribed Books:
• Luthar and Passi, Modules (Narosa Publishing House).
• Vivek Sahai and Vikas Bist, Linear Algebra (Narosa Publishing House).
3
MIM 102 : C-Programming
1. Introductory Concepts: Introduction to computer, computer characteristics,
types of programming languages,introduction to C.
2. C Fundamentals: The character set, identifier and keywords, data types,
constants, variables and arrays, declarations, expressions, statements, symbolic
constants.
3. Operators and Expressions: Arithmetic operators, unary operators,
relational and logical operators, assignment operators, library functions.
4. Data Input and Outputs: Preliminaries, single character input-getchar()
function, single character output-putchar() function, entering input datascanf
function, writing output data- printf function, formatted inputoutput,
gets and puts functions.
5. Preparing and Running a Program: Planning and writing a C Program,
compiling and executing the program.
6. Control Statements: Preliminaries, the while statement, the do- while
statement, the for statement, nested loops, the if-else statement, the switch
statement, the break statement, the continue statement, the comma operator,
the goto statement.
7. Functions: A brief overview, defining a function, accessing a function,
passing arguments to a function, specifying argument data types, function
prototypes, recursion.
8. Program Structures: Storage classes, automatic variables, external
variables, static variables, multifile programs, more about library functions.
9. Arrays: Defining an array, processing an array, passing arrays to a function,
multidimensional arrays, arrays and strings.
10. Pointers: Fundamentals, pointer declarations, passing pointer to a function,
pointer and one dimensional arrays, operations on pointers, pointers
and multidimensional arrays, array of pointers, pointer to a function, passing
functions to other functions, more about pointer declarations.
11. Structures and Unions: Defining a structure, processing a structure,
user-defined data types (typedef), structures and pointers, passing structure
to a function, self-referential structures, unions.
12. Data Files: Opening and closing a data file, creating a data file, processing
a data file, unformatted data files.
4
Prescribed Books: 1. Byron S, Gottfried, Programming with C, Schaum’s
Outline series.
2. Yashwant Kanetkar, Let us C, BPB Publications.
Reference Book: Brian W, Kernighan, Dennis M, Ritchie, The C Programming
Language, Prentice Hall Publication.
5
MIM 103 : Operating Systems
1. Introduction to Operating Systems : Batch System, Time sharing
system, personal computer system, Parallel system, Distributed System,
Real Time System
2. File System : File Systems, File Concepts, Allocation Methods, Access
Methods, Directory Structure
3. Threads : Overview, Multithreading models, Threading Issues.
4. CPU Scheduling : Basics, Scheduling criteria, Scheduling Algorithms,
Multiple Processor Scheduling.
5. Disk and Drum Scheduling
6. Memory Management : Background, Swapping, Contiguous allocation,
Paging, Segmentation, Segmentation and paging- combined system,
virtual memory concept, Demand paging, Paging replacement algorithms.
7. Concurrent Processing and programming : Review of process concepts,
Hierarchy of processes, Problem and solution algorithm, Semaphores,
Overview of Concurrent programming, Modularization, Synchronization
in Windows 2000, Concurrent languages.
8. Deadlocks : System model, Deadlock characterization, methods of handling
Deadlocks, Deadlock Prevention, Deadlock Avoidence, Deadlock Detection,
Recovery from Deadlock.
Prescribed Book:
• Silberschatz, Operating System Concepts .
6
MIM 104 : Algebra
1. Prerequisites: Semigroups and groups, Homomorphisms, Subgroups and
cosets. Rings, Examples of rings, types of rings, subrings and characteristic
of a ring.
2. Cyclic groups, permutation groups, generators and relations.
3. Normal subgroups and quotient groups. Isomorphism theorems, automorphisms,
conjugacy and G-sets.
4. Normal series, Solvable groups, Nilpotent groups.
5. Group Homomorphisms, First Isomorphism Theorem, Fundamental Theorem
of Finite Abelian Groups.
6. Permutation Groups, Cyclic decomposition, Alternating group An, Simplicity
of An.
7. Structure of groups, Direct products, Finitely Generated Abelian Groups,
Invariants of a finite abelian group
8. Sylow Theorems, Groups of order p2, pq.
9. Ideals and homomorphisms, maximal and prime ideals, nilpotent and nil
ideals, Zorn’s lemma
10. . Unique Factorisation Domains, Principal Ideal Domains, Euclidean Domains.
Polynomials over UFD.
Prescribed Book:
• P. B. Bhattacharya, S. K. Jain and S. R. Nagpaul, Basic Abstract
Algebra (Second Ed.), Cambridge Univ. Press (Indian Ed. 1995).
Reference Book:
• Joseph A. Gallian,Contemporary Abstract Algebra (Fourth Ed.), Narosa,
1999.
• I. S. Luthar and I. B. S. Passi, Algebra-Vol. 1: Groups, Narosa, New
Delhi, 1996.
7
MIM : 105 Numerical Analysis
1. Iterative solutions of nonlinear equation: bisection method. Fixedpoint
interation, Newton’s method, secant method, acceleration of convergence,
Newton’s method for two non linear equations, polynomial equation
methods.
2. Polynomial interpolation: interpolation polynomial, divided difference
interpolation, Aitken’s formula, finite difference formulas, Hermite’s interpolation,
double interpolation.
3. Linear systems of Equations: Gauss Elimination, Gauss-Jordan method,
LU decomposition, iterative methods, and Gauss- Seidel iteration.
4. Numerical Calculus : Numerical differentiation, Errors in numerical
differentiation, Numerical Integration, Trapezoidal rule, Simpson’s 1/3 -
rule, Simpson’s 3/8 rule, error estimates for Trapezoidal rule and Simpson’s
rule.
5. Numerical Solution of Ordinary differential Equations : Solution
by Taylor series, Picard Method of successive approximations, Euler’s
Method, Modified Eular Method, Runge- Kutta Methods, Predicator-
Corrector Methods.
6. Eigenvalue Problem : Power method, Jacobi method, Householder
method.
7. Practicals with Scilab.
Prescribed Book:
• S. S. Sastry, Introduction Methods of Numerical Analysis ( 4th Edition)(
Prentice-Hall).
Refrence Book:
• K .E. Atkinson,: An Introduction to Numerical Analysis.
• J. I. Buchaman and P. R. Turner, Numerical Methods and Analysis..
8
SEMESTER II
MIM 201 : Foundations of Analysis
1. A Taste of Topology: Metric space concepts, Compactness, Connectedness,
Coverings, Cantor sets.
2. Functions of a Real Variable: Differentiation, Reimann integration,
Series.
3. Function Spaces: Uniform convergence and C0[a, b], Power series, Compactness
and equicontinuity in C0.
4. Multivariate Calculus: Derivatives, Higher derivatives, Smooothness
classses, Implicit and inverse functions.
5. Lebesgue Theory: Outer measure, Measurability, Regularity, Lebesgue
integrals.
Prescribed Book:
• C. C. Pugh, Real Mathematical Analysis, Springer, New Delhi, 2004.
(Ch. 2: Sec 1 to 5; Ch. 3, Ch. 4: Sec 1 to 5; Ch. 5: Sec 2 to 5; Ch. 6:
Sec 1 to 4.)
Reference Books:
• N. L. Carothers, Real analysis, Cambridge University Press India, 1999.
• H. Royden, Real Analysis, Third Edition, Prentice Hall of India, 1988.
9
MIM 202 : Complex Analysis
1. Pre-requisites:
(a) Topological and Analytical Preliminaries: Point sets in the
plane, sequences, compactness, stereographic projection, continuity.
(b) Elementary Functions: Exponential functions, mapping properties,
logarithmic function, complex exponents.
2. Analytic Functions: Cauchy-Riemann Equations, analyticity, harmonic
functions.
3. Power Series: Sequences, uniform convergence, Maclaurin and Taylor
series, operations on power series.
4. Complex Integration and Cauchy’s Theorem: Curves, parameterizations,
line integral, Cauchy’s Theorem.
5. Applications of Cauchy’s Theorem: Cauchy’s integral formula, Cauchy’s
inequality and applications, maximum modulus theorem.
6. Laurent Series and Residue Theorem: Laurent series, classification
of singularities, evaluation of real integrals, argument principle.
7. Bilinear Transformations and Mappings: Basic mappings, linear
fractional transformations, other mappings.
Prescribed Book: S. Ponnuswamy and Herb Silverman, Complex Variables
with Applications, Birkh¨auser.
Reference Book: J. B. Convey, Functions of one complex variables, Narosa
Publishing House.
10
MIM 203 : Data Structure with C
1. Basic Concepts : Overview,Pointers and Dynamic memory Allocation,
Algorithm Specification, Data Abstraction, Performance Analysis.
2. Arrays and Structures : Arrays, Dynamically allocated arrays, Structures
and Unions, Polynomials,Sparse Matrices, Representation of multidimensional
arrays, Strings.
3. Stack and Queues : Stacks, Stacks using Dynamic Arrays, Queues, Circular
Queues using Dynamic Arrays, Evaluation of Expressions, Multiple
Stacks and Queues.
4. Linked Lists : Singly Linked Lists and Chains, Representing Chains in
C, Linked Stacks and Queues, Polynomials, Additional List Operations,
Sparse Matrices, Doubly Linked Lists.
5. Trees : Introduction, Binary Trees, Binary Tree Traversals, Additional
Binary Tree Operations, Threaded Binary Trees, Heaps, Binary Search
Trees, Selection Trees, Forests, Counting Binary Trees.
6. Graphs : The Graph Abstract Data Type, Elementary Graph Operations,
Minimum Cost Spanning Trees, Stortest Paths and Transitive Closure,
Activity Networks.
7. Sorting : Motivation, Insertion Sort, Quick Sort, How fast we can sort?,
Merge Sort, Heap Sort, List and Table Sorts.
8. Hashing : Introduction, Static Hashing, Dynamic Hashing, Bloom Filters.
Prescribed Book :
• Horowitz, Sahni, Anderson-Freed, Fundamentals of Data Structures
in C, 2nd Edition (Universities Press)
Reference Books :
• Donald E. Knuth, The Art of Computer Programming, Volume 1,
Third Edition ( Pearson Education )
• Seymour Lipschutz, Data Structures (Tata McGrawHill).
• Aaron M. Tenenbaum, Data Structures Using C (Pearson Education).
11
MIM 204 : Progremming in C++
1. Introduction : Declarations, const declartions, Namaespaces, cin and
cout, Loops, Functions, references, Function Overloading, Function with
default parameters, passing arguments with reference and pointers, new
and delete operators.
2. Classes : Procedural and object-oriented programming, the class, public
and private, implementing class member functions, inline functions, constructor
and desructor, const memeber fuctions, static members, ”‘this”’
pointer an array of objects, class scope.
3. Working With Classes : class in class, initialiser list, operator overloading,
friend functions, automatic conversions, conversion fuctions, copy
constructor, assignment operator, classes and dynamic memeory.
4. Class Inheritance : Beginning with simple base, inheritance is a relation,
declaring derived classes, protected members, virtual funtions, pure
virtual functions, abstract classes, public, protected and private inheritance,
operators new and delete, virtual base, multiple inheritance.
5. Templates : Generic programming, template functions, defining a class
template, using a template class, using template with family of classes,
template versality, template specilization, inheritance.
6. Exception Handling : Exception, the exception mechanism, exception
versality, multiple try blocks, exception and classes, exception and inheritance,
the exception class.
7. Files and Streams : cin, cout cerr, clog streams, operators >> and
<<, formating output, manipulators, reading string and single character,
stream states, Files, ifstream, ofstream and fstream classes, file modes,
text and binary files, overloading << and >> operators for user defined
operators, user defined manipulators.
12
Prescribed Book:
• Stephen Prata, C++ Primer Plus (Tecmedia).
Reference Books:
• Bruce-Eckele, Thinking in C++ (vol-I and vol -II).
• B. Stoustroup, Programming Language C++ .
13
MIM 205 : Differential Equations
1. Prerequisites: Linear equations of the first order.
2. Linear equations with constant coefficients : Second order homogeneous
equations, Initial value problems, Linear dependence and independence,
Nonhomogeneous equations of n-th order, Algebra of constant
coefficients.
3. Linear equations with variable coefficients : Initial value problems,
Solutions of the homogeneous equation, Wronskian and linear independence,
Reduction of order, Nonhomogeneous equations, Legendre equation.
4. Linear Equations with regular singular points : Euler equation,
Second order equation with regular singular points, Exceptional cases,
Bessel equation.
5. Existence and uniqueness of solutions to first order equations:
Separation of variables, exact equations, Method of successive approximations,
Lipschitz condition, Approximation to and uniqueness of solutions.
6. Existence and uniqueness of solutions to systems and n-th order
equations: Complex n-dimensional space, Systems as vector equations,
Existence and uniqueness of solutions to systems, Existence, Uniqueness
for linear systems and equations of order n.
Prescribed Book:
• E. A. Coddington, An Introduction to Ordinary Differential Equations
(Prentice- Hall).
Reference Book: G. F. Simmons and S. G. Krantz, Differential Equations
(Tata McGraw-Hill).
14
SEMESTER III
MIM 301 : Web Programming
1. Web Programming HTML Programming CSS JavaScript DOM DHTML
2. Extensible markup Language (XML) The Purpose and Nature of
XML XML Syntax and Structure Rules XML Document Type Declaration
(DTD) XML Schema XSL Extensible Stylesheet Language XPath XQuery
XML Parsers Java and XML
3. AJAX Introduction to Ajax Ajax Architecture XMLHttpRequest Ajax
Framework and DOM Ajax using HTML,CSS,JavaScript
15
MIM 302 : Discrete Structures
1. Order Relations and Structures: Partially ordered set, Extremal Elements
of Partially ordered sets,Lattices, Finite boolean algebras, Functions
on boolean algebras, Circuit designs.
2. Trees: Trees,Labeled Trees, Tree Searching, Undirected Trees, Minimal
Spanning Trees
3. Topics in Graph Theory: Graph, Euler Paths and Circuits, Hamiltonian
Paths and Circuits, Tranport Networks, Matching Problems, Coloring
Graphs,
4. Combinatorics: Combination, Permutation, Generating Functions, Odinary
and Exponential Generating Functions, Recurrence Relation, Methods
of Solution of Recurrence Relatiion , Substitution Method, Characteristic
Method, Generating Function Method, Principle of Inclusion and
Exclusion.
Prescribed Book:
• Kolman, Busby, Ross, Discrete Mathematical Structures,Fifth
Edition (Pearson Education).
• Purna Chandra Biswal, Discrete Mathematics and Graph Theory,
Second Edition (PHI.).
Reference Book: Alan Tucker, Applied Combinatorics, Forth Edition
(John Willey).
16
MIM 303 : Theory of Computer Science
1. Propositions and Predicates: Propositions (or statements), Normal
Forms of Well-formed Formulas, Rules of Inference for Propositional Calculus
(Statement Calculus), Predicate Calculus, Rules of Inference for
Predicate Calculus.
2. Mathematical Preliminaries: Sets. Relations and Functions, Graphs
and Trees, String and Their Properties, Principal of Induction, Proof by
Contradiction, Supplementary Examples.
3. The Theory of Automata : Definition of an Automaton, Description
of a Finite Automaton, Transition Systems Properties of Transition Functions,
Acceptability Systems, Nondeterministic Finite Stare Machines,
The Equivalence of DFA and NDFA, Mealy and Moore Models, Minimization
of Finite Automata, Supplementary Examples
4. Formal Languages:Basic Definition and Examples, Chomsky Classification
of Language, Languages and Their Relation, Recursive and Recursively
Enumerable Set, Operations on Language, Language and Automata,
Supplementary Examples.
5. Regular Sets and Regular Grammars: Regular Expressions, Finite
Automata and Regular Expressions, Pumping Lemma for Regular Set,
Application of Pumping Lemma, Closure Properties of Regular Sets Regular
Sets and Regular Grammars.
6. Context Free Languages: Context-free Languages and Derivation Tree,
Ambiguity in Context-free Grammars Simplification of Context-free Grammars,
Normal Forms for Context-free Grammars, Pumping Lemma for
Context-free Languages, Decision Algorithms for Context-free Languages.
7. Pushdown Automata:Basic Definitions, Acceptance by pda, Pushdown
Automata and Context-free Languages, Parsing and Pushdown Automata,
Supplementary Examples.
8. Turing Machines and Linear Bounded Automata: Representation
of Turing Machine, Language Acceptability by Turing Machines, Design
of Turing Machines, Descriptions of Turing Machines.
Prescribed Book:
• K. L. P. Mishra and N. Chandasekaran, Theory of Computer Science
(PHI Learning Private Ltd).
17
MIM 304 : Design and Analysis of Algorithms
1. Mathematical Foundation: Growth Functions, Summations, Recurrences
Substitutions, Iterations, Master Methods, Counting and probability
.
2. Sorting :Heap Sort, Quick Sort, Merge Sort, Sorting in linear Time,
Medians and Order Statistics.
3. Dynamic Programming : Matrix chain Multiplication, longest common
subsequence, optimal polygon triangularisation.
4. Greedy Algorithm.
5. Graphs : Traversals, Topological sort, Minimum spanning trees, single
source shortest path, All pair shortest path, Maximum flow problems.
6. Sorting Networks : Comparision, bitonic sort and merge sort networks.
7. Parallel Algorithms : CRCW, EREW algorithms efficiency sorting linear
system problem, Matrix Operations, Strassens Algorithm and matrix
inversion.
8. FFT :Polynomials DFT, FFT.
9. Number Theoretic Algorithm : Rabin - Karp, KMP, Bower - Moore
algorithms.
10. Geometric Algorithms : Finding convex hall, closes pair of points,
linear programming problem.
11. NP Completeness : P and NP classes, NP completeness and reducibility.
12. Approximation Algorithms : Vertex cover problem, traveling salesman
problem, set covering and subset sum problems.
Prescribed Book:
• T. H Coreman, Leiserson, Rivest, Introduction to Algorithms .
18
MIM 305 : JAVA PROGRAMMING
1. Introduction to Java Programming - Overview, Java Tools, Java
Byte Code
2. Elementary Programming Concepts : Variables and Identifiers, Java
keywords, Data Types, Operators, Expression, Constants, Statements,
Arrays
3. Classes and Packages : Defining classes, Static Members, Using packages,
Access Specifiers, Constructors, Finalisers referencing objects
4. Inheritance, nested and inner class : Extending classes, Abstract
Class Interface, Super Keyword, Final classes, Constructors and Inheritance,
Dynamic Binding, Overriding methods
5. Exception and Input and Output : Byte streams, Character streams,
File i/o basics, Introduction to exception, Try and catch block and finally
block, Inbuilt Exception.
6. String Handling and Exploring Java.lang : String Operations, Character
Extractions, Data Conversions, Modifying strings.
7. Applet and Event Handling and Controls
8. Input and Output package : Object serialization, reader and writer
9. Swings : - Layout Manager Layout Manager swing Controls Components
Organizers, Jlish, Jtree, Jtables, Dialogue, File chooser, color chooser.
10. JDBC : The design of JDBC, JDBC programming concepts making the
connection, statement and result set class, Executing SQL commands,
Executing Queries.
11. Multithreading : Running multiple threads, The runnable interface
Threads priorities Daemon, Thread States, thread groups Synchronization
and Interthread Communication Deadlocks. Prescribed Book:
• Herbert Schildt, A Complete Reference Java 2.
19
MIM 401 : Field Theory
1. Prerequisites: Definitions and basic properties Rings and fields, Ideals
and homomorphisms, Characteristic of fields, Euclidean domains, Unique
factorization, Polynomials.
2. Field Extensions: The degree of an extension, Extensions and polynomials,
Polynomials and extensions.
3. Applications to Geometry: Ruler and compass construction, An algebraic
approach.
4. Splitting Fields.
5. Finite Fields.
6. The Galois Group: Monomorphisms between fields, Automorphisms,
Groups and subfields, Normal extensions, Separable extensions, The Galois
correspondence, The fundamental theorem, An example.
7. Equations and Groups: Solution by radicals of quadratics, cubics and
quartics. Cyclotomic polynomials, cyclic extensions.
8. Groups and Equations: Insoluble quintics, General polynomials.
9. Prescribed Book:
• J. M. Howie, Fields and Galois Theory, Springer Undergraduate
Mathematics Series, 2006.
(Chapters 1 to 8 and Chapter 10).
Reference Books:
• M. Artin, Algebra, Prentice-Hall, Englewood Cliffs, N.J., 1991.
• P. B. Bhattacharya, S. K. Jain and S. R. Nagpaul, Basic Abstract
Algebra, Second Ed., Cambridge University Press, Cambridge,
1995.
20
MIM 402 : Differential Geometry
1. Graphs and Level Sets
2. Vector Fields
3. The Tangent Space
4. Surfaces
5. Vector Fields on Surfaces;Orientation
6. The Gauss Map
7. Geodesics
8. Parallel Transport
9. The Weingarten Map
10. Curvature of Plane Curves
11. Arc Length and Line Integrals
12. Curvature of Surfaces
13. Parametrized Surfaces
14. Local Equivalence of Surfaces and Parametrized Surfaces
15. Surface Area and Volume
16. The Exponential Map
17. The Gauss-Bonnet Theorem
21
Prescribed Book:
• J. A. Thorpe, Elementary Topics in Differential Geometry, Springer,
Second Edition
(Chapters 1 to 12 and Chapter 14, 15, 17, 19, 22).
22
MIM 403 : Data Base Management Systems I
1. Database Concepts
2. Relational Algebra
3. Database Design Concepts
4. ER Diagrams and Normalization SQL
23
MIM 404 : MS.NET
1. Introducing .NET Platform: .NET and Windows DNA .NET Architecture
2. Features of .NET Platform: Multilanguage Support, Platform and
Processor Independence, Memory Management, Versioning, Deployment,
Interoperability with Unmanaged Code.
3. .NET Architecture: .NET Runtime, Managed/Unmanaged Code, Intermediate
Language, Common Language Specification/Common Type
System, .NET Base Class Library (BCL), Assemblies, Metadata, Assemblies
and Modules, Assembly Cache, Reflection, Just In Time Compilation,
Garbage Collection, Object Oriented in .NET.
4. Introducing C hash Programming: Data Types, Control Structures,
Properties and Indexers, Delegates and Events, Exception Handling, Basics
of Inheritance.
24
MIM 405 : Computer Networks
1. Introduction to Networking Hardware Architecture Topologies, Media,
Devices Transmission Techniques Twisted Pair, Coaxial Cable, Fiber
optics
2. The OSI Reference Model Protocol Layering, TCP/IP Model, OSI vs.
TCP/IP
3. Common Network Architecture Connection oriented N/Ws Connectionless
N/Ws Example of N/Ws-P2P, X, 25, ATM, Ethernet Wireless
LANs - 802.11, 802.11x, Gigabit Wireless Transmission Switching Circuit
Switching, Message Switching, Packet Switching
4. Local Area Networks Components and Technology, Transmission Protocol
and Media
5. IP Addressing Routing IP addresses Network part and Host Part
Network Masks, Network addresses and Broadcast addresses, Address
Classes, Loop back address, IP routing concepts,Routing Tables, Stream
and Packets TCP - a reliable pipe, TCP Connection IPV6: The next
generation Protocol.
6. Domain Network Services (DNS) Domain Names, Authoritative Hosts,
Delegating Authority, Resource Records, SOA records, DNS protocol,
DHCP and Scope Resolution
7. Network Applications Http, MIME, SMTP, POP
8. Network security Packet filtering, Encryption, Virtual Private network,
Digital signatures
• Prescribed Book :
• Andrew S. Tanenbaum , Computer Networks 4e, PHI, India.
Reference Books:
1. Douglas E. Comer, Computer Networks and Internets with Internet
Applications , Pearson Education, forth Edition
2. William R. Cheswick,, Firewalls and Internet Security 2nd Edition
Pearson Education.
25
SEMESTER V
MIM 501 : Coding Theory
1. Error detection: correction and decoding: Communication channels,
Maximum likelihood decoding,Hamming distance,Nearest neighbour
/ minimum distance decoding, Distance of a code.
2. Linear codes: Vector spaces over finite fields, Linear codes, Hamming
weight, Bases of linear codes, Generator matrix and parity check matrix,
Equivalence of linear codes, Encoding with a linear code,Decoding of linear
codes, Cosets, Nearest neighbour decoding for linear codes, Syndrom
decoding.
3. Cyclic codes: Definitions, Generator polynomials, Generator and parity
check matrices, Decoding of cyclic codes, Burst-error-correcting codes.
4. Some special cyclic codes: BCH codes, Definitions, Parameters of
BCH codes, Decoding of BCH codes.
Reference Books:
1. San Ling and Chaoing xing , Coding Theory- A First Course .
2. Lid and Pilz, Applied Abstract Algebra - 2nd Edition
26
MIM 502 : Probability Theory
1. Introduction to Discrete Probability : Intuitive concepts: probability
of an event as a measure between 0 and 1; random variable; probability
distribution; frequency interpretation of probability; random numbers;
coins, dice, and other games; simulations; odds; historical development of
probability; random walks.
2. Formal concepts: sample space, outcomes, and events; random variable;
discrete distribution functions and axioms of probability; unions,
intersections, and complements; properties of probabilities, principle of
inclusion and exclusion; tree diagrams; uniform distributions over finite
sets, symmetry; infinite sample spaces with discrete probabilities.
3. Introduction to Continuous Probability : The intuitive problems
with probabilities over space (line, plane, Rn in general). Monte Carlo
simulations, Buffon’s needle. Formal concepts: density function for a continuous
random variable; integration; cumulative distribution functions;
derivatives; exponential density function;
4. Conditional Probability : Intutive concept of conditional probability;
formal definition of conditional probability; Bayes’ formula for inverting
conditional probabilities; independent events; joint distribution functions;
independent random variables; independent trials. Conditional density
functions for continuous distributions; the beta distribution
5. Distributions and Densities : Uniform continuous distributions; geometric
distribution; Poisson distribution; exponential and gamma distributions;
introduction to queueing theory; normal (Gaussian) distribution;
Chi-squared distribution
6. Expected Value and Variance : Expected value for discrete random
variables, expectation; linearity of expectation; expectation of independent
random variables; conditional expectation; variance and standard
deviation; variance of various distributions. Expectation and variance for
continuous random variables.
7. Sums of Random Variables : Analysis of sums of independent random
variables with identical distributions, that is, independent trials.
8. Law of Large Numbers : Chebychev inequality, law of averages, law
of large numbers.
9. The Central Limit Theorem :The central limit theorem for Bernoulli
trials, binomial distributions again, the normal distribution, the general
central limit theorem.
Prescribed Book:
27
• Charles M. Grinstead and J. Laurie Snell, Introduction to
Probability, the American Mathematical Society, 1997.
(Chapters 1 to 8 and Chapter 10).
28
MIM 503 : Advanced Data Base Management Systems II
1. Advanced Database Concepts
2. Database Architecture
3. PL/SQL
29
MIM 504 : Software Engineering
1. Introduction To Software Engineering
Definition, System Concepts,
Types of System, Element of System
A generic view of Software Engineering
Characteristics of software
McCall’s Quality Factors
Software Process
Challenges Facing Software Engineering
2. Requirement Analysis
Definition of System Analysis
Fact Finding Techniques
Requirement Anticipation, Investigation
Feasibility Study
User Requirements
System Requirement Specification
Requirements Engineering
Requirements Validation
System Requirement Specifications (SRS)
3. Analysis and Design Tools
Decision Tree and Decision Tables
Data Flow Diagrams [Physical and Logical]
Data Dictionary
Input and Output Design
(Case Study: Minimum two case studies on each of the above topic should
be covered.)
4. Software Development Methodologies
System Development Life Cycle. - Classical Model
Waterfall Model
Spiral Model
Prototyping Approach
Agile Methods
Rapid Application Development
5. System Testing
Testing and Debugging Definition.
Verification and Validation
Testing Objectives and Principles.
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Testing Strategies
- Black Box Testing.
- White Box Testing
- Performance Testing
- User Acceptance Testing
- Stress Testing
Test Case Design
Report Test Result
Test Automation
(Case Study: Minimum two case studies on test case design should be
covered.)
6. System Maintenance
Importance of Maintenance
Software Maintenance
Types of Maintenance
Maintenance Side Effects/Ripple Effects
Re-engineering
Reverse Engineering
Reference Books:
1. Ian Sommerville , Software Engineering , 7th/8th Edition [Pearson Education]
2. Roger S. Pressman, Software Engineering - A Practitioner’s Approach
7th Edition - [McGraw Hill International Edition]
3. James Senn, Analysis of Information Systems
4. Pathasarthy and Khalskar, System Analysis and Design.
Ch 1, -:Reference Book 1,2
Ch 2 -:Reference Book 1,2
Ch 3 -:Reference Book 1,3 (case studies from Ref Book 3)
Ch 4 -:Reference Book 2
Ch 5 -:Reference Book 2
Ch 6 -:Reference Book 4
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MIM 505 : Advanced JAVA
1. JAVA Basic Reveiws
Java streaming - Networking - Event handling - Multithreading - Byte code
Interpretation - Customizing application - Data Structures - Collection
classes.
2. Distributed Computing
Custom sockets - Remote Method Invocation - Activation - Object serialization
-Distributed garbage collection - RMI - IIOP - Interface definition
language - CORBA - JINI overview.
3. JAVA Beans And Swing
Bean concepts - Events in bean box - Bean customization - Persistence -
Application - deployment using swing - Advanced swing techniques - JAR
file handling.
4. JAVA Enterprise Applications
JNI - Servlets - Java Server Pages - JDBC - Session beans - Entity beans
- Programming and deploying enterprise Java Beans - Java transactions.
5. Related JAVA Techniques
Java Media Frame work - 3D graphics - Internationalization - Case study
- Deploying n-tier application, E- commerce applications.
Reference Books:
1. Deitel and Deitel , Java How to program, Prentice Hall , 4 th Edition,
2000.
2. Gary Cornell and Cay S. Horstmann, Core Java Vol 1 and Vol 2 ,
Sun Microsystems Press, 1999.
3. Stephen Asbury, Scott R. Weiner, Wiley, Developing Java Enterprise
Applications, 1998.
32
SEMESTER VI
Industrial Training
33
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