Home / Syllabus / M.Tech / M.Tech CS

M.Tech CS

Click Here to Download M.Tech CS Syllabus



SECTION A: Discrete Mathematical Structure


Algebraic Structures:

Semigroups, Monoids, Groups, Substructures and Morphisms, Rings, Fields, Lattices, distributive, modular and complemented lattice, Boolean Algebras.


Formal Logic:

Propositional logic: Predicate logic, limitations of predicate logic, universal and existential quantification; modus ponens and modus tollens. Proof technique: Notions of Implication, converse, inverse, contra positive, negations and contradiction


Introduction to Counting

Basic counting techniques, principles of inclusion and exclusion, permutations, combinations, summations, probability, Recurrence Relations, Generating Functions.


Introduction to Graphs:

Graphs and their basic properties, Eulerian and Hamiltonian walk, graph colouring, planar graph, enumeration, vector graph



  1. Kenneth Rosen, Discrete Mathematics and its application, TMH
  2. C.L. Liu , Element of Discrete mathematics ,TMH
  3. D.B. West ,Introduction to Graph Theory ,PHI
  4. J.P.Trebley and R.Manohar , Discrete Mathematical Structure with Applications to computer science, TMH


SECTION B: Data Structures and Algorithm


Algorithm and Complexity, Notation of complexity. Sorting and Divide and Conquer Strategy: Merge-Sort, Quick Sort with average case analysis. Heaps and heap sort. Lower bound on comparison –based sorting


Advanced search Structures: Representation, Insertion and Deletion operations on Red-Black trees, B-Trees, Hashing

Dynamic programming , matrix multiplications, longest common subsequence, Greedy method, Knapsack Problem, 8 queens Problems , Backtracking, branch and bound , Fibonacci Heap

Graph Algorithm

Graphs and their representation. BFS, DFS, Minimum spanning trees, shortest paths Kruskal and Prim’s algorithms, connected components.



1.Coreman ,Leiserson and Rivest, Algorithm , MIT Press

2.E. Horowithz and S. Sahni , Fundamentals of Computer Algorithm, Galgottia

3.Donald Knuth,, The Art of Computing Programming –vol-1 and 3 ,Pearson

4.V.Aho, J.E.Hopcroft and Ullman, Design and Analysis of Computer Algorithm ,Addison Wesley

5.K. Melhorrn, Datastructures and Algorithms, Vol II Springer Verlag


SECTION C: Theory of Computation

Regular Languages

Alphabet Langauges and grammars, Regular grammars, regular expressions and finite auotomata, deterministic and non-deterministic. Closure and decision properties of regular sets. Pumping lemma of regular sets. Minimization of finite automata.

Context free Language

Context free grammars and pushdown automata. Chomsky and Griebach normal forms. Cook, younger and Kasami Algorithm, Ambiguity and properties of context free languages pumping lemma. Deterministic pushdown automata. Closure properties of deterministic context free languages.

Turing Machine

Turing machines and variation of turing machine model, Halting problem, Universal turing machine, Type 0 Languages. Linear bounded automata and context sensitive languages. Turing Computable functions, Church Turing hypothesis. Recursive and recursively enumerable sets, Universal Turing machine and undecidable problems, Rice’s Theorems for RE sets, Undecidability of Post correspondence problem. Valid and invalid computations of Turing machines, undecidable properties of context free language problems, Basics of Recursive function theory.


1. C. Papadimitrou and C.L. Lewis Elements of Theory of Computation,PHI

2. J.E. Hopcroft and J.D. Ullman, Introduction to Automata Theory,Languages of Computations, Addison-Wesley




Computer Organization


Unit I                         

Basic Computer Organization and design:  Instruction set Principles: Classifying Instruction set Architectures, Memory Addressing , Type and Size of operands, Operations in the instruction set; Instruction Codes, Computer Register, Register , Register Transfer Language, time and Control , Instruction Cycle, Memory references instructions, Input Output and Interrupt, Design of Basic Computer and Arithmetic and Logic Unit.

Micro programmed Control: Control Memory, address Sequencing, Design of Control unit

Central Processing Unit: General Register Organization, Stack Organization, Instruction format, Data Transfer and manipulations program control.


Unit 2                                                                                               

Computer Arithmetic: Addition, Subtraction, Multiplication and Division Algorithms. Floating point arithmetic operation, IEEE-754, Decimal arithmetic unit and Decimal Arithmetic operations.


Unit 3

Input- Output Organization:  Peripheral Devices, Input–Output Interface, Asynchronous data transfer, Modes & Transfer, Priority interrupt, Direct Memory access, I/O Performance Measures, Benchmarks of Storage Performance and Availability.

Memory Organization: Memory Hierarchy, Main Memory, Auxiliary Memory, Associative Memory, Shared Cache memory

Cache Memory and its performance, Reducing Cache Miss Penalty, Reducing Miss Rate, Reducing cache Miss Penalty or Miss Rate via Parallelism, Reducing Hit Time, Virtual Memory

Computer Architecture

Unit 4

Principle of Scalable Performance:  Performance metric and measures, speedup performance laws, scalability analysis and approaches. Parallel processing and application

Advanced Processor Technology: Design space of processors, Instruction set architectures, CISC, RISC

Pipelining: Linear and Non-Linear pipeline processors, Instruction pipeline design, arithmetic pipeline design, super scalar and super pipeline design, Superscalar and Vector processors.

Unit 5

Multiprocessor system Interconnects, Cache coherence and synchronization and mechanisms, message passing mechanism

System Interconnect Architecture: network property and routing, static connection network and dynamic connection network.


1. Mano M: computer System Architecture –PHI 3rd Edition

2. Henessy J L, Patterson D A: Computer Architecture: A Quantitative approach – 3rd (Elsevier)

3. Kai Hwang: Advanced Computer Architecture TMH

4. Hamacher V C, et al: Computer Organization – 4 Edition (McGraw Hill)



Unit I                                                                                                            

Operating System: Structure, Components and Services, Time Sharing and Real-Time System, process Management, Concurrency Critical Section, Semaphores, InterProcess Communication, Process scheduling producer/ consumer and reader writer problem, Concept of Distributed and Real-Time operating system.

Unit II                                                                                                             

CPU Scheduling: Concept and Scheduling algorithm, multiprocessor scheduling, deadlock prevention, avoidance and detection, recovery from deadlock.

Memory Management: Multiprogramming with fixed partition, multiprogramming with variable partition, segmentation virtual memory and demand paging. Page Replacement Policies Thrashing and pre-paging

Unit III                                                                                                          

I/O Management, File System:  File organization and access mechanism, file sharing and file directories, Case Study of Linux Kernel- File Management, Memory Management and Process Management

Unit IV                                                                                                           

Overview of Database Management System,  Data Model- Relational Algebra, Relational Calculus –Tuple Relation Calculus and Domain Relation Calculus, Normal Forms


Unit V                                                                                                             

Deadlock – Prevention and avoidance, Transaction and Data Recovery Method. Introduction of Object Oriented DBMS, Object Relational DBMS, Distributed DBMS and Data mining & Data warehousing


1. A.S. Tanenbaum: “Modern Operating System” , Prentice Hall

2. William Stalling: “Operating System” Maxwell McMellon

3. J. Peterson ,A. Silberschatz  and P. Galvin: Operating System Concepts, Addison Wesley ,3rdedition

4. Milenkovic :Operating System Concept ,TMH

5. Korth and Silberschatz :Database System Concept; Second Edition, Tata McgrawHill,1991

6. R. Elmasri and N.Navathe :Benjamin Cumming, Fundamental of Database System , 2nd 1994

7. Boveti et al:Understanding the Linux Kernel 3rd O’Reilly

8.C.J. Date Database management Systems.



Unit-I  Overview of Wired and Wireless DataNetworks                 

Review of Layered Network Architecture ,ISO-OSI and TCP/IP Network Model Datagram Networks and Virtual Circuit Networks, Point to Point and Point to Multipoint Networks Layer 2 Switches.

IEEE 802.3U(Fast Ethernet) and IEEE 802.3Z(Gigabit Ethernet)

Virtual LAN

Wireless LAN: IEEE 802.11, Bluetooth

Broadband Wireless LAN : 802.16, WIMAX

Unit-II Internetworking                                                                              

Review of IP Addressing and Routing

Internet Architecture :Layers 3 Switch, Edge Router and Core Router

Overview of Control Plane, Data Plane ,Management Plane

Internet Routing Protocols: OSPF, BGP

Broadcast and Multicast Routing:  Flooding, Reverse Path Forwarding, Pruning, Core based trees, PIM

Mobility Issues and Mobile IP

Adhoc Routing: Dynamic Source Routing, Destination Sequenced Distance Vector Routing, Hierarchial Routing

Signalling :Introduction ,ICMP,LDP and MPLS Architecture

Unit III Transport Layer Protocols                                                             

Process to Process Delivery

Review of UDP, TCP

SCTP Protocol: Services, Features, Packet Format, Association, Error Control Wireless TCP and RTP, RTCP

Real Time Application: Voice and Video over IP

Unit-IV Traffic Control and Quality of Service                                

Flow Control: Flow Model, Open Loop: Rate Control, LBAP, Closed Loop: Window scheme, TCP and SCTP Flow Control

Congestion Control: Congestion Control in packet networks, ECN and RED Algorithm, TCP and SCTP Congestion Control

Quality of Service: IP Traffic Models, Classes and Subclasses, Scheduling: GPS, WRR, DRR, WFQ, PGPS, VC Algorithm; Integrated Services Architecture, Differentiated Services Architecture, RSVP and RSVP- TE

Traffic Management Framework: Scheduling, Renegotiation, Signaling, Admission Control, Capacity Planning


Security Issues,

Symmetric Encryption: DES , TripleDES ,Modes, AES

Public Key Encryption: RSA , Diffie Hellman, Elliptic Curve

Hashing :MDS , SHA-1 , DSA

Protocols: Kerberos,SSL/TLS, IPSec


  1. Srinivasan Keshav” An Engineering Approach To Computer Networking “,Pearson
  2. W. Richard Stevens “TCP/IP ILLustrated “-Vol1 Pearson
  3. D. Bertsekas , R Gallagar ,”Data Networks and Internets” PHI
  4. W. Stalling “High Speed Networks  and Internets”, Pearson
  5. W. Stallings, “ Wireless Communication and Networks” Pearson
  6. W. Stallings,” Cryptography and Networks Security”,Pearson
  7. A. Tanenenbaum, “ Computer Network”,PHI




Appendix II: Streams and their Courses

1. Distributed Stream

Distributed Computing

 Basic Concepts                                                                                                            

Characterization, Resource Sharing, Internet Implementations, Name Resolution, DNS

Computation: Full Asynchronism and Full Synchronism, Computation on Anonymous Systems, Events, Orders, Global States, Complexity

Distributed Synchronization                                                                          

Processes and Threads, IEEE POSIX.1c

Mutual Exclusion: Classification, Algorithms, Mutual Exclusion in Shared Memory; Clock Synchronization, NTP

Distributed Deadlock: Detection Methods, Prevention Methods, Avoidance Methods

BSD Sockets                                                                                                       

TCP/IP Model, BSD Sockets Overview, TCP Sockets and Client/Server, UDP Sockets and Client/Server, Out of Band Data, Raw Sockets, PING & TRACEROUTE Programs, Routing, Multicasting using UDP Sockets


Distributed OS                                                                                                  

Communication between distributed objects, RPC Model and Implementation Issues, Sun RPC, Events and Notifications, Java RMI and its Applications

CORBA Architecture: Introduction and Applications

Distributed File System Design and Case Studies: NFS, Coda, Google FS

Distributed Databases

Introduction, Structure, Data Models, Query Processing, Transactions, Nested Transactions, Atomic Commit Protocols, Transaction Recovery, Transactions with replicated data, Concurrency Control Methods, Distributed Deadlocks


1. Tanenbaum, “Distributed Systems”, Pearson

2  W Richard Stevens, “UNIX Network Programming Vol 1 & 2”, Pearson

3. Sinha, ”Distributed Operating Systems”, Prentice Hall of India/ IEEE Press

4. Barbosa, “Distributed Algorithms”, MIT Press

5. Ceri, Palgatti,”Distributed Databases”, McGraw-Hill

Mobile Computing


Basic Concepts, Principles of Cellular Communication, Overview of 1G, 2G, 2.5G, 3G and 4G technologies, GSM and CDMA Architecture, Mobility Management, Mobile Devices: PDA, Mobile OS: Palm OS, Mobile Linux Initiative, Symbian.

Process Migration

Kernel Support for Migration: Mobility Enhancement in modern UNIX Systems, Transparent Process Migration Design Alternatives, Removing Process Migration Bottlenecks, Task Migration Issues

User Space support for Migration: Checkpointing, Process Migration

Data Issues

Workload Balancing Strategies in migration, Process lifetime distributions for dynamic load balancing, Disconnected Operations in Coda File System, Weak Connectivity for Mobile File Access, Weakly Connected Replicated Storage System.

Mobile Data Networking                                                                               

Mobile IPv4 and Mobile IPv6, Mobile Internetworking Architecture, Internet Mobility Issues, Route Optimization, Performance of Wireless TCP, GPRS Services, IP over CDMA

Mobile Agents

Basic Concepts, OS support for Mobile Agents, Java Aglet API, AGENT TCL, Network Aware Mobile Programs, Mobile Objects and Agents, OMG MASIF Framework, Mobile Agent Security Issues


1.       Richard Wheeler, ”Mobility: Processes, Computers and Agents”

2.       Charles Perkins et.al.,”Mobile IP: Design Principles and Practices”, Pearson

3.       Tomasz Imielinski, “Mobile Computing”, Springer Verlag


 Analysis and Design of Real-Time Systems

  Basic Concept

IEEE Definition of Real-Time Systems, Characterization of Real-Time Systems, Process, IEEE POSIX.1c Threads, Tasks and Priorities, Pre-emptive and Non-Preemptive Tasks, Soft and Hard Real-Time Systems


Scheduling Paradigms: Priority Driven, Time Driven, and Share Driven

Priority Driven Scheduling of Periodic, Aperiodic and Sporadic tasks

Static Priority Scheduling: Rate Monotonic Scheduling Algorithm and its exact analysis using Response Time Test

Dynamic Priority Scheduling: Analysis of EDF and LLF Algorithms and their open issues


Specification and Verification

Modeling Real-Time System, Requirement Specification, Assumptions, Design, Basic Duration Calculus, Specification of Scheduling Policies, Probabilistic Duration Calculus, Applications of Duration Calculus


Introduction, Requirement of Real-Time Guarantees in industrial applications, Soft and Hard RTOS, Commercial RTOS Examples

IEEE POSIX.1b: Priority Scheduling, Real-Time Signals, Timers, Binary Semaphores, Counting Semaphores, MUTEX operations and usage, Message Passing, Message Queues operations and usage, Shared Memory, Synchronous and Asynchronous I/O, Memory Locking

RTOS Services, Case Studies of Real Time Capabilities of Linux Kernel 2.6, RTLinux and VxWorks


Real-Time Application Design, Real-Time Application Interface (RTAI), Real-Time Java, Real-Time Communications and Networking


1. JWS Liu, “Real-Time Systems”, Pearson

2. Mathai Joseph, ”Real-Time Systems: Specification, Verification and Synthesis”, Prentice-Hall

3. Qing Li, “Real-Time Concepts for Embedded Systems”, CMP Books

4. Krishna, Shin, “Real-Time Systems”, TMH

5. Burns, Wellings, “Real-Time Systems and Programming Languages”, Pearson

Dedicated System Design


Review of Digital Computer & Digital Arithmetic                             

Algorithm and Algorithmic Notation, Timing, Synchronization and Memory, Fixed and Floating point Arithmetic operations, Arithmetic primitives, Sequential and Distributed Arithmetic.

Hardware Elements and Hardware Design using VHDL

Gates, Flip-Flops, Registers, Synchronization Signals, Power Consumption and related design rules, Pulse generation and Interfacing, Chip Technology: Semiconductor Memories, Processors and Configurable Logic, Chip Level and Board Level Design Considerations

Hardware Design Languages, Simulation of Hardware Elements using VHDL, Timing Behavior and Simulation, Test Benches, Synthetic Aspects

Sequential Control Circuits and Processors                                          

Mealy and Moore Automaton, Designing the Control Automaton, Implementing Control Flow and Synchronization

Designing for ALU efficiency, Memory Subsystems, Simple Programmable Processor Design, Interrupt Processing and Context Switching, Interfacing Techniques, Standard Processor Architectures

System Level Design

Aspects of System Design, Scalable System Architecture, Regular Processors, Network Architecture, Integrated Processor Networks, Static Application Mapping and Dynamic Resource Allocation, Resource Allocation on Crossbar Networks and FPGA Chips, Communication Data and Control Information, P(Pi)-nets Language for Heterogeneous Programmable Systems

Digital Signal Processors        

DSP Elements and Algorithms, Integrated DSP Chips, Floating Point Processors, DSPs on FPGA, Typical Applications



1. Mayer, Lindenberg, ”Dedicated Digital Processors”, Wiley

2. R Gupta, “Co-Synthesis of Hardware and Software for Embedded Systems”, Kluwer

3. “Digital Signal Processing”, IEEE Press


VLSI Design & Testing

 Manipulation of Boolean expressions                                                

Two level realizations with NAND or NOR gates, Standard form of Boolean functions, Minterm & maxterm designation of functions, simplification of functions on Karnaugh Maps, Map minimization of product-of-sums expression, incompletely specified functions, logic Hazards, Elimination of Hazards.

Algorithms for optimization of combinational logic, impact of logic synthesis, cubical representation of Boolean functions, determination of prime implicants selection of optimum set of prime implicates, multiple output circuit, programmed logic array, minimization of multiple output function, Tabular determination of prime implicats, field programmable logic arrays.

VLSI Realizations of Combinational Logic                                       

Introduction, pass transistor network realization, Steering of 0,1,X & X to the output, tree networks, negative gate realization, logic design with CMOS standard cells, pre charged clocking of CMOS PLA.

Multilevel logic using complex (MSI) ports & cells:- The place for complex parts & cells, decoders, ROM as a logic element, binary adder, design with multiplexers, more than two level realizations with basic primitives, combinational MSI parts & cells, multilevel logic manipulation & optimization.

Sequential circuits                                                                                               

Sequential activity, memory elements, general model for Sequential circuits, clock mode Sequential circuits., Synthesis of clock mode Sequential circuits: Analysis of a sequential circuit, design procedure, synthesis of state diagrams, equivalent state & circuits, simplification by implication tables, state assignment & memory element input equations.


VLSI Realization of Digital Systems                                                

Alternative Structural descriptions, levels of descriptions, Standard cell CMOS layout & delay model, Timing analysis & simulation, Event driven gate level simulations, Switch level simulation, PLD & programmable gate arrays

Test Generation for VLSI                                                                         

Fault detection & diagnosis, Stuck at fault model, test generation strategy, test generation by evaluation & search, modeling CMOS, Stuck-open faults, fault simulation in sequential systems, boundary scan, built-in-self test.  Fault Tolerant Design: Hardware redundancy, Information redundancy, time redundancy, software redundancy, system level Fault Tolerance. Self-checking sequential circuit Design: Faults in state machines, self checking state machines design Techniques, Synthesis of redundant fault-free state machines.


1.       Parag K. Lala , “Fault-Tolerant & Fault Testable Hardware” , B-S-Publication Hyderabad

2.       Parag K. Lala ,“Self checking & Fault-Tolerant Digital Design”, Morgan Kaufman Publishers

3.       Frederick J. Hill and Gerald R. Peterson, “Computer Aided Logical Design with Emphasis on VLSI”, John Wiley & Sons Inc.


2. Software Engineering Stream

Engineering and Testing Structured Systems


Scope of Software Engineering, The Software Crisis, The functional approach. Structuring a problem. Notion of analysis. Design as synthesis.

The Yourdon method: need for Event Partitioning, Context Diagram, Event typology, converting from events to software system functions

Data Flow diagrams, Constraints, Data Dictionary, Process specification techniques.

 Construction Design: Coupling and Cohesion. Afferent and Efferent modules, Design Heuristics for Module Design


Maturity levels of testing, Unit, Module, Sub-System and System Testing Interaction., Top down and bottom up testing, Constructing Stubs and Drivers. Notion of a test case, test design approach to software design

White box testing: Testing Hypotheses, Statement testing, branch testing, branch and statement testing, Path, predicate path, path interpretation, Cyclomatic complexity, condition testing, loop testing.


Black box testing: Cause-effect technique

Implications of software systems on underlying IT infrastructure


1. Yourdon, “Modern Structured Analysis”, Pearson

2. Beizer, “Software Testing”, Van Nostrand Reinhold CO.

3. Pressman, “Software engineering”, McGraw-Hill

4. Sommerville, “Software Engineering”, Pearson


Object –Oriented Programming

 The OO manifesto for Programming Languages. Definition of Object, representing an object, Object classes: constructor, destructor, copy constructor and their defaults, public and private protection.


Complex Objects and complex classes, their constructors and destructors and policies for these. Privacy for complex objects. Inheritance: simple, multiple, repeated. Resolving inheritance conflicts. Rules for constructors, destructors. Protection policies for Inheritance.


Notion of Late Binding. Polymorphism and its forms. Abstract classes and their use, Meta-classes and templates.


Special language features like friend functions, type casting etc. Separation of specification  from implementation. Object-orientation for reuse and maintenance.

 All the above to be introduced through C++.


1. Bjarne Stroustrap, “The C++ Programming Language”, Pearson

2. Parimala N. “Object orientation Through C++”, MacMillam

3. Lippman, Lajoie, and Moo, “C++ Primer”, Addison Wesley

4. Robert Lafore, “Object Orientation in C++”, Galgotia


Engineering OO Systems


OO manifesto for OO Analysis. Object modeling and difference with data-oriented, process-oriented and behaviour modeling.


Object modeling: classes, complex object classes, inheritance. Sub systems and systems in OO modeling. State transition diagrams.

Dynamic Modeling: Modeling an event. Event typology, event as trigger

Functional Modeling: Review of Structured techniques, Cross model constraints and linkages. Conversion to OO implementation, UML notation


1. Rumbaugh et al, “Object Oriented Modeling and Design”, Prentice Hall

2. Odell and Martin, “Object Oriented Analysis and Design”, Prentice Hall


Multimedia Systems


Components of multimedia, multimedia and hypermedia, Multimedia authoring: metaphor, production, presentation, automatic authoring, VRML,


 Graphics and Image data representation, Colour in Image and Video- colour science, colour models in image and video, Fundamentals of video: types of video signals, analog and digital video,

Basics of Digital Audio: digitization, quantization, MIDI, multimedia data compression: lossy compressions; Image compression standards, basic video compression techniques, MPEG video coding, MPEG audio compression,


   Multimedia communication: quality of multimedia transmission, multimedia over IP, video delay in ATM, multimedia, across DSL


1. Ze-nian and Drew, “Fundamentals of Multimedia”, Prentice Hall

2. Rao, K.R. et al., “Multimedia Communication Systems. Techniques, Standards, and Networks”, Pearson

3. Y. Ramesh, “Multimedia Systems Concepts Standards and Practice, Kluwer

Internet Programming and Web Service Engineering

 Notion of mark up. HTML and XHTML. Style sheets, Cascading style sheets. Javascript, Dynamic HTML.

SGML. XML, DTD, XML schema. ASP.Net, Perl/CGI and Python

Notion of a web service. Service Oriented Architecture, SOAP, UDDI, WSDL, WSQM. Issues in providing QoS. Elements of Service oriented software engineering.


1. Deitel, Deitel and Goldberg, “Internet & World Wide Web How to Program”, Pearson

2. W3 SOAP Standard

3. UDDI Standard

4. WSDL standard


3. Information Systems Stream


Conceptual Modeling

 Why conceptual modeling, ANSI/SPARC framework, 100 % principle, conceptualization principle


Data-oriented Models: ER, SHM, SHM+.

Translation of into relational schemata

Behaviour-oriented Models: Why these models? Interpretations of an Event, Remora model

Benefits of Conceptual Modeling


1. Batini, Ceri, Navathe,” Conceptual Database Design: An Entity-Relationship Approach”,The Benjamin-    Cummings Pub

2. Loucopoulos and Zicari,” Conceptual Modeling, Databases, and Case: An IntegratedView of Information Systems Development”, John Wiley & Sons


Requirements Engineering

 Why requirements engineering? Difference between Conceptual Modeling and RE. Context Diagram and RE. Organizational versus Technical requirements,

Preparing IEEE SRS document                                                                                                

Stakeholders and their identification. Designing and conducting interviews, questionnaires, brainstorming sessions                                                                                                                              

RE in functional systems: Types of goals, goal satisfaction and satisficing, Goal modeling and decomposition, Goal operationalizing.                                                                                                        

Scenario modeling. Scenario classification. Goal-scenario coupling. Handling RE problems like conflicts                                                                                                                                   

RE in decisional systems: the changed role of RE. notions of goals, decisions, and information. Informational scenarios.


1. Hull, Jackson, and Dick, Requirements Engineering, Springer

2. Macaulay: Requirements Engineering, Springer

3. Jackson M., “Software requirements & specifications: a lexicon of practice, principles and prejudices”, ACM Press/Addison-Wesley

                                       Method Engineering                                                                                                                                      

 Notion of a method. Method models, meta-models, and generic models. CAME, CASE, meta CASE  and their differences.

Product oriented meta-models: The OPRR model, the GOPRR model, Product-Process meta-models: The fragment model

Integrated meta-models: The contextual approach, the decisional approach

The generic method model: Engineering methods for diverse domains

Situational method engineering. SDLC for method engineering. Intentional approach to method engineering. Method engineering processes. Open Issues


1. Brinkkemper et al, “Method Engineering”, Chapman and Hall, 1996

2. Jolita R.et al, “Method Engineering”, Chapman and Hall, 2007

 Process Engineering

SDLC in S/W and IS engineering, Relationship of SDLC to process models, Classical process models: Code and Fix, Waterfall, Prototype, Spiral, V, Fountain. Iterative and Incremental process models

Process meta-models: Activity based models, IBIS, Contextual model, and Map model, Tracing, Backtracking, and Guidance

The personal process and team process, CMM and its variants, ITIL, Six Sigma, ISO9000

Workflow Modeling


1. Pressman, “Software Engineering”, Mcgraw-Hill

2. Sommerville, “Software Engineering”, Pearson

3. Pfleegar, “Software Engineering Theory and Practice”, Pearson


Simulation and Modeling


Basic Simulation Modeling: The Nature of simulation system, models and simulation, discrete-event simulation, simulation of a single-server queuing, alternative approaches to modeling and coding simulations, network simulation, parallel and distributed simulation, simulation across the internet and web based simulation, steps in a sound simulation study, other types of simulation: continuous simulation, combined discrete-continuous simulation, Monte Carlo simulation, advantages, disadvantages and pitfalls of simulation.


Modeling Complex Systems: Introduction, list processing in simulation, approaches to stering lists in a computer linked storage allocation

 Simulation examples using any simulation language: Single-server Queuing simulation with time-shared computer model, job-shop model, and event-list manipulation.

Discrete System Modeling: Classification of simulation models the simulation process, system investigation validation and translation, simulation of complex discrete-event systems with application in industrial and service organization tactical planning and management aspects, Random variable generation and analysis.

Simulation Software: Comparison of simulation packages with programming languages classification of simulation software, general-purpose simulation packages, object-oriented simulation, building valid, credible and appropriately detailed simulation models, experimental design, sensitivity analysis and optimization simulation of manufacturing systems.


Embedded System Modeling: Embedded systems and system level design, models of computation, specification languages, hardware/software code design, system partitioning, application specific processors and memory, low power design.

Real-Time system modeling, Fixed Priority scheduling, Dynamic Priority Scheduling

Data Communication Network modeling, IP network intradomain (e.g. OSPF, RIP) routing simulation.


1. Law Kelton,”Simulation Modeling and Analysis”, McGraw-Hill

2. Geoffrey Gordon,”System Simulation”, PHI


4. Data Management Stream


Distributed DBMS

Review of computer networks and centralized DBMS, Why distributed databases, basic principles of DDBMS, distribution, heterogeneity, autonomy,                                                                                                                        

DDB architecture: client-server, peer-to-peer, federated, multidatabase,                                                                                                                            

DDB design and implementation: fragmentation, replication and allocation techniques,                                                                                                                                  


Distributed query processing and optimization,                                                                                                                   

Distributed transaction management, concurrency control and reliability, DDB interoperability


1. Ceri and Pelagatti, “Distributed Data Base Systems”, Addison

2. Ozsu,Valduriez, “Distributed Data Base Systems”, Pearson

Data Warehousing

 The organizational perspective, the technical perspective, Dimensional Modeling: facts, dimensions, slowly and rapidly changing dimensions,  Data Warehouse operations

Aggregation, historical information, Query facility, OLAP functions and Tools, Data Mining interfaces,

Relational representation, Multidimensional representation, Meta-data and CWM, DW process and architecture.

SDLC of a Warehouse project: business process driven, Information systems product driven and goal driven approaches.

Design approaches: data driven design, user driven design. Information Package, Diagram driven design.

Physical design: clustering, partitioning etc.


1. Ponnaih, “Data Warehouse Fundamentals”, Wiley

2. Inmon, “Building the Data Warehouse”, Wiley

3. Kimball and Ross, “The Data Warehouse Toolkit” Wiley

4. Murray, “Data Warehousing in the Real World”, Wiley

5. Imhoff C., “Mastering Data Warehouse Design” Wiley


Multi-media Databases

 Relational versus multimedia databases, Handling object data, Multidimensional structures: insertion, deletion, search in 2-d trees, point quadtrees, MX-quadtrees, and R-trees


Image databases: Raw and compressed images, Discrete Fourier transform and Discrete Cosine transform, segmentation, similarity based and spatial layout retrieval, image representation in relations and R-trees                                                                                                             

Document databases: precision and recall, Latent semantic indexing, operating on TV trees, inverted indices and sequential files.

Video databases: organization of video content, querying content of video libraries, video segmentation, video standards


Audio databases: general model, metadata, signal based audio content, discrete transformations for audio content, indexing techniques

 Multimedia databases: Principle of Uniformity, media abstractions, query languages, indexing, query relaxation/expansion

Physical storage and retrieval: retrieving form disk, CD-ROM, Tapes: recording and placement methods, retrieval techniques.

Open issues: security, compression for special data bases e.g. in medicine.


1. Subrahmaniam VS, “Principles of Multimedia Systems”, Morgan Kaufman

2. Apers et al, “Multimedia Databases in Perspective, Springer

3. Dunckley, “Multimedia Databases: An Object Relational Approach”, Holborn


Artificial Intelligence

 Knowledge: Introduction, definition and importance, knowledge base system, representation of knowledge, organization of knowledge, knowledge manipulation, knowledge acquisition, introduction to PROLOG.

Formalized symbolic Logics, Syntax and Semantics for FOPL, Inference rules, The resolution principle, No deductive inference methods, Bayesian probabilistic informer, Dimpster-Shafer theory, Heuristic Reasoning Methods.

Search and Control strategies: introduction, concepts, uniformed or blind search, informal search, searching and-or graphs, Matching techniques, structures used in retrieval techniques, integrating knowledge in memory, memory organization system.                                                                                                                                 

Fuzzy Logic: Basic concepts, Fuzzy sets, Membership Function, Types of membership Function, Basic operations in Fuzzy sets, Intersection & Union-Complementary, Subsethood, Properties of Fuzzy sets.

Expert System architectures: Rule-Based system architectures, Non production system architecture, dealing with uncertainty, knowledge organization and validation.


1. Dan W Patterson, “Introduction to Artificial Intelligence and Expert System”. PHI

2. Peter Jackson, “Introduction to Expert System”, Pearson

3. A Gonzalbz and D.Dankel,  “The Engineering Knowledge Base System”, PHI

4. Stuart Russell and Peter nerving, “Artificial Intelligence: A Modern approach”, PHI

5. John Yen & Reza Langari , “Fuzzy: Intelligence, Control and Information” , Pearson


Learning Systems 

Introduction: Definition, Human Brain, Model of Neuran, Feed back, Network Architectures, Knowledge Representation, AI & Neural Networks.

Learning Processes: Introduction, Error-correction Memory-Based Learning, Hebbian Learning, Competitive Learning, Boltzmann Learning, Learning with a teacher, Learning without a teacher, Memory Adaptation. 

Single Layer Perceptrons: Concepts, Adaptive Filtering, Unconstrained optimization, Steepest Descent Method, Newton’s Method, Perceptron, Perceptron Convergence Theorem.

Multilayer Perceptrons: Preliminaries, Back-propagation algorithm, activation function, Rate of learning.                                                                                                                              

Neurodynamics: Introduction Associative Memory, Linear Associater, Dynamical Systems, Stability of Equilibrium States, Attractros, Hopfied models, Brain-state-in-a-box model. 

Genetic Algorithms: Basics of genetic algorithms, binary GA implementation, Real coded GA, Design issues in GA, Choice of encoding, selection probability, mutation and cross over probabiltity, fitness evaluation function.


1. Simon Haykin, “Neural Networks”, Pearson

2. Mohamad H. Hassoun, “Fundamentals of Artificial Neural Networks”, PHI

3. James A. Anderson , “An Introduction to Neural Networks”, PHI

4. Melanie Mitchall, “An Introduction to Genetic Algorithm”, PHI


Data Mining            

Overview, types of mining, Mining operations, introduction of statistical Data Mining, Heuristic Mining, Introduction of mining in data  warehousing ,  Stages of DM process. Decision-Tree based classifiers: infomation gain, decision tree learning.                                                                                                                                                                                                                                                                                             

Data Mining Techniques: Association- Rule mining methodes, supervised neural network, perceptron, back propagation, bayesian methods, cross-validation, Time sequence discovery.

Clustering: Similarity and distance measures, hierarchical algorithms, partitional algorithms, clustering large databases, clustering with categorical attributes. K – means.

Introduction to information retrieval, Query optimization, Unstructured and semi-structured text, Text encoding, Tokenization, Steaming, Lemmatization, Index Compression, Lexicon Compression, Gap encoding, gamma codes, Index constructions, Dynamic indexing, Positional indexes, n-gram indexes, real-world issues, Vector-Space Scoring, Nearest neighbor techniques.                                                                                                                       

 Introduction to information retrieval , Inverted indices and Boolean queries, Query optimization, Unconstrained and semi constrained text, Text encoding, Tokenization, Stemming, Lemmatization, Tolerant retrieval:  Spelling correction and synonymes, permuterm indices, n-gram indices, Edit distance, Index compression, Lexicon compression, Gap encoding, Gamma codes, Web structure,the user, search engine, optimization/spam,web characteristic, web size measurement, near duplicate detection, crawling and web indexes, link analysis.


1. M.H. Dunham, “Data mining: Introductory and Advanced Topics”, Pearson

2. J. Han and M. Kamber, “Data Mining: Concept and Techniques”, Morgan Kaufman

3. Mallach, “Data Warehousing System”, McGraw-Hill

4. Rechard J. Roiger and michal W. Greatz, “Data Mining: A Tutorial based primer”, Pearson

5. Tom Mitchell, “Machine Learning”, McGraw-Hill

Natural Language Processing                                                                                                                                                                                

Context Free grammars, Lexical analysis, Introduction to parsing, Context Sensitive grammars                                                                                                                                                                                           

Linguistics of English: Review of English Grammar, Morphology, syntax, semantics, structure of discourse. Words and the lexicon: word classes.

Semantic Grammars, TN, ATN, Case grammars, Paninian Grammars, Parsers of NL statements, Determiners and quantifiers, Noun-noun modification, pronoun resolution, relative clauses                                                                                                                                                                                    

Deep structure, shallow structure, Differences between English and Hindi Application

(a)                 MT

(b)                 ASR

(c)                 IR

(d)                 Q & A


1.Manning,C.D, Schutze H, “Foundations of statistical natural language processing”, MIT press

2.Jurafsby D. Martin J.H, “Speech and language processing” , PHI

3.Allen , J., “Natural language understanding.”, Benjamin/ Cummins Publishing

4. Wall L. et W, ”Programming PERL”, O’Reilly




Number Theory                                                                                             

Prime numbers, Euler’s Totient function, Fermat’s and Eulers Theorem, Primality Testing, Chinese Remainder Theorem, Discrete Logarithms, Group, Rings, Fields, Modular Arithmetic, Euclidean Algorithm, Finite Fields of the form GF(p), Polynomial Arithmetic, Fields of the form GF(2n), Random Number Generation and Testing

Public Key Encryption                                                                                                                 

RSA System, Implementing RSA, Attacks on RSA, Rabin Crypto System, Factoring algorithms. The (p-1) method, Dixon’s algorithm and Quadratic sieve

Elliptic Curve Cryptography: Elliptic curves over GF(p), Elliptic curves over GF(2m), Elliptic curve cryptography, factoring with ECC, Key Management and Diffie Hellman Key Exchange,

Symmetric Encryption                                                                                                                


Block Cipher and DES, The strength of DES, Differential and Linear Cryptanalysis of DES, Advanced Encryption Standard, Stream Ciphers and RC4,

 Hash Functions                                                                                                        

Hash Functions, Security of hash functions, MD5, Secure Hash Algorithm, Whirlpool, HMAC, CMAC, The birthday attack problem.

Digital Signatures, Requirement, Authentication protocols, Digital Signature Standard, ECDSA

Finite Automata and Ciphers                                                                 

Finite Automata and Ciphers, Structure of Ciphers, Selection of the Ma, h and g functions, Cipher Design using Automata


1. Douglas R Stinson, “Cryptography Theory and practice”, CRC Press

2. William Stallings, “Cryptography and Network Security 4e”, Pearson

3. Simon J Shepherd, “Cryptography: Diffusing the Confusion”, Research press studies


Network and System Security

 Network Security                                                                                                     

AH and ESP Protocols, Security associations, Key management, Web security Considerations, secure socket layer and Transport layer security.

PKI Infrastructure                                                                                                  

Concept of an infrastructure, application enables secure single sign-on, comprehensive security, defining PKI, LDAP and X500.

Core PKI Services: Authentication, Integrity and confidentiality, Mechanism required to create PKI enabled services X-509 certificate.


System Security: Intrusion Detection, Password Management, Base Rate Fallacy.

Malicious Software: Virus and related threats, virus countermeasures, Distributed Denial of Service attacks.

Firewalls: Design principles, Trusted Systems common criterion for IT security evaluation

OS and Database Security                                                                                                        

Structure of an OS and application, application and OS security, security in Unix and Linux Pluggable Authentication Modules, Access Control Lists, SELinux.

Database Security:Database Security Evolution, Role-based an object-oriented encapsulation procedural extension to SQL, Security through Restrictive Clauses.

Secure Applications                                                                                               

PGP and SMIME, Kerberos version IV and V, Security in Cellular Communication System, Secure Electronic Transaction.


1. William Stalling, “Cryptography and Network Security 4e”, PHI

2. C Adams, Steve Lloyd, “Understanding PKI”, Addison Wesley

3. Jay Ram Chandran, ”Designing Security Architecture”, Wiley Computer Publishing

4. C Kaufman, Radia Perlman and Mike, “Network Security 2e”, Pearson.


Digital Forensic                                                                                                                                                                                   

Transform Methods: Fourier Transformation, Fast Fourier Transformation, Discrete Cosine Transformation, Mellin-Fourier Transformation, Wavelets, Split Images in Perceptual Bands, Applications of Transformation in Steganography.

Biometrics:  Overview of Biometrics, Biometric Identification, Biometric Verification, Biometric Enrollment, Biometric System Security.

Authentication and Biometrics: Secure Authentication Protocols, Access Control Security Services, Authentication Methods, Authentication Protocols, Matching Biometric Samples, Verification by humans.

Common biometrics: Finger Print Recognition, Face Recognition, Speaker Recognition, Iris Recognition, Hand Geometry, Signature Verification, Positive and Negative of Biometrics.

Matching: Two kinds of errors, Score distribution, Estimating Errors from Data, Error Rate of Match Engines, Definition of FAR and FRR


Introduction to Information Hiding: Technical Steganography, Linguistic Steganography, Copy Right Enforcement, Wisdom from Cryptography

Principles of Steganography: Framework for Secret Communication, Security of Steganography System, Information Hiding in Noisy Data , Adaptive versus non-Adaptive Algorithms, Active and Malicious Attackers, Information hiding in Written Text.


Survey of Steganographic Techniques: Substitution systems and Bit Plane Tools, Transform Domain Techniques: – Spread Spectrum and Information hiding, Statistical Steganography, Distortion Techniques, Cover Generation Techniques.

Steganalysis: Looking for Signatures: – Extracting hidden Information, Disabling Hidden Information.


Watermarking and Copyright Protection: Basic Watermarking, Watermarking Applications, Requirements and Algorithmic Design Issues, Evaluation and Benchmarking of Watermarking system.


  1. Katzendbisser, Petitcolas, “ Information Hiding Techniques for Steganography and Digital Watermarking”, Artech House.
  2. Peter Wayner, “Disappearing Cryptography: Information Hiding, Steganography and Watermarking 2/e”, Elsevier
  3. Bolle, Connell et. al., “Guide to Biometrics”, Springer



Parallel Algorithms

Sequential model, need of alternative model , parallel computational models such as PRAM , LMCC , Hypercube , Cube Connected Cycle , Butterfly , Perfect Shuffle Computers , Tree model , Pyramid model , Fully Connected model , PRAM-CREW , EREW models , simulation of one model from another one.


Performance Measures of Parallel Algorithms , speed-up and efficiency of PA , Cost-optimality , An example of illustrate Cost-optimal algorithms- such as summation , Min/Max on various models.


Parallel Sorting Networks , Parallel Merging Algorithms on CREW/EREW/MCC/ , Parallel Sorting Networks on CREW/EREW/MCC/, linear array

Parallel Searching Algorithm , Kth element , Kth element in X+Y on PRAM , Parallel Matrix Transportation and Multiplication Algorithm on PRAM , MCC , Vector-Matrix Multiplication , Solution of Linear Equation , Root finding.

Graph Algorithms – Connected Graphs , search and traversal , Combinatorial Algorithms- Permutation , Combinations , Derrangements.


1. M.J. Quinn, “Designing Efficient Algorithms for Parallel Computer” by Mc Graw Hill.

2. S.G. Akl, “Design and Analysis of Parallel Algorithms”

3. S.G. Akl, ”Parallel Sorting Algorithm” by Academic Press

Randomized Algorithms


Introduction:  Basic Probability Theory, Probability Spaces; Bayes’ Rule; Independence; Expectation; Moments; Common Distributions , Randomized Algorithm: General concepts and definitions, Quicksort ,  Min-Cut, Random Partitions,  Probabilistic recurrences , Randomized Complexity Classes: RPPPBPP

Game Theoretic Techniques and Lower Bounds: Game theory concepts; Applications to lower bounds, Examples: Sorting and Game tree evaluation


Moments and Deviations: Random sampling/bucketing, Tail bounds : Markov and Chebyshev inequalities, High confidence selection, Pairwise independence,  Applications : The stable marriage problem

Tail Inequalities : Chernoff bounds; Applications: Network routing and gate-array wiring


Markov Chains and Random Walks: A 2-SAT Example, Markov Chains, Random Walks on Graphs, Graph Connectivity, Expanders , Probability Amplification by Random Walks on Expanders

Algebraic methods: Fingerprinting and Freivald’s technique, Verifying polynomial identities, Randomized pattern matching


Data  Structures: Random treaps; Skip listsRandomized Graph Algorithm: Shortest paths; Minimum spanning tree

7 Hours

Parallel and Distributed Algorithms: The PRAM Model, Sorting on a PRAM, Maximal Independent Sets, Perfect Matchings,

Number Theory and Algebra: Elementary number theory,  Quadratic residues, Primality testing, RSA cryptosystem


1. R. Motwani and P. Raghavan, “Randomized Algorithms”, Cambridge University Press

2. Michael Mitzenmacher, Eli Upfal , “Probability and Computing”, Cambridge UniversityPress


 Approximation Algorithms


Introduction, Overview of Complexity Theory: Class NP, NP-Completeness, reductions, Randomized Complexity Classes,  Basics of Probability Theory, Expectation and moments, basic distributions

Vertex/set cover, Greedy algorithm, Hardness of approximating Traveling Salesman Problem (TSP), Set cover, layering algorithm, shortest superstring,

Steiner tree, Metric Steiner tree, Metric TSP; Minimum weight multiway cut

minimum weight k-cut , k-center

Knapsack problem, Pseudo polynomial time algorithms PTAS, Fully polynomial time approximation scheme FPTAS, Strong NP-hardness, Bin packing, Asymptotic PTAS, Euclidean TSP, Proof of correctness

LP Duality, LP Duality Theorem, Dual-fitting -based analysis for the greedy set cover algorithm

Rounding Algorithm: set cover, randomized rounding

Half-integrality of vertex cover; Primal-dual Schema: set cover

Scheduling on Unrelated Parallel Machines, Primal-Dual algorithms, Facility Location and the k-Median Problem, Steiner Network Design


1. Vijay V.Vazirani, “Approximation Algorithm”, Springer

2. D. S. Hochbaum, “Approximation Algorithms for NP-Hard Problems”, PWS 1997

Complexity Theory

 Models of Computation, resources (time and space), algorithms, computability, complexity;

Complexity classes, P/NP/PSPACE, reductions, hardness, completeness, hierarchy, relationships between  complexity classes

Randomized computation and complexity; Logical characterizations, incompleteness; Approximability

Circuit complexity, lower bounds; Parallel computation and complexity; Counting problems; Interactive proofs;

 Probabilistically checkable proofs; Communication complexity; Quantum computation.


1. Christos H. Papadimitriou, “Combinatorial Optimization: Algorithms and Complexity”

2. Sanjeev Arora and Boaz Barak , “Complexity Theory: A Modern Approach”

3. Steven Homer, Alan L. Selman, Computability and Complexity Theory , Springer

Computational Geometry

 Convex hulls: construction in 2d and 3d, lower bounds; Triangulations: polygon triangulations, representations, point-set triangulations, planar graphs;

Voronoi diagrams: construction and applications, variants; Delayney triangulations: divide-and-conquer, flip and incremental algorithms, duality of Voronoi diagrams, minmax angle properties.

Geometric searching: point-location, fractional cascading, linear programming with prune and search, finger trees, concatenable queues, segment trees, interval trees; Visibility: algorithms for weak and strong visibility, visibility with reflections, art-gallery problems;

Arrangements of lines: arrangements of hyper planes, zone theorems, many-faces complexity and algorithms; Combinatorial geometry: Ham-sandwich cuts 

Sweep techniques: plane sweep for segment intersections, Fortune’s sweep for Voronoi diagrams, topological sweep for line arrangements; Randomization in computational geometry: algorithms, techniques for counting; Robust geometric computing; Applications of computational geometryReferences:


1. Franco P. Preparata, Michael Ian Shamos, “Computational Geometry: An Introduction” SpringerVerlag.


2. Mark Berg, Marc van Kreveld, Mark Overmars, and Otfried Schwarzkopf, Computational Geometry, Algorithms and Applications”. Springer.



Professional Aspects in Software Engineering (1/2 Unit)


Intellectual Property rights                                                                          

Confidential Information, Copyright, Infringement of Copyright, Acts permitted in Relation to Copyright Works, Licensing and Assignment of Copyright, Moral Rights, Designs, Trademarks, The tort of passing off, Domain Names, Patents.

Software Licenses                                                                                                 

Copyright, Contract, Patent, Free Software and Open Source Software, MIT License, BSD License, GNU General Public License, GNU Lesser General Public License, Q Public License, Proprietary License, Sun Community License,

Software Contracts:                                                                                            


Basics of Software Contracts, Extent of liability, Contract for the supply of custom-built software at a fixed price, other types of software service Contract, Liability for defective software.

Software Crime Prevention                                                                                                          

Computing and criminal Activity, Reforms of Criminal Law, Categories of Misuse, Computer Fraud, Obtaining Unauthorized Access to Computer, Unauthorized Alteration or Destruction of Information, Denying Access to an Authorized user, Unauthorized Removal of Information Stored in a Computer.

Data Protection Regulations                                                                         

Data Protection and Privacy, The impact of the Internet, Factors Influencing the Regulation of Data Processing, Convergence of Data Protection Practice, Defamation and the protection of Reputation.



1. Andrew M. St. Laurent, “Open Source and Free Software Licensing”, O’Reilly Publications

2. Frank Bott, et. al, “Professional Issues in Software Engineering”, Taylor & Francis


Appendix III



Thesis Requirements for M.Tech. Courses in Computer Science and Information Technology


 The work reported in the thesis shall be an extension of the state of the art to demonstrate the capability of the student to do creative work, develop the idea, prove its efficacy, report it in a convincing manner and finally, defend it. The work must have scientific and/ or industrial relevance.


The thesis shall be done in two parts. During the third semester, the student shall carry out literature survey and develop the necessary background (familiarity with tools, techniques) for the work to be carried out in the fourth semester. At the end of the third semester, the student shall submit a synopsis clearly stating the problem to be addressed, report on the background developed, and layout a concrete project plan for the fourth semester. A Pre-thesis examination consisting of a presentation and viva shall be conducted after the synopsis has been submitted.


Passing the Pre-thesis examination is a pre-requisite for continuing with the thesis in the fourth semester.


The thesis shall be submitted following the format of UPTU. It shall be examined by an external expert decided by UPTU. After a written report is received expressing satisfaction with the thesis, a viva voce examination shall be conducted in the presence of the external expert. The thesis requirement shall be fulfilled upon the student passing the viva examination.




One comment

  1. Avatar for uptu

    It is correct time to make a handful of programs with the long term plus its time to be at liberty. I’ve find out this post of course, if I could truthfully I personally desire to give you advice couple of interesting troubles and also guidance. Perhaps you may write following articles or blog posts regarding this report. I have to discover more concerns about this!

Leave a Reply

Your email address will not be published. Required fields are marked *