SYLLABUS OF III SEMISTER B.E. COMPUTER SCIENCE (SEMISRER PATTERN)
33CSI: Applied Mathematics Unit 1 : Integral TransformsFourier integral theorem, Fourier and Laplace transforms and their simple properties, Simple properties of Laplace transforms to-solve ordinary differential equation including Application to one dimensional partial differential equations. The z-transform definition and properties, inversion, with Laplace transform, Application of z-transform to solve difference with constant coefficient.
Unit 2: Complex VariableAnalytic function, Cauchy-Riemen condition, conjugate, function, singularities, Cauchy's integral theorem and integral formula (statement only) Taylor's and Laurent theorem (statement only) Residue theorem, contour integration
. Unit 3 : Calculus of VariationsMaxima and Minima of functional, variation and its properties Euler's-equation, functional dependent on first and second order derivatives, simple applications.
Unit 4 : Fourier SeriesPeriodic function and their Fourier expansion. Even and odd function, change of interval half range expansion. Partial Differential Equation: Partial-Differential Equation of first order first degree,i.e, Langrange's form, Linear Homogeneous P.D.E. of North order with constant coeffient method of separation of variables.
Unit 5 : MatricesInverse of matrix by partitioning method, Inverse of a matrix by adjoint method and its use solving- simultaneous equation, Rank of matrix, Consistency of a system of Equation, Linear dependence, linear and orthogonal transformation.
Unit 6 : MatricesCharacteristic equation, Eigenvalues, eigenvectors, Reduction of a diagonal form, Statement and verification of Cayley-Hamilton theorem; Sylvester's theorem, Association of matrices with linear differential equation of second order with a constant coefficient, Determination of largest eigenvalue by iteration method.
Test Books:
· Advanced Engineering Mathematics, kreyzig
· Higher Engineering Mathematics, B.S. Grewal
Reference Book :
· Mathematics of Engineer, Chandrika Prasad
· Advanced Mathematics for Engineer, Chandrika Prasad
· Applied Mathematics for Engineer, L.A. Pipes & Harville
· A Text Book of Applied Mathematics, P.N. Wartikar & J.N. Wartikar 33CS2 : Programming Fundamentals In "C"
Unit - I:
Introduction to programming , programming languages, algorithms, flowchart. C: Data types, Identifiers, Storage class, Constant, Operators, expression, Statement, console I/O statement, Selection statement: if-else, switch, Iteration Statement: for, while, do-while, jump statement: return, go, back, continue, comment.
Unit IIFunction, Call by value, Call by reference, calling function with arrays, argument to main(), return statement, recursion, function prototypes, inline keyword, preprocessor directives. Pointers: pointer variables, pointer operator, pointer expression, array of pointers, multiple indirection, pointers to function, dynamic allocation function, Unit IIIArrays - single dimensional arrays, two dimensional arrays, variables length array. Strings, array of strings. Unit IVStructures : array of structures, passing structure to function, structure pointer, structure within structure. Union, bit-fields, enumerations, size, type def. Unit VFile I/O : Streams and files, file system basics, fread, fwrite, fseek, random access I/O, fprint(), fscan(), standard streams. Unit VIAdvanced Concept in C: Different types of pointers, ROM-BOIS function, Elementary TSRs.
Text Book :
· The Complete Reference C (4 th Edition): Herbert Scheldt [TMH]
· C how to program, 4th Edition by H.M.Deitel & P.J. Deitel, Pearson Education.
· Writing TSRs through C: Yashwant Kanetkar [BPB]
Reference Book:
· The C Programming Language: Dennis Ritchie & Dietel, Pearson Kernighan [Pearson]
· Programming with C: K.R. Venugopal & S.R. Prasad [TMH]
· Let us C: Yashwant Kanetkar [BPB]
33 CS3 : DIGITAL CIRCUITS & FUNDAMENTALS OF MICROPROCESSORUnit - I:
Motivation for digital system - Logic and Boolean algebra, Number system: Binary, Hexadecimal, Octal, Gray. Gates & truth tables, propositions, Demogran's law minimization of combinational circuits using Karnaugh maps.
Unit II :
Multiplexers, Demultiplexer, Enconds, Decoders, Code, Converters, Address, Subtract(Half, full), BCD Adder/ Subtractor, ripple and carry look-ahead addition. Unit IIIStorage elements, flip-flops and latches: D,T,J/K, s/R flop-flops. Master Slave Conversion of one of type of F/F to another. Unit -IVCounters, asynchronous and synchronous-design using state and excitation tables. Unit -VIntroduction of 8085, Addressing modes, Instruction Set of up 8085 Unit -VIInterrupts of 8085, Programming of up 8085.
Text Book :
33CS4 : Combinatorial Theories
Unit I :
Combinatory : Basic counting techniques, pigeon-hole principle, recurrence relations, generating function. Examples using ordinary power series and exponential generating functions, general properties of such functions. Dirichleet Series as generating function.
A general family of problems described in terms of 'cards, deck and hand' with solution methods using generating function. Unit IIGenerating function proofs of the sieve formula and of various combinatorial indenties. Certifying combinatorial indenties.
Some analytical methods and asymptotic result.
Polya's counting theorem.
Basics of graphs theory.
Introduction to probabilistic method in combinatory. Unit IIINumber Theory
Examples of continued fractions.
The study of the continued fraction.
Alpha has infinite continued fraction if alpha is irrational.
Formal logic: Prepositional logic: proof system, semantics, completeness, compactness.
Length of proofs, polynomial size proofs, efficiency of proof system. Unit IVAlpha has periodic continued fraction if alpha is quadratic irrational.
Application to approximation of irrational by rational. Hurwitz's Theorem.
First order logic: models, proof system, compactness, Examples of formal proofs in say, number theory or group theory. Some advanced topics.
Unit V:
Application to solution of Pell's equation. Proof that means cos{(p x pi)/q}, for natural number p and q are irrational (apart from obvious exceptions).
Example : CS application of logic, introduction to modal and temporal logics, Or formal theory including incompleteness theorem.
Unit VI :
Lowville's Theorem on algebraic numbers. Construction of transcendental numbers.
Elements of proof theory including cut elimination, Or zero-one law for first order logic.
Text Book :
33CS5 : Principle Of Management Unit I:Nature and function of Management, Management yesterday and today, Planning and Decision making. Unit II:Management Information System: Introduction, Conceptual Foundation, Information System Requirement Unit III:Marketing Management : Marketing concept, Indian Marketing Environment, Market segmentation, Market Planning, International Marketing.
Unit IV:
Financial Management
Unit V:
Human Resource Management : Human Resource Planning, Recruitment, Selection, Training and development, Security , safety and Health.
Unit VI:
Organization Behavior : Organization Structure and design. Designing Effective Organization, Managing Job Stress, Organization Development
Text Book:
33CS6 : Computer Workshop
Practical to be based on following topics:
3. Working under UNIX / LINUX Operating System:
Introduction to Networking Accessories:
Books:
SYLLABUS OF IV SEMISTER B.E. COMPUTER SCIENCE (SEMISRER PATTERN)
44CSI: Discrete Mathematics and Graph Theory Unit 1: Set TheoryOperation of sets - relation and functions, partial order, equivalence relation peano and inductions
Unit 2: Mathematical Logic
Proposition, predicate logic, formal mathematical system, algebra, Homomorphism, Automorphism
Unit 3: Groups
Element of theory of some Algebras, semi group, monoid group.
Unit 4: Rings
Rings, fields, lattices, Boolean Algebra.
Unit 5: Graph Theory
Graphs, Hyper Graph, Transitive Closure, Spanning Tress.
Unit 6: Combinators
Generating Function, recurrences, counting theorem and application
Text Books:
44 CS2 Data and program design in "C"
Unit 1
General concept and linear data structure : Abstract data structure as an organization of data with specified properties and operations, Time and space analysis of algorithms, Big oh and theta notations and omega notations. Average, best and worst case analysis, Representation of Arrays - single and Multi dimensional - Address calculation using column and row major ordering. Representation of stacks and queues using arrays- Circular queues, Dequeue, Application of stacks, Conversion from infix to post fix and pre-fix expression, Evaluation of postfix expression using stacks, Multiple stacks.
Unit II
Linked list : Linked lists, Simply linked list Implementation of linked list using and dynamic memory allocation-dynamic memory allocation, operation on list linked stacks and queues, polynomial representation and manipulation are using linked list, circular linked list, doubly linked list, Generalized list.
Unit III
Trees: General and binary trees, Representations and traversals, General tress as binary trees, Binary search trees, Application, the concept of balancing and its advantages, B-trees, B+ Trees, AVL Trees, Threaded Binary Trees.
Unit IV
Hashing : Hash functions, Collision resolution, Expected behavior, Application
Unit V
Graphs and digraphs : Representations, Breadth and depth first searches, Connectivity algorithms, shortest path, Minimal spanning tree, the union find problem, Hamilton path
Unit VI
Sorting : Elementary sorts : selection , insertion, bubble sort, Radix sort, Quick sort, merge sort, heap sort, Bucket sorting, External sorting, Worst case and average behavior, Lower bound for sorting using comparisons
Text Books:
44CS3: Business Data Processing
Unit I:
Structural Organization of COLBOL: Character set, Words, Sentences, Identification Division, Environment Division, Data Division, Data types- numerical, Alphabetic & alphanumeric, Input-output sections, Working storage sections, PROCEDURE division features : ACCPET, DISPLAY, MOVE, Arithmetic & COMPUTE verbs, levels, Errors Handling, Sample programs, PERFORM & GOTO verbs, sample programs using PERFORM, Miscellaneous COBOL statement.
Unit II:
Conditional statements & Handling Relation condition, Nested condition, Class conditions, Condition name condition Justified clause, Structured programming forms of program structure, Structural floe charts, subscripting, OCCOURS CLAUSE, multidimensional tables, Tables handling with PERFORM verb.
Unit III:
Business Files : Structured flow charts, Operation on files, Master files, Transaction file, Report file, Batch processing, on-line processing, case studies.
Sequential Access Files: Principle of magnetic storage and accessing, Blocking, Inter record gap, label records, COBOL language instruction for sequential files.
Unit IV:
Direct Access File : Characteristic of disk storage and timing index sequential files, COBOL instruction for indexed sequential files, relative file organization, Division - Remainder method, digital analysis method, COBOL instruction for handling relative files.
Unit V:
Sorting, Searching and merging : Linear search sort, Merge sort, Chained record sort, Linear search, Binary search, File sorting and Merging using sequential files.
Report Generation : Output layout design, Heading, Date & Detailed summaries.
Control break, Language specification for COBOL report writing.
Unit VI:
Advanced Tool manipulators like STRING, UNSTIRNG, INSPECT & COPY verb, COBOL subprogram and main program.
Text Books:
· COBOL Programming with business application - N.L. Sarda
· Information System through COBOL -Philippakis & Kazmier
· Structured COBOL Programming - Stern & Stern
· COBOL Programming by M.K. Roy, D. Ghosh Dastidar.
44CS4: Theoretical Foundations Of Computer Science
Unit 1
Mathematical preliminaries - Sets, operation, relation strings, transitive closure, accountability and diagonaalisation, induction and proof methods- pigeon-hole principle and simple application - concept of language - grammar and production rules- Chomsky hierarchy.
Unit II
Finite state machine, regular language, deterministic finite automata, conversion deterministic automata , E- closures- regular expression finite automata, minimization of automata, Moore and Mealy machine and their equivalence.
Unit III
Pumping lemma for regular sets-closure properties of regular sets-decision properties for regular sets, equivalence between regular language and regular grammar. Context - free language -parse trees and ambiguity, reduction of CFGS, chomsky and Griebach normal forms
Unit IV
Push -down Automata (PDA)-non Determinism-acceptance by two methods and their equivalence, conversion of PDA to CFG CFLs and PDAs-closure and decision properties of CFLs.
Unit V
Turing machines-various-recursively enumerable (r.e.)set-recursive sets
TM as computer of function- decidability and solvability- reductions- post correspondence problem (PCP) and unsolvability of ambiguity problem of CFGs, Church's hypothesis.
Unit VI
Introduction to recursive function theory- primitive recursive and partial recursive functions, Parsing top down and bottom up approach, derivation and reduction
Text Books
Reference Books
44CS5: Computer Architecture & Organization
UNIT 1
BASIC STRUCTURE OF COMPUTERS :
Functional units , Basic operational concepts, Bus structure Addressing modes , subroutine : parameter passing , instruction formats, expanding opcodes method.
BASIC PROCESSING UNITS: bus architecture, execution of a complete instruction, sequencing of a control signals, hardwires control, micro programmed control, microinstruction format, bit slice concepts.
UNIT II:
ARITHAMETIC : Numbers representation and their operations , design of fast Adders, Singed multiplications, Booth's Algorithm's bit pair recording, Integer Division, Floating point numbers and operations , guard bit and rounding.
UNIT III:
THE MEMORY SYSTEM : various technologies used in memory design , higher order memory design, multimode memories and interleaving , Associative Memory , Cache Memory, Virtual Memory.
UNIT IV:
INPUT / OUTPUT ORGANISATION: I/O mapped I/O and memory mapped I/O , interrupts and interrupts handling mechanism , vectored interrupts , synchronous vs.
Asynchronous data transfer , Direct memory Access COMPUTERS PERIPHERALS : I/O devices such as magnetic disc, magnetic tape. CDROM system.
UNIT V:
RISC philosophy , pipelining , basic, delayed branch, branch prediction, data dependency, influence of pipe lining on instruction set design ,, multiple execution units, performance considerations,
UNIT VI:
Basic Concepts in parallel processing & classifications of parallel architecture. Vector processing , Array processors.
BOOKS:
· V.C Hamachare , Z.G.Vranesis and S.G Zaky, Computer organizations.
McGraw Hills 5th Edition, 2002.
· Computer Architecture & Organizations III rd Edition J.P Hayes.
· A.S. Tanenbaum, Structured Computer Organizations" 4th Edition , Person
Educations.
REFERENCE BOOKS:
· M. Mano, " Computer System & Architecture" Pearson Education.
· W. Stalling " Computer System & Architecture" , Pearson Educations.
44CS6: Internet Technologies
Practical to be conducted based on following topics:
1) HTML: standard use for www documents on internet , GML, SGML, HTML tags, special characters, Fonts, Lists, Images, Tables, Forms and Frames.
2) DHTML:Introduction to CSS, Fonts in CSS, Text in CSS, Boxes in CSS, CSS positioning, Tables in CSS, Generated content and lists in CSS.
3) XML: XML basics, understanding markup languages, structures and syntax, valid Vr well formed XML, DTD (document type definition) classes, Scripting XML, XML processor, parent child relationship, XML as a data, data type in XML, XML namespaces, linking with XML simple link, the HTML way, XSL with style: style sheet basics, XSL basics, XSL style sheets.
4) FRONTPAGE:
5) SECURITY:
6) Scripting Language: Perl Scripts, Java Scripts:
7) PHP
TEXT BOOKS:
· XML in action web technology by William J. Pardi (PHI) Pub.
· Web Technology by Ramesh Bangia (Firewall Media).
. · Programming the web using XML by Ellen Pearlman (Tata McGraw - Hill).
SYLLABUSS OF V SEMESTER B.E. COMPUTER SCIENCE (SEMESTER PATTERN)
55CS1: Data Communication
UNIT 1:
SIGNALS:
ANALOG AND DIGITAL : Analog and digital data, Analog and digital signals; PERIODIC AND APERIODIC SINGNSLES, ANALOG SINGALE: simple analog signals; TIME AND FREQUENCY DOMAINS; COMPOSITE SINGLES: Frequency spectrum and Bandwidth; DIGITAL SIGNALS : Decomposition of digital signal; TRANSMISSION MODES: Serial and Parallel transmission, Asynchronous and Synchronous Transmission, simplex, Half- Duplex communication.
UNIT 2:
ENCODING AND MODULATING:
DIGITAL -TO - DIGITAL CONVERSION : Unipolar , Polar, Bipolar;ANALOG- TO DIGITAL COVERSION:Pluse Amplitude Modulation(PAM),Pules Code7 Modulation(PCM),Sampaling Rate,How many Bits per Sample? Bit rate;
DIGITAL -TO- ANALOG CONVERSION: Aspects of Digital -to -Analog conversion, Amplitude Shift Keying(ASK),Frequency Shift Keying(FSK) ,Phase shift keying( PSK), Quadrature Amplitude modulation (QAM), Bit / Baud comparison ; ANALOG-TO- ANALOG CONVERSION: amplitude modulation (AM), Frequency Modulation (FM) , Phase modulation(pm);
UNIT 3:
INTERFACES AND MODEMS: DIGITAL DATA TRANSMISSION: Parallel transmission , Serial Transmission ; DTE- DCE INTERFACE: Data terminal Equipment (DTE), Data Circuit - Terminating Equipment (DEC), Standards, EIA-232 Interface; OTHER INTERFACE STANDARDS: EIA-530, X21; MOODEMS; Transmission rate, Modem standards; 56k MODAMS:Traditional Modams,56Modems;
UNIT 4:
COMMUNICATION MIDIA: GUIDED MEDIA: Twisted pair cable, Coaxial cable, Optical Fiber cable; UNGUIDED MEDIA: Radio frequency allocation, Propagation of Radio waves, Terrestrial microwave, Satellite communication, Cellular Telephony; TRANSMISSION IMPAIRMENTS : Attenuation , Distortion, Noise ;PERFORMANCE: Throughput, Propagation Speed, Propagation time;
UNIT 5:
MULTIPLEXING: FREQUENCY DIVISION MULTIPLEXING (FDM). TIME DIVISION MULTIPLEXING (TDM); Inverse Multiplexing, WAVE- DIVISION MULTIPLEXING, MULTIPLEXING APPICATION : THE TELEPHONE SYSTEM: Common carrier services and hierarchies, Analog services, Digital Services; DIGITAL SUBCRIBER LINE(DSL):ADSL, RADSL, HSDL, SDSL, VDSL; FTTC:FTTC in the Telephone Network, FTTC in the Cable TV Network.
UNIT 6:
DATA COMPRESSION: Huffman code, Run -Length Encoding, Relative Encoding, Lempel-Ziv Encoding, Image Compression, JPEG, MPEG
Text Books:
Data Communication and Networking by Behrouz A.Forouzan, 4th Edition, Tata McGraw Hill Understanding Data Communication and Networks by William A. Shay, 2ND Edition , Vikas Publishing House.
Reference Book:
Electronic communication Systems by Kenney.
Communication Systems by Singh and Sapre
Data communication by Fred Halsall, Pearson Education.
55CS2: Numerical Computing
Polynomial Equation : Newton -Raphson method, Regula Falsi Method, Bairstow method, Multipoint iteration method, Convergence/ Rate of Convergence of iterative method, Evaluation of Multiple & complex roots. Simultaneous equations.
Linear System and Matrices Gauss elimination with pivoting, Gauss- Seidal iteration,Triangularization/ Cholesky methos, Iterative determination of Eigen values. Interpolation & Approximation: Lagrange's divaricates interpolation , Least squares approximation, Uniform approximation , Rational Approximation, Hermite Iterpolation. Differentiation / Integration: Doubleintegrals by Trapezoidal & Simpson rule, Methods of undermined coefficients for numerical integration, GaussOLegendre, Gauss- Hermite formula, Romberg Integration, Approximation of derivates, Richardson's Extrapolation. Differential Equations: Initial value problems by Euler's method, Picard's, Taylor series, Runge- Kutta methods, Predictor- Corrector methods, Boundary value problems (Second order)by finite difference methods.
Related topics: Simplex method for linear programming programming problems,Errors & Method of errors analysis.
Text Books:
55CS3: Object Oriented Methodologies
UNIT 1:
The Object Oriented Paradigm
What is Object Orientation ?, What is Object Oriented Development ?, The Object Oriented Themes ;The Object modeling Technique (OMT).
Object Modeling
Objects and Classes; Links and Association ; Advanced Links and Associations Concepts; Generalization and Inheritance; Grouping Constructs; A Sample Object Model. Advanced Object Modeling Aggregation; Abstract and Concrete Classes;
Generalization as Extension and Restriction ;Multiple Inheritance; Metadata; Candidate Keys.
UNIT 2:
Dynamic Modeling
Events and States; Operations; Nested State Diagrams; Concurrency of State; Advanced Dynamic Modeling Concepts; A Sample Dynamic Model; Relation of Dynamic Model to Object Model .Functional Modeling The Functional Model; The Data Flow Diagrams (DFD) ; Properties of DFD; Construction of DFD; Specifying Operations; Constraints; A Sample Functional Model; Relationship between the Object, Dynamic and the Functional Models.
UNIT 3:
Pre- Analysis the need for Pre-Analysis ; Pre -Analysis Steps: Interviews, Questionnaire, Observation, Documentation and Notations; the Bus Stop Problem Domain Example. Analysis: The Analysis Overview ; the Problem Statement; the ATM example; Object Modeling in ATM; Dynamic Modeling in ATM; Functional Modeling in ATM; Adding Operations; Iterating Analysis ; Recording Analysis.
UNIT 4:
Design
How does Design differ from Analysis ? The Logical and Physical Design ; Qualities and Objectives of Analysis and Design; Measurable Objectives in Design; Planning for Design. System Design Overview of System Design; Breaking System into Subsystems; Identifying Software Control Implementation; Handling Boundary Conditions; Setting Trade-Off Priorities; Common Architectural Frame Works; the Architecture of ATM System.
UNIT 5:
The object design paradigm:
Overview of Object Design; Class Specifications; Interfaces; Criteria for Good Design; Designing Algorithms; Design Optimization ; Implementation of Control ; Adjustment of Inheritance; Design of Associations; Integrity Constraints; Object Representations ; physical Packaging; Documenting Design Decision.
UNIT 6:
The Human Computer Interaction
What is Human Computer Interaction ? Qualities of Good User Interface; Approaches to User Interface Design; the Standards and Legal requirements. The Programming Style the subject-Oriented Style; Extensibility and Robustness; Programming -in-the-Large; Last Binding and Early Binding. Reusable Components What is meant by Reuse ?, Why Reuse ? , Planning Strategy for Reuse; the Reusability approaches.
Software Development Methodologies The Method and the Methodology; Why use Methodology ? the Unified Software Development Process; Participative Design Approaches ; Issues in Choosing Methodology; Hard Vs Soft Methodologies.
(Practical Implementation in "c++")
Text Books:
REFERENCES:
Pearson Education.
55CS4: Concept in Programming Language
UNIT I
Definition of Programming Language , Implementation of high -level languages, Data elements , binding time , binding identifiers to names, binding of attributes, Binding time. Concept of r-value and I- value and their implementation . Effect of Environment on a language, Language paradigms. Language translation issues.
UNIT II
Data type, Type checking and type conversion, elements of specification and implementation of data type . . Implementation of elementary data types; integer, real, character, Boolean Pointer, enumerated type Implementation of structured data types. Vectors & arrays, sets, Files.
UNIT III
Abstract data type, encapsulation . Implementation of new data types, Subprogram definition and activation, their Implementation, parameter passing methods, generic subprograms, Scope rules.
Unit IV
Type equivalence, type definitions with parameters , Implementation of Inheritance. Storage management issues like static and dynamic allocation, stack based allocation and management, Heap based allocation and management.
UNIT V
Sequence control, Implicit and explicit sequence control, Sequencing with arithmetic expression, Sequence control between statements, prime programs, implementation of case statement.
UNIT VI
Subprogram sequence control, recursive and non recursive subprogram. Data control , referring environment, dynamic and static scope, static chain implementation and display implementation.
BOOKS:
§ Programming Languages, 1st edition by T.W. Pratt and M.V.Zelkowitz &T.V. Gopal by Pearson Education, 2006
§ Programming Languages, Ravi Sethi, Addison Wesley.
55CS5: System Programming
UNIT I:
IBM 360/370 & Assembler- Introduction to System Programming & its components. M/C Architecture, Data Formats & Register Formats, Concept of assembler, design of single pass and two pass assembler.
UNIT II:
Microprocessor -concept of macro , macro call within macro, macro definition within macro, recursive macro calls, design of macro processor.
UNIT III:
Linker and Loader- concept of static and dynamic relocation , external symbols, design of linker, design of object file for different loading schemes.
UNIT IV:
Common Object file format & System Utilities - Structure of object file and executable file, section or segment headers, symbol table , concept of storage class, string various, data type line insert, character, arrays structures . Source code control system, make , link editor, symbolic debugger.
UNIT V:
Unix Device Drivers- Definition, Anatomy and Types, Device programming, Installation, Incorporation of driver routines, Basic device driver operation, Implementation with Line Printer & Disk , Comparative study between device drivers for UNIX & Windows.
UNIT VI :
Compiler- Phases of Compilers, Overview of Databases and Algorithms required for all phases. Role of lexical analyzer, recognition of tokens, Study of LEX &YACC.
BOOKS:
SYLLABUS OF VI SEMESTER B.E. COMPUTER SCIENCE (SEMESTER PATTERN)
66CS1: DESIGN AND ANALYSIS OF ALGORITHMS
UNIT I:
Mathematical foundations, summation of arithmetic and geometric series, n, n2, bounding summation using integration, recurrence relations, solution of recurrence relations using technique of characteristic equation and generating functions, Complexity calculation of various standard function s, principles of designing algorithms.
UNIT II:
Asymptotic notations of analysis of algorithms, analyzing control structures, worst case and average case analysis , amortised analysis, application of amoterized analysis, Sorting networks, comparison networks, biotonic sorting network, advanced data structures link Fibonacci heap , disjoint set reprentation, red and black trees and their applications.
UNIT III:
Divide and conquer basic strategy, binary search, quick sort, merge sort, matrix operations, Greedy method- basic strategy, application to job sequencing with deadlines problem, minimum cost spanning trees, single source shortest path etc.
UNIT VI:
Dynamic Programming basic strategy, multistage graphs, all pairs shortest path, single source shortest paths, optimal binary search trees, traveling salesman problem, graph colouring , Hamiltonian cycles etc, Approximation algorithm and concepts based on approximation algorithms.
UNIT VI:
NP-hard and NP- complete problems, basic concepts, non-deterministic algorithms, NP- hard and NP- complete, decision and optimization problems, graph based problems on NP Principle, Computational Geometry, Approximation algorithm.
Text Books
· Thomas H. Cormen et al "Introduction to Algorithms" , Prentice Hall of India.
· Design & Analysis of Computer Algorithms by Aho, Pearson education. Horowitz, Sahani , Rajsekharam
· "Computer Algorithms", Galgotia Publications Pvt. Ltd. Brassard , Bratley, "Fundamentals of Algorithms" ,Prentice Hall.
Reference Books:
· Computer Algorithems: Introduction to Desing and analysis, 3rd Edition , By Sara Baase & A.V. Gelder Pearson Education.
66CS2: Database Management Systems
UNIT I:
Database system concepts and Architecture- concept of relational database, Relational algebra, SQL- the relational database standard, introduction to PL/SQL.
UNIT II:
Database design theory- Functional dependencies and normalization, relational database design algorithms, practical database design and demoralization, Relational constants, programmatic ways for implementing constraints, tiggers.
UNIT III:
Physical database design- concept of physical and logical hierarchy, storage structures link cluster, index organized table, partitions, various table storage parameters, concept of index , B-trees, hash index, function index ,bitmap index.
UNIT IV:
Process and memory management in database: Various type of tasks in database, database buffer management, log buffer management code reuse, concept of two tier and N-tier architecture, data dictionary and catalog information database recovery technique. Aries Algorithm for recovery.
UNIT V:
Query optimization and performance tuning - Various techniques for query optimization strong and weak equivalence, cost base optimization, Use of different storage structures in query optimization.
UNIT VI:
Transaction Processing- Transaction and system concepts, Desirable properties of transaction, Schedules and recoverability, serializability of schedules, concurrency control, lockbase protocols and time stamp based protocols , red consistency.
BOOKS:
· Fundamentals of Database System- Elmasiri, Navathe & Gupta, Pearson Education.
· Database System by S.K.Singh, Pearson Education.
· Principles of Database System- Ullman, Golgotia Publications 1998.
REFERENCE BOOKS:
66CS3: computer networks
UNIT I:
Uses of Computer Networks, Network Hardware:- LAN, WAN, MAN ,Network Software- protocol hierarchies, design issues for layers, connection oriented and connection oriented and connection less service primitives, Services to protocol relationship . reference models-OSI and TCP/IP . Performance : Bandwidth and Latency, Delay X Bandwidth Product, High Speed Networks, Application Performance Needs.
UNIT II:
Switching and MAC Layer: Packet Switching: Multiplexing: TDM FDM.
Multiple Access: Random Access, Controlled Access, Channelization, LAN: Token Ring, FDDI, Ethernet, Gigabit Ethernet, Wireless LANs: IEEE 80.211.
UNIT III:
Data Link Layer : Error Detection and Correction, Flow Control protocols, Error control protocols, HDLC, PPP.
UNIT IV:
Network Layer: Routing Algorithms - Shortest path Algorithm, Flooding, Flow based routing , Distance vector routing , Link state routing , Hierarchical routing.
Congestion Control Algorithms: Leaky bucket algorithm, Token bucket algorithm . Congestion prevention Policies, Traffic shaping , Choke packets, Load shedding, Jitter Control.
UNIT V:
Transport Layer: The transport Service : Service Provided to upper layers, Transport Service primitives, Berkeley sockets, Elements of Transport protocols: Addressing, Connection establishment, Connection release, Flow control and buffering, Multiplexing, Crash recovery, Introduction to Internet Transport protocols: Introduction to UDP, Remote procedure call, Introduction to TCP, Performance issues: Performance problems in Computer Network, Network performance measurement, System design for better performance, Fast TPDU processing, Protocols for Gigabit Networks.
UNIT VI:
Wide Area Network : Packet switching principals, X.25, ATM and frame relay: ATM protocol Architecture, cells, cell format, Segmentation and reassembly in ATM, ATM adaptation Layer 5:
Introduction to Frame relay and frame relay protocol architecture.
TEXT BOOK:
· Computer Networks: 4th ed by Andrew .S. Tanenbaum, Pearson Education.
· Data Communications and Networks: 4th ed by Behrouz. A. Forouzan. Tata McGraw Hill Publication.
· Computer Networks: A system approach by Larry L. Peterson and Bruce S. Davie, 3rd Edition, Morgan Kaufmann Publishers.
· Data & Computer Communications: William Stallings, Sixth Edition, Pearson Edition Asia.
REFERENCE BOOK:
· Communication Networks: By Alberto Leon -Garcia & Indara Widjaja, 2nd Edition, McGraw Hill.
·
66CS4: MICROPROCESSOR & INTERFACING
UNIT I:
8085 based Microprocessor organization , 8085 Instruction set , Assembly language programming.
UNIT II:
Memory & I/O organization, Address decoding, interrupts of 8085, Basic timing of 8085.
UNIT III:
8085 Interfacing with 8255, Sample keyboard matrix interfacing with 8085,Interfacing of 7 segments LED with 8085,Introduction to DAM using HOLD/HLDA Signals.
UNIT IV:
8279 Keyboard/ display controller, Interfacing of Stepper motor with 8085.
UNIT V:
8051 architecture, code/ data memory interfacing, I/O interfacing, Address decoding logic , Interrupts.
UNIT VI:
Serial data communication, UART operation, 8051 Instruction set, assembly language programming.
TEST BOOKS:
§ Microprocessor Architecture, Programming and Applications with 8085/8080 A by R.S. Gaonkar, Wiley Eastern Ltd.
§ The 8051 Microcontroller & Embedded Systems. By Mazidi , Pearson Education.
§ The 8051 Microcontroller, Architecture, programming & applications, second edition by K.J. Ayala, Penram International.
§ Microcontrollers: Architecture, Programming , Interfacing & System design by Rajkamal, Pearson Education.
§ The 8 bit microprocessor & Microcontroller by V.J. Vibhute.
·
·
66CS5: SOFTWARE ENGINEERING AND PROJECT MANAGEME
COURSE MODULES:
MODULE
LEARNING OBJECTIVE
INDICATIVE HOURS
Software Engineering an Introduction
Introduction to Software Engineering, Software Myths, Software Engineering- A Layered Technology, Software Process Framework, Software Process Models. The waterfall Model, Incremental Process Models, Evolutionary Process Models, Specialized Process Models, The Unified Process Model, Agile Process Models.
8
Software Engineering Practice
An Overview, Communication Practices, Planning Practices, Modeling Practices, Construction Practice & Deployment, System Engineering Hierarchy, Business Process Engineering, Product Engineering, System Modeling, Requirements Engineering.
7
Software Engineering Analysis & Design
An overview, Requirements analysis, analysis Modeling Approaches, Data Modeling, Object- Oriented Analysis, Scenario- Based Modeling, Flow- Oriented Modeling, Class- based Modeling, Behavioral Model.
Design Engineering Concepts, Design Model, Pattern- Based Software Design.
8
Testing Strategies and Tactics
An overview, Unit Testing, Integration Testing, Validation Testing, System Testing Debugging.
Software Testing Fundamentals, Black- Box Testing, White- Box Testing .
5
Product Metrics
An overview, Software Quality, A Framework for Product Metrics, Metrics for Analysis & Design Models, Metrics for Testing & Maintenance.
7
Software Project Management
An overview, Software Measurements, Metrics for Software Quality, Software Project Estimation Techniques, Project Scheduling, Risk Management, Quality Management, Change Management, Software Reengineering.
9
Total
44
§ Text Books:
§ Software Engineering - A Practitioner's Approach (Sixth Edition )-Roger Pressman(TMH)
§ Reference Books:
§ Software Engineering (Seventh Edition)- Ian Summerville, Pearson Education.
§ The 8 bit microprocessor & Microcontroller by V.J. Vibhute.
§ tice by Pfleeger, Pearson Education
§ Software Engineering - Schaum's Series (TMH)
Object - Oriented Analysis and Design using UML in Rational Rose 2003 Enterprise Edition (Case Studies)
Soft6ware Engineering Theory and
SYLLABUS OF VII SEMESTER B.E. COMPUTER SCIENCE (SEMESTER PATTERN) 77CS1: TCP/ IP & Internet
UNIT I:
Introduction and Overview. Comparison of OSI Model and TCP/IP model. Networking Technologies: LANS, WANS, Connecting Devices. Internetworking concept and Architectural model. Internet Backbones, NAP, ISP's, RFC's, internet Standards.
UNIT II:
Internet Addresses: IP address classes, subnet mask, CIDR, ARP, RARP, Internet Protocol, Routing IP Datagrams, ICMP and IGMP.
UNIT III:
UDP, TCP, Sockets and socket Programming Routing in Internet, Routing protocols- RIP, OSPF and BGP Introduction to Multicasting and Multicast routing.
UNIT IV:
Host Configuration :BOOTP, DHCP; Services; Domain Name System ,FTP, TFTP and Electronic Mail: SMTP, MIME, IMAP, POP.
UNIT V:
Network Management: SNMP, WWW: HTTP, Mobile IP Multimedia: RTP, RTCP.
UNIT VI:
Middiewares: RPC, RMI, Introduction to IPv6and ICMPv6, Internet Security: IPSec, PGP, Firewalls, SSL.
BOOKS:
Reference Book:
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77CS2: Language Processors
UNIT I:
Introduction to Compilers : Compilers and translators, Phases of compiler design , cross compiler, Bootstrapping, Design of Lexical analyzer, LEX.
UNIT II:
Syntax Analysis: Specification of syntax of programming languages using CFG, Top - down parser, design of LL (1)Parser, bottom up parsing technique, LR Parsing algorithm, Design of SLR, LALR, CLR parses.
UNIT III:
Syntax directed translation : Study of syntax directed definitions & syntax directed translation schemes, implementation of SDTS, intermediate notation : postfix, syntax tree, TAC, translation of expression, controls structures, declarations, procedure calls, Array reference.
UNIT IV:
Storage allocation & Error Handling: Run time storage administration, stack allocation, symbol table management, Error detection and recovery : lexical, syntactic, semantic.
UNIT V:
Code optimization : Important code optimization techniques, loop optimization, control flow analysis, data flow analysis Loop invariant computation, Induction variable removal, Elimination of Common sub expression.
UNIT VI:
Code generation - Problems code generation , Simple code generator, Register allocation and assignment, Code generation from DAG, Peephole optimization.
TEXT BOOKS:
§ Compilers: Principles Techniques and Tools 1st edition by A.V. Aho, Sethi, Ullman, Pearson education.
§ Principal of Compiler Design - Alfred V. Aho & Jeffery D. Ullman, Narosa Pub. House.
77CS3: Elective I:- Digital Signal Processing:
UNIT I:
Basic elements of a Digital Signal Processing system, Classification of signals, Concept of frequency in Continous-time and discrete - time singles, Sampling theorem, Quantization of continous-amplitude signals, quantization of sinusoidal signals. Discrete- time signals, Discrete-time systems, Analysis of discrete-time LTI systems, Correlation of discrete-time signals.
UNIT II:
The Z-transform, Properties, Rational Z-transforms, The inverse Z-transform by Contour Integration , Power series expansion, Partial- faction expansion, Decomposition of rational Z-transforms, One sided Z- transform, Properties, Solution of difference equations.
UNIT III:
Frequency analysis of Continous- time signals, Frequency analysis of discrete- time signals, Fourier series for discrete- time periodic signals, Power density spectrum of periodic signals, Fourier transform of Discrete- time aperiodic signals, Energy density spectrum of aperiodic signals, Concept of bandwidth, Symmetry properties of the Fourier transform theorems and properties.
UNIT IV:
The Discrete Fourier Transform : Its properties and application , Frequency domain sampling: The DFT, Properties of the DFT, Linear filtering methods based on the DFT, Use of THE DFT in linear filtering ,Filtering of long data sequences, Frequency analysis of signals using the DFT.
UNIT V:
Introduction to FFT algorithms: Decimation in time - FFT algorithm, Decimation in frequency- FFT algorithm, Quantization effect in the computation of the DFT, Quantization errors in the direct computation of the DFT, Quantization errors in FFT algorithms, DCT.
UNIT VI:
Design of digital filters: Design of FIR filters based on windows, Design of IIR filters from analog filters, IIR filter design by approximation of derivatives, Impulse invariance, Bilinear transformation, Examples of digital filter designs based on the bilinear transformation
Text Books:
§ Digital Signal Processing : Alan V. Oppenheim .W. Schaffer, Pearson Education.
§ Digital Signal Processing: John G. Proakies and D. Monalkies & D. Sharma, Pearson Education.
Reference Books:
§ Digital Signal Processing , 2nd Edition by E. Pearson Education.
§ Theory and application of signal processing -Rabiner & Gold (PHI) .
§ Digital filter design and analysis- Andreas Antonius.
77CS3: Elective I:- Computer Graphics
UNIT I:
Basic fundamentals of random scan, raster- scan devices and LAD displays. Video Basics , Interactive Devices. Line, Circle, Ellipse drawing techniques and Algorithms.
UNIT II:
Polygon filling method : Scan Conversion Algorithms: Simple Ordered edge Fill, Fence fill and Edge Fill, Fence fill and Edge Flag Algorithm, Seed fill Algorithms: Simple and Scan Line Seed Fill Algorithm, Antialiasing and Halftoning techniques.
UNIT III:
2D Clipping algorithms for regular and irregular windows: Sutherland Cohen Subdivision, Mid - Point subdivision , Cyrus Beck and Sutherland Hodgman polygon clipping Algorithm. Clipping about Concave regions. 2D Transformations, Normalized Device Coordinates and Viewing Transformation.
UNIT IV:
3D System Basics and 3D Transformations, Prarallel and Perspective projections, Hidden line/ surface Removal Algorithms. Rendering- Shading, Ray tracing techniques and Color Systems.
UNIT V:
Curve generation- Interpolation Technique, B-spline and Bezier curves, Graphics Software Packages- Rules for designing Graphics Package, Segmentation and Display file Compilation.
UNIT VI:
Graphics Systems- Display Processors, Device Independent Graphics Systems, User Interface Design. Graphics Standard -Basic principles of X-windows, X-terminal.
Test Books :
§ Computer Graphics, Hearn and Baker, Pearson Education
§ Procedural Elements of Computer Graphics III Edition, Rogers, McGraw Hill.
§ Principles of Interactive Computer Graphics, Newman and Sproull, McGraw Hill.
Reference Books:
Computer Graphics: Principles and Practice in "C" by J.D. Foley Pearson Education.
77CS3: Elective- I:- Real Time Operating Systems
UNIT I :
Introduction : Car & driver example, Issues in real time systems, Structure of a Real time systems ,Structure of a Real time system. Hard versus soft real time systems: Jobs & processors, release times, deadlines, timing , constraints, Hard & Soft timing constrains, Hard real time systems, soft real time systems. A Reference model of Real-time systems: processors and resources, temporal parameters of real-time workload, periodic Task model, precedence constraints & data dependencies other types of dependencies, functional parameters, resource parameters of Jobs & parameters of resources, scheduling Hierarchy.
UNIT II:
Effective release times and deadlines, Optimality and non optimality of EDF & LST, Challenges in validating timing constraints in priority- driven systems, off-line versus on-line scheduling. Clock- driven scheduling, Priority driven scheduling of periodic tasks.
UNIT III:
Scheduling aperiodic & sporadic jobs in priority-driven systems: Deferrable servers, Sporadic servers , Constant utilization, total bandwidth and weighted fair-queuing servers, scheduling of sporadic jobs. Resource and resource access control : assumption on resources and their usage, effects of resource contention & resources access control, non preemptive critical sections, basic priority- inheritance protocol, basic priority - ceiling protocol, stack- based priority-ceiling protocol, use of priority-ceiling protocol in dynamic-priority systems, preemption- ceiling protocol, controlling accesses to multiple- unit resources.
UNIT IV:
Model of multiprocessor & distributed systems, Task assignment, Multiprocessor priority- ceiling protocol, Elements of scheduling algorithms for end-to end periodic tasks, Scheduability of fixed priority end-to-end periodic tasks, end-to- end tasks in heterogeneous systems.
Programming Languages and Tools: Desired language characteristics, Data typing , control structures, Facilitating hierarchjical decomposition, packages, Run time error handling , Overloading and generics, Multitasking , Lowlevel programming, Task scheduling, Timming specifications, Programming environments, Run time support.
UNIT V:
Real Time Database: Introduction, Basic Definations, real time vs. general purpose databases, main memory databases, Transaction priorities, Transaction aborts, concurrency control issues, disk schedulinh algorithms, maintaining serialization consistency, database for hard real time systems
Real Time Communication : Introduction, Network Topologies, Contention based protocol, token based protocol, Stop and go protocol, Polled bus protocol, Hierarchical round pro5tocol, Deadline based protocols, Fault tolerant routing.
UNIT VI:
Fault Tolerance Techniques: Causes of failures, Fault types, Fault detection, Fault and error containment, Redundancy, Data diversity, Reversal checks, Integrated failure handling.
TEXT BOOK:
§ Real- Time Systems: Jane W.S. Liu, Pearson Education.
§ Real Time System: C.M. Krishna & Kang G. Shin (TMH)
77CS3: Elective- I: Fundamentals of Multimedia
UNIT I:
Multimedia Authoring and Data Representations;
Introduction to Multimedia, Multimedia Authoring and Tools, Graphics and Image Data Representations.
UNIT II:
Color in Image and Video, Fundamental Concepts in Video, Basis of Digital Audio.
UNIT III:
Multimedia Data Compression: Lossless Compression Algorithms, Run-Length Coding, Variable- Length Coding (VLC), Huffman Coding, Adaptive Huffman Coding, Lossy Compression Algorithms, Quantization, Transform Coding, Discrete Cosine Transform (DCT), Image Compression Standards.
UNIT IV:
Basic Video Compression Techniques, MPEG Video Coding I-MPEG- I and 2, MPEG Video Coding II- MPEG Video Coding II-MPEG-4,7 and Beyond, MPEG Audio Compression .
UNIT V:
Multimedia Communication : Computer and Multimedia Networks, Multimedia Network Communications and Applications, Interactive TV (ITV) and Set-Top Box (STB),, Broadcast Schemes for Video-on -Demand, Buffer Management, Further Exploration, Wireless Networks, Multimedia over Wireless Networks, Trends in Wireless Interactive Multimedia.
UNIT VI :
Multimedia Retrieval: Content - Based Retrieval in Digital Libraries, Minimum three Case studies.
Text book :
§ Fundamentals of Multimedia 1st Edition by Mark S. Drew & Ze- Nian Li, Pearson Education.
Refverence Books:
§ Multimedia Fundamentals, Volume 1: Media Coding and Content and Content processing, 2nd Edition by Ralf Steinmetz, Klara Nahrstedt, Pearson Education .
§ Multimedia Marking Work (TMH Pub.) by Tay Vaughan.
§ Advanced Multimedia Programming (McGraw Hill Pub)- Steve Rimmer
§ Digital Image Processing- Gonzalez and Woods, Pearson Education.
77CS4::Elewctive I;- Advanced Computer Architecture
UNIT I:
Models of parallel computer, multiprocessors and multicomputers, multivector and SIMP computers, PRAM and VLSI models conditions of parallelism, data and resource dependencies, grain size and latency, grain packing and scheduling , program flow mechanisms, system interconnect architectures.
UNIT II:
Principles of scalable performance, performance metrics and measures, speedup performance laws, advanced processor technology, superscalar and vector processors, verified memory organizations, shared memory organizations.
UNIT III:
Pipeline and superscalar techniques, liner pipeline processors, reservation and latency analysis, collision free scheduling, pipeline schedule optimization, instruction pipeline design, arithmetic pipeline design , arithmetic pipeline design, superscalar and superscalar and superpipeline design.
UNIT IV:
Multiprocessors and multicomputers, multiprocessor system interconnects, cache coherence and synchronization mechanisms, messing passing schemes.
UNIT V:
Multivector and SIMD computers vector processing principles, compound vector processing, SIMD computer organizations scalable multithread and dataflow architectures.
UNIT VI :
Introduction to parallel Programming Models, Parallel Language Constructs ,
Elementary theory about dependence analysis, Code optimizations and Scheduling.
Books:
Kai Hiwang, "Advanced Computer Architecture" McGraw Hill Richard Y.Kausi, "Advanced Computer Architecture" Prentice Hall of India.
Advanced Computer Architecture by D. Sima, Fountain & Kacsuk, 1st Edition, Pearson Education.
77CS4: Elective-II:-Artificial Intelligence
UNIT I:
Introduction: Scope of AI, AI problems, AI technique, Production system Characteristics, Basics of problem solving :problem representation paradigms Defining problem as a state space representation.
UNIT II:
Search Techniques: Problem size, complexity , approximation and search; depth, breadth and best search; Heuristic Based Search; Heuristic search, Hill climbing, best - first search, branch and bound.
UNIT III:
Knowledge representation: First order logic, Unification , Resolution in Predicate Logic.
Structured Knowledge Representation: Semantic Nets, Frames and Scripts.
Learning : Block architecture of learning system, Types of learning, performance Measures.
UNIT IV:
Uncertainty Treatment: Formal and empirical approaches including Bayesian theory, belief functions, certainty factors and fuzzy sets.
UNIT V:
Expert Systems: Fundamental blocks, knowledge Engineering, knowledge Acquisition , Need and justification for expert systems, Detailed Discussion form Example Domains- (form)Industry, Language, Medicine, Verification, Vision, Knowledge Based Systems; concept of shells.
UNIT VI:
Language Machine: Introduction to Natural Language understanding Level of knowledge in NLU, Approaches to NLU, Problems in NLU, Basic parsing techniques.
Text Books:
Reference Books:
77CS4: Elective:-II:- Enterprise Resource Planning
Course Modules:
Module
Learning Objective
Indicative Hours
ERP- Curtain Raiser
An overview, Accommodating variety, Integrated Management Information, Seamless Integration, Supply Chain Management, Resource Management, Integrated data model, scope, Technology, Benefits of ERP, Evolution, ERP revised, ERP & Modern Enterprise, problems.
6
ERP& Related Technologies
An overview, Business Process Reengineering(BPR), Management Information System(MIS), Decision Support Systems (DSS), Executive Information System (EIS), Data Warehousing, Data Mining, OLAP.
6
Business Engineering & ERP
An overview, What is Business Engineering (B.E.)? Significance of BE, Principles of BE, BPR, ERP & IT, BE with IT, ERP and Management concerns, problems.
Business Modeling: An overview, Building the Business Model, problems.
6
ERP Implementation and the Competitive Advantage
An overview, Role of consultants, vendors & users, customization, precautions, ERP: Post- implementation options, ERP implementation Lifecycle, Guidelines for ERP implementation problems. ERP & competitive strategy, problems.
8
The ERP Market & Making of ERP
An overview, SAP AG , SAPR/3 Applications, Baan, Oracle, People Soft, JD Edwards, Examples of Indian ERP packages, problems.
An overview, Market Dynamics & Competitive Strategy, problems, Future Directions in ERP.
8
ERP Case Studies
Various ERP Case studies.
6
Total
40
Text Books:
( 3,10)
8
8
True because in both equations x = 0 or x = -4
That system of equations has no solution. When the two equations are graphed, they turn out to be the same straight line, so there's no such thing as a single point where the two lines intersect. There are an infinite number of points that satisfy both equations.
( 3,10)
8
8
x=3
True because in both equations x = 0 or x = -4
That system of equations has no solution. When the two equations are graphed, they turn out to be the same straight line, so there's no such thing as a single point where the two lines intersect. There are an infinite number of points that satisfy both equations.
x + y + x = 2x + y
Without any equality signs the given terms can't be considered to be equations
{-1,-2}
4+4=8 2+6=8
It is an inconsistent system of equations. --- Or perhaps you want examples? One pair of inconsistent equations: x + y = 4 x + y = 1 Another pair: y = x2 + 3 y = 1 (In the first equation of this pair, y is minimised when x = 0, when its value is 3. But the second equation claims that y = 1.)
It is (5 and minus1).