DISCRETE MATHEMATICAL STRUCTURES€¦ · Web viewDISCRETE MATHEMATICAL STRUCTURES Logic, Sets and...

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DEPARTMENT OF COMPUTER SCIENCE VIKRAMA SIMHAPURI UNIVERSITY: NELLORE – 524 004 SECTION B DISCRETE MATHEMATICAL STRUCTURES Logic, Sets and Functions – Logic Proportional equivalence, Predicates and Quantities, Nested quantifiers, Methods of proof, sets, set operations, functions. The Integers and Divisions, Integers and Algorithms, Applications of number theory, Mathematical Reasoning, Induction and Recursion – Proof strategy, Sequences and Summations, Mathematical induction. Recursive definitions and Structural induction, Recursive algorithms, Program correctness. The basics of counting, the pigeonhole principle, Permutations and combinations, Binomial coefficient, Generalized Permutations and combinations, Generating Permutations and combinations, Recurrence relations, solving Recurrence relations. Relations – Relations and their properties, n-ary Relations and their applications, Representing Relations, Closures of relations, Equivalence relations, Partial orderings. Languages and Grammars, Finite state machines with output, Finite state machines with no output, Language recognition, Tuning machines. Graphs – Introduction to Graphs, Graph terminology, Representing Graphs and Graph isomorphism, Connectivity, Euler and Hamilton Paths, Shortest path problems, Planar Graphs, Graph coloring. COMPUTER ORGANIZATION Logic circuits: Logic Functions – synthesis of Logic Functions – Minimization of Logic – Synthesis with NAND and NOR gates implementation of Logic gates – Flip-flops – Registers and shift registers – counters – decoders – Multiplexers – PLDs – sequential circuits. Basic structures of computers: Functional units – Basic operational concepts Bus structures performance Multiprocessors and Multi computers: Functional Units – Basic operational concepts – Bus structures performances – Multi processor and multi computers – Historical Perspective. Machine Instruction and programs: Numbers, Arithmetic operations and characters – Memory locations and Address, operations – instructions and instruction, sequencing-addressing modes-assembly language-basic VSURESET Computer Science Ph.D. Entrance Examination Syllabus & Model Questions Page 1 of 12

Transcript of DISCRETE MATHEMATICAL STRUCTURES€¦ · Web viewDISCRETE MATHEMATICAL STRUCTURES Logic, Sets and...

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DEPARTMENT OF COMPUTER SCIENCE VIKRAMA SIMHAPURI UNIVERSITY: NELLORE – 524 004

SECTION B

DISCRETE MATHEMATICAL STRUCTURESLogic, Sets and Functions – Logic Proportional equivalence, Predicates and Quantities, Nested quantifiers, Methods of proof, sets, set operations, functions.

The Integers and Divisions, Integers and Algorithms, Applications of number theory, Mathematical Reasoning, Induction and Recursion – Proof strategy, Sequences and Summations, Mathematical induction. Recursive definitions and Structural induction, Recursive algorithms, Program correctness. The basics of counting, the pigeonhole principle, Permutations and combinations, Binomial coefficient, Generalized Permutations and combinations, Generating Permutations and combinations, Recurrence relations, solving Recurrence relations. Relations – Relations and their properties, n-ary Relations and their applications, Representing Relations, Closures of relations, Equivalence relations, Partial orderings. Languages and Grammars, Finite state machines with output, Finite state machines with no output, Language recognition, Tuning machines. Graphs – Introduction to Graphs, Graph terminology, Representing Graphs and Graph isomorphism, Connectivity, Euler and Hamilton Paths, Shortest path problems, Planar Graphs, Graph coloring.COMPUTER ORGANIZATIONLogic circuits: Logic Functions – synthesis of Logic Functions – Minimization of Logic – Synthesis with NAND and NOR gates implementation of Logic gates – Flip-flops – Registers and shift registers – counters – decoders – Multiplexers – PLDs – sequential circuits. Basic structures of computers: Functional units – Basic operational concepts – Bus structures – performance – Multiprocessors and Multi computers: Functional Units – Basic operational concepts – Bus structures performances – Multi processor and multi computers – Historical Perspective.

Machine Instruction and programs: Numbers, Arithmetic operations and characters – Memory locations and Address, operations – instructions and instruction, sequencing-addressing modes-assembly language-basic input/output operations –subroutines-encoding of machine instructions. Instructions-Assembly language-O/I operations-Registers and addressing-Instructions language-program flow control-I/O operations logic instructions of 6300 and Intel Pentium.

Input/output organization: accessing I/O devices-Interrupts-Direct Memory Access-buses 240-interface circuits-standard I/O interfaces. Memory system, concepts-semiconductor RAM memories-Read-only memories –cache memories-performance considerations-virtual memories management requirements-secondary storage arithmetic: addition and subtraction of signal members-design of fast adders-multiplication of positive members- signed operand multiplication-fast multiplication-integer division-floating point numbers and operations. Basic processing unit: concepts-execution of a complete instruction-Multiple-Bus organization- hardware control-micro programmed control.

Pipelining: concepts-Data hazards-instruction hazards-influence on instruction sets- data path and control constructions-supers cal operation-ultra SPARC II-performance considerations.

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DATA STRUCTURESJava: Introduction-structure of a java program-The java compiler and virtual machine-Documentation Comments-Data types-Methods-Exceptions-Your very own data type-Access Moderns-Inheritance And Method-Overriding-Currency Revisited-Defining an Exception class-Generic Methods-Garbage Collection-Recursion-Testing and Debugging.

Performance Analysis of programs: What is performance? –Space complexity-Time complexity Asymptotic Notation: Introduction-Asymptotic Notation-Asymptotic Mathematics (optional) - Complexity Analysis Examples-practical complexities.

Linear Lists – Array Representation: Data objects and Structures –The Linear List Data Structure-Array Representation-Vector Representation Linked Lists and Chains-Circular Lists and Header Nodes-Doubly Linked Lists.

Arrays and Matrices: Arrays-Matrices-Special Matrices-Sparse Matrices

Stacks: Definition and Applications-The Abstract Data type-Array Representation-Linked Representation-Applications. Queues: Definition and Applications –The Abstract Data Type- Array Representation-Linked Representation –Applications.

Binary and Other Trees: Trees Binary Trees-Properties of Binary Trees-Representation of Binary Trees-Common Binary Tree operations-Binary Tree Traversal-The ADT Binary Tree-The Class Linked Binary Tree- Applications.

Binary Search Trees: Definitions-Abstract Data Types-Binary Search Tree Operations and Implementation-Binary Search Trees with Duplicates-Indexed Binary Search Trees-Applications Balanced Search Trees: AVL trees-Red –Black Trees-Splay Trees-B Trees- References and Selected Readings.Graphs: Definitions-Applications and more Definitions-Properties-The ADT Graph- Representation of Unweighted Graphs-Representation of Weighted Graphs-Class implementations-Graph Search Methods-Application Revisited.

OPERATING SYSTEMSIntroduction to Operating Systems, Types of Operating Systems, Computing Environments, Computer System operation, I/O structure, and Hierarchy protection, Hardware, protection, Network structure Operating system Components and services-system calls, System programs, System structure, Virtual machines, System Design and implementation.

CPU Scheduling: Scheduling criteria, scheduling Algorithms, Multiple processor scheduling, Real-Time scheduling .Process Synchronization: The critical-section problem, synchronization, hardware, Semaphores, classic Problems of synchronization, critical regions, monitors, operating system Synchronization and Atomic Transactions.

Dead Locks: Dead Lock characterization, Dead Lock handling, Dead Lock prevention, Dead Lock Avoidance, Dead Lock Detection and Recovery.

Memory Management: Swapping, contiguous memory allocation, paging, segmentation with paging Concept of virtual memory demand paging page replacement, Allocation of frames, Thrashing. File System Interface & Implementation: File concept, Access methods, Directory structure, File System Mounting, File sharing protection, File system structure, and implementation, Directory Implementation, Allocation methods. Free space management, Efficiency performance, recovery, Log structured file system, NFS.

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I/O systems: Overview, I/O hardware, Application I/O interface, Kernels I/O subsystem, Transforming I/O to hardware operations, STREAMS, performance of I/O. Mass Storage Structure: Disk Structure, Disk scheduling. Disk management, Swap-space Management, RAID structure, Disk Attachment, stable-storage implementation, Teritory-storage Structure.

Distributed System Structure: Background, Topology, Network Types, Communication Protocols, Robustness, Design issues.

Protection: Goals, Domain of protection, Acess matrix and implementation, Acess rights, capability Based systems, Language-based protection.

The security problem: User authentication, program threats, system threats, security systems Facilities intrusion detection, cryptography, computer-security classification. Linux system: History, design principles, Kernel modules, process management, scheduling Memory management, File systems, Input and Output, IPC, Network structure, security.

WINDOWS 2000: History, design principles, system components, Environment subsystems, File system, Network programming interfaces.

DATA BASE MANAGEMENT SYSTEMIntroduction, Database System Application-purpose of Database Systems-View of Data-Database Languages-Relational Databases-Database Design-Object based analysis-Data architecture.

Entity Relationship model: Structure of Relational Databases, Relational Algebra operations, Modifications of database.

SQL: Data definition-Structure of Queries-set operations, Aggregate Functions-Nested Sub Queries-Complex Queries-SQL data types and schemas-Integrity Constraints-Authorization Embedded SQL –Dynamic SQL.

The Entity-Relationship Model-Constraints-Entity Relationship diagrams, Design Issue-Weak Entity sets-Database Design for Banking Enterprise. The unified a Modeling temporal data-User Interfaces to database-Web Fundamentals- Servlets and JSP Building Large web applications-Triggers-Authorization in SQL.

OBJECT-DATABASES AND XML: Complex data type-structured types and inheritance in SQLTable Inheritance Array and Multi set Types in SQL-Object-Identity and Reference Types in SQL-Implementing O-R Features-persistent programming Languages-object oriented versus object Relational Structure of XML Data XML Document Schema-Querying and Transformation-Application program Interfaces to XML-Storage of XML data.

Query Processing: Measures of Query cost-Selection Operation-Sorting-Joint Operation-Evaluation of Expressions-Query Optimization: Transformation of Relational Expressions- Estimating Statistics of Expression results-Choice of Evaluation plans.

Transactions: Transaction concept, Transaction state-Implementation of Atomicity and Durability Concurrent Executions-Serializability-Recoverability-Implementation of Isolation-Testing for Serializability, concurrency control: Lock Based protocols-Timestamp based protocols-validationBased protocols –Multiple Granularity-Multi version schemes-Dead Lock handling-Insert and Delete Operations-Weak Levels of consistency-concurrency in index structures

Recovery Systems: Failure classification-storage structure-Recovery and Atomicity-Log Based Recovery- Recovery with concurrent Transactions-Buffer Management Failure with lose of Non Volatile storage-Advanced Recovery Techniques-Remote backup systems.

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DATA COMMUNICATION AND COMPUTER NETWORKIntroduction, Network models-Internet model, OSI model Physical Layer: Signals, Analog, Digital, Transmission-Coding, Sampling, Analog Transmission- Modulation of digital and analog signal, Telephone modem, Multiplexing-FDM,WDM,TDM, Transmission Media-cable, wireless, circuit Switching and Telephone network, DSL Technology, cable modern, SONET.

Data Link Layer: Error detection and correction, Data link control and protocols-Stop and Wait, Godack-N, Selective repeat, HDLC, point to point access, Channelization, LANS-Traditional Ethernet, Gigabit Ethernet Wireless LAN’S-IEEE 802.11,Blue tooth, connecting LAN’S-connecting devices, Backbone networks, virtual LANS, Cellular telephony, satellite networks, virtual circuit switching,Frame relay, ATM. Network Layer: Inter-networks, Addressing, Routing, Network layer protocols-ARP, IP, ICMP, IPV6, Routing-Introduction, Unicast routing protocols-RIP, OSPF,BGP, Multicast Routing, protocols-DVMRP, MOSPF, CBT, PIM.

Transport Layer: Process to process Delivery, UDP, TCP, Data traffic, congestion and control, Quality of Service (QOS) and techniques to improve QOS, Integrated services, QOS in switched networks.

Security: Introduction, Symmetric-Key Cryptography, public key cryptography, Message security, Digital signature, user authentication, key management, Kerberos, IP level security: IPSEC, Transport Layer security, Application layer security: PGP, Firewalls, Virtual private networks.

Application Layer: Client-Server model, socket interface Introduction to DNS, Distribution of name Space ,DNS in the Internet, Resolution, DDNS, Electronic mail, SMTP, File Transfer, FTP, HTTP, World Wide Web, Multimedia fundamentals, Digitizing and compression of audio, video, streaming Audio/Video- stored and live, Real time interactive audio/video, voice over IP.

SOFTWARE ENGINEERINGSoftware Engineering – Introduction, Generic view of process, models, an agile view of process. Software Engineering practice- Software Engineering, communication, planning, modeling, Construction Practices and deployment.

System Engineering-Computer-based systems, the system engineering Hierarchy, business process Engineering, product engineering and system modeling. Building the analysis model-Requirement Analysis, modeling approaches, data modeling, Behavioral model. The web engineering process, Analysis models for web apps.

Design Engineering-design process and quality, design concepts the design model, and pattern-used Software design. Architectural design-Software architecture, data design, architectural styles and Patterns, architectural design mapping data flow into a software architecture. Component-level Design- component, designing class-based components, conducting component-level design, objects Constraint language, and design conventional components. Interface Design-Design steps, Web apps Design issues and architecture design.

Testing Strategies–strategies and issues, testing strategies for and Object-Oriented software. Validation Testing and system testing. Software testing tactics-Fundamentals, black box and white box testing, White-box testing basis path testing. Control structure testing, black box testing, Object-oriented testing Methods. Testing methods applicable at the class level inter class testing case design. Testing for Specialized environments, architectures and applications, web application testing- concepts, testing process, component level testing.

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Product Metrics- Software quality, framework, metrics for analysis model design model, source case Testing. Managing software projects- The management spectrum, the W5 HH principle, metrics in process, software measurement and metrics for software quality integrating metrics within the software process. Estimation- observations, decomposition techniques, empirical models, estimation for object oriented projects other estimation techniques, project scheduling, risk management, quality management, reengineering, change management, component based development. DESIGN AND ANALYSIS OF ALGORITHMSDivide and Conquer and Greedy Methods.Dynamic Programming; Basic Traversal and Search Technique.Backtracking; and Branch and Bound Technique.Lower bound Theory; NP-Hard and NP-Complete Problems.Mesh and Hypercube Algorithms. DATA WARE HOUSING AND DATA MININGFundamentals of Data Mining, Data Mining Functionalities, Classification of Data Mining systems, Major issues in data mining, Data Warehouse and OLAP Technology for Data Mining, Data Ware House ,Multidimensional Data Model, Data system Architecture, Data Warehouse implementation, Further Development of Data Cube Technology, from Data Warehousing to Data Mining.

Data preprocessing: Needs of preprocessing the data, Data Cleaning, Data Integration and Transformation. Data reduction, Disretizarion and concept Hierarchy generation. Data Mining Primitives, Languages and System Architectures: Data Mining primitives, Data Mining Query languages, designing Graphical User Interfaces based on a data mining query language Architectures of Data Mining Systems.

Data Generalization and Summarization based Characterization, Analytical characterization: analysis Of Attribute Relevance, Mining Class Comparisons: Discrimination between different Classes, Mining Descriptive Statistical Measures in Large Databases. Mining Association Rules in Large Databases: Association rules from Transactional Databases, Mining Multilevel association Rules from Transaction Databases, Mining Multidimensional association Rules Relational databases and data warehouses, from association mining to Constraint-Based Association Mining.

Classification and Prediction: Issue regarding classification and prediction, Classification by Decision Tree Induction, Bayesian Classification, Classification based on concepts from association Rule Mining, Other classification Methods, Prediction, Classifier Accuracy, Cluster Analysis Cluster Analysis Introduction: Type of data in cluster analysis, A Categorization of Major Clustering Methods, Portioning Methods, Density based methods, Grid-Based methods, Model-Based Clustering Methods, Outlier Analysis.

Mining Complex Types of Data: Multidimensional Analyses and Descriptive Mining of Complex data Objects, Mining spatial databases, Mining, Multimedia databases, Mining Tie-series and sequence data, Mining Text Databases, Mining World Wide Web.

NETWORK SECURITYCryptography-Technology, Conventional Encryption Model, Steganograophy, Classical Encryption Techniques, DES Data Encryption Standard, Block Cipher Design Principles and Modes of operation.

Conventional Encryption Algorithms: Triples DES, International Data Encryption Algorithm, Blowfish, RC5, Characteristics of advanced symmetric Block Ciphers, Confidentiality using Conventional Encryption.

Public-Key Cryptography, Introduction to Number Theory: Prime Numbers, Modular Arithmetic, Euler’s Theorem, primality and Factorization, Discrete Logarithms: Message Authentication and Hash Functions-hash and MAC algorithms.

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Digital Signatures and authentication protocols, Digital Signature Standard, Network Security practice Authentication Applications.

Basic overview of: Electronic Mail Security: pretty Good privacy’s/MIME: IP Security, Web Security Intruders, Viruses and Worms-Firewalls.

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MODEL QUESTIONSVSURESET-2014

Time: 2 Hours Max. Marks: 120(Each question carries 1 mark the candidate has to answer 30 questions from Section A

Carrying in 30 marks and 90 questions from Section B carrying 90 marks)

SECTION – A(GENERAL APTITUDE)

1. 196, 256, 324, 400, 484 ______________A) 576 B) 441 C) 529 D) 625

2. 1/9, 2/27, 8/81 __________ 124/729A) 32/243 B) 128/ 243 C) 256/ 243 D) 64/243

3. A man walks 30m towards of south then turning to his right, he walks 3m then turning to his left, he walks 2 m, again he turns to his left and walks 30m how far is the from his initial position.A) 20m B) 30m C) 60m D) 50m

4. 64, 16:: 70;-A) 17.5 B) 18.5 C)21.5 D) 20.5

5. Solve the given equation

X2 - y2 = 34 X2 - y2 = 544

The value of X and Y are

A) ±4 , ±3 B) ±5, ±3 C) ±3, ±5 D) ±3, ±46. Mathematical standard deviation is represented by

B)

___________ __________N N

C) 2 D) 2

__________ _________ N N2

7. Which of the following is not an internet Browser ?A) Internet Explorer B) Netscape C) Opare D) AQL

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8. Data transfer rate in modems is measured inA) Bits for minute B) Bits for SecondC) Bond widthD) None of the above

9. Basics of steps of research process includesA) Problem definition B) Research designC) Data collection D) All

10. Which of the following comes under quantitative objective o researchA) A Study of estimate the demand of productB) A Study of testing the effect of level of educationC) A Study on the impulse buying behavior of customersD) None.

. . .

30.SECTION –B

(COMPUTER SCIENCE)

31. A Sequential circuit is a combination ofa) Flip flops and registers b) logic gates and registersc) Logic gate and flip flops d) registers and shift registers

32. NAND is the complement of which functiona) XOR b) ORc) NOT d) AND

33. What is the purpose of memory management?a) Deallocate the blocks b) Allocate and deallocate blocks (ANS)c) Allocating blocks d) None

34. What are the TCL COMMANDS in SQL?a) Insert, delete b) create, alterc) Commit, rollback d) grant, revoke

35. What is the full form of SONET?a) Synchronous optical network b) signal optical networkc) Software optical network d) none

36. TCP breaks data into small pieces called a) Files b) Packets c) Envelops d) Bytes37. Encryption and Decryption of data are responsibility of which of the following layer?

a) Physical Layer b) Data Link Layer c) Presentation Layer d) Session Layer 38. Which of the following testing methods is normally used as the acceptance test for a software System

a) Regressing testing b) Integration testing c) Unit Testing d) Functional Testing

39. The 2’s complement representation of the decimal value -15 is a)1111 b) 11111c) 111111 d) 10001

40. Memory protection is of no use in a a) Single user system b) Non-multiprogramming systemc) Non-multitasking system d) None of the above

.

.

.120).

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