Modern Algebra (MC - 301) L T P C

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1 Modern Algebra (MC - 301) L T P C UNIT-I Groups, Abelian groups, Subgroups, Order of a group and an element, Coset, Lagrange s Theorem, Cyclic groups, Cyclic subgroups of prime order, Cayley s theorem. UNIT-II Normal subgroup, quotient group, homomorphism, isomorphism, kernel of homomorphism, fundamental theorem of homomorphism. Permutation groups, alternating group, important examples such as S 3 and K 4 (Klein4 group). UNIT-III Ring, subring, quotient rings, ring homomorphism elementary properties, ideal of a ring, Maximal Ideals, Prime ideals, Characteristic of a ring. UNIT-IV Integral domain, Field, Imbedding theorem, Euclidian domain, Principal ideal domain, Unique factorization domain. Text: 1. Herstein, I.N., Topics in algebra (2nd edition), Wiley eastern limited 2. Vijay K. Khanna, Bhambri, S.K., A course in Abstract Algebra (3rd edition), Vikas Publishing House Pvt. Ltd. 1

2 Operations Research (MC - 302) L T P C Unit I: Introduction to Operations Research and Linear Programming Problem Modeling in Operations research, Mathematical formulation of problems, LPP: Basic concepts, Graphical Solution of Linear programming problem, General and standard forms of LPP, Simplex method, Two phase method, Big M method, Application of Simplex algorithm, Case study. Unit II: Duality in LPP Dual problem, Duality theorems, Complementary slackness, Economic interpretation of duality, Dual simplex method, Sensitivity Analysis: Variation in cost vector, Variation in Requirement vector, Variation in Coefficient matrix, Case study. Unit III: Integer programming problem Problem formulation, Branch-and-bound method, Cutting plane algorithm, Application on IPP, Case study Unit IV: Transportation, assignment, and transshipment models Transportation problem, Duality in transportation problem, Degeneracy in transportation problem, Transportation algorithm (MODI method), Transshipment problem, Assignment problem, Hungarian method, Travelling salesman problem, Case study. Unit V: Network Scheduling Network and basic components, Network construction, Critical path method (CPM), Program evaluation and review technique (PERT), Case study Books: 1. Hamdy A. Taha, Operations Research: An Introduction, Prentice Hall 2. Suresh Chandra, Jayadeva and Aparna Mehra, Numerical Optimization with Applications, Narosa Publications 3. Antonions and L.W. Sheng, Practical Optimization and Engineering Application, New Age Publication (2010). 4. Frederick S. Hillier & Gerald J. Lieberman, Introduction to Operations Research, McGraw-Hill 5. G Hadley, Linear programming, Narosa publications 2

3 Financial Engineering (MC-303) L T P C Unit I: Introduction Some basic definitions and terminology: Basic Notions and Assumptions, No- Arbitrage Principle, One-Step Binomial Model, Risk and Return, Forward Contracts, Call and Put Options, Managing Risk with Options. Unit II: Basic Theory of Option Pricing: Single and Multi-Period Binomial Pricing Models, Cox Ross-Rubinstein (CRR) Model, Black-Scholes Formula for Option Pricing as a Limit of CRR Model. Unit III: Brownian and Geometric Brownian Motion, Theory of Martingales. Stochastic Calculus, Stochastic Differential Equations, Ito s Formula to Solve SDE s.feymann Kac Theorem. Applications of Stochastic Calculus in Option Pricing. Black-Scholes Partial Differential Equation and Black-Scholes Formula. Unit IV: Mean-Variance Portfolio Theory: Markowitz Model of Portfolio Optimization and Capital Asset Pricing Model (CAPM). Limitations of Markowitz Model and New Measures of Risk. Unit V: Interest Rates and Interest Rate Derivatives: Binomial Lattice Model, Vasicek, Hull and White, and Cox-Ingersoll-Ross (CIR) Models for Bond Pricing. Books 1. D. G. Luenberger: Investment Science, Oxford University Press, M. Capińsky and T. Zastawniak: Mathematics for Finance: An Introduction to Financial Engineering, Springer, Thomas Mikosch Elementary Stochastic Calculus with Finance in view, World Scientific, S. E. Shreve: Stochastic Calculus for Finance, Vol. I & Vol. II, Springer,

4 INFORMATION AND NETWORK SECURITY MC-304 L T P C UNIT I: Introduction to Computer Networks: Network structure and architecture, The OSI reference model, Services of OSI layers, Network Topology, Brief overview of :Physical Layer, MC sub-layer protocols, Data Link layer protocols, Network layer, Switching methods, TCP / IP, IP packet, IP address, IPv4, IPv6 UNIT II: Introduction to Information security: Need for security, Introduction to security attacks, services and mechanism, introduction to cryptography, Conventional Encryption: Conventional encryption model, classical encryption techniques- substitution ciphers and transposition ciphers, cryptanalysis, stereography, stream and block ciphers, Intruders, Viruses and related threads. UNIT III: Modern Block Ciphers: Block ciphers principals, Shannon s theory of confusion and diffusion, fiestal structure, data encryption standard(des), strength of DES, crypt analysis of DES, block cipher modes of operations, triple DES, IDEA encryption and decryption, strength of IDEA, key distribution. UNIT IV: Introduction to graph, ring and field, prime and relative prime numbers, modular arithmetic, Fermat s and Euler s theorem, primarily testing, Euclid s Algorithm, Chinese Remainder theorem, discrete logarithms, Principals of public key crypto systems, RSA algorithm, security of RSA, key management, Diffle-Hellman key exchange algorithm. UNIT V: Message Authentication and Hash Function: Authentication requirements, authentication functions, message authentication code (MC), hash functions, security of hash functions and MC, MD5 message digest algorithm, Secure hash algorithm(sha), Public Key Infrastructure(PKI): Digital Certificates, private key management, Digital Signatures: Digital Signatures, authentication protocols, digital signature standards (DSS). UNIT VI: Authentication Applications: Kerberos and X.509, directory authentication service, password, challenge-response, electronic mail security-pretty good privacy (PGP), S/MIME. IP Security: Architecture, Authentication header, Encapsulating security payloads, combining security associations, key management. Web Security: Secure Socket Layer(SSL) and transport layer security, TSP, Secure Electronic Transaction (SET), Electronic money, WAP security, firewall design principals, Virtual Private Network (VPN) security. Text Books: 1. S. Tananbaum, Computer Networks, 3 rd Ed, PHI. 2. William Stallings, Cryptography and Network Security: Principals and Practice, Prentice Hall, New Jersy. 3. Atul Kahate, Cryptography and Network Security, TMH. 4. Behrouz A. Forouzan, Cryptography and Network Security, TMH. 4

5 Reference Books: 1. Johannes A. Buchmann, Introduction to Cryptography, Springer-Verlag. 2.Bruce Schiener, Applied Cryptography. 5

6 Database Management System MC-305 L T P C UNIT-I Introduction: Data base system concepts and its architecture, Data models schema and instances, Data independence and data base language and interface, Data definition languages, DML. Overall data base structure. Data modeling using Entity Relationship Model: ER model concept, notation for ER diagrams mapping constraints, Keys, Concept of super key, candidate key, primary key generalizations, Aggregation, reducing ER diagrams to tables, extended ER model. UNIT-II Relational Data Model and Language: Relational data model concepts, integrity constraints, Keys domain constraints, referential integrity, assertions, triggers, foreign key relational algebra, relational calculus, domain and tuple calculus, SQL data definition queries and updates in SQL. UNIT-III Data Base Design: Functional dependencies, normal forms, 1NF, 2NF, 3NF and BCNF, multi-valued dependencies fourth normal forms, join dependencies and fifth normal forms. Inclusion dependencies, loss less join decompositions, normalization using FD, MVD and JDs, alternatives approaches to database design UNIT-IV File Organization, Indexing and Hashing Overview of file organization techniques, Indexing and Hashing- Basic concepts, Static Hashing, Dynamic Hashing, Ordered indices, Multi-level indexes, B-Tree index files, B+- Tree index files, Buffer management UNIT-V Transaction processing concepts: Transaction processing system, schedule and recoverability, Testing of serializability, Serializability of schedules, conflict & view serializable schedule, recovery from transaction failures, deadlock handling. Concurrency Control Techniques: Locking Techniques for concurrency control, time stamping protocols for concurrency control, concurrency control in distributed systems. multiple granularities and multi-version schemes. UNIT-VI Case Studies: Commercial databases, Oracle, Postgress, MySQL Suggested Readings: Text Books: 1. Elmasri, Navathe, Fundamentals of Database systems, Addison Wesley 2. Korth, Silbertz, Sudarshan, Data base concepts, McGraw-Hill. 6

7 3. Ramakrishna, Gehkre, Database Management System, McGraw-Hill Reference Books: 1. Date C.J., An Introduction to Database systems 7

8 DBMS LAB (MC 306) L T P C Lab based on the paper MC OR LAB (MC - 307) L T P C Lab based on the paper MC INFORMATION SECURITY LAB (MC - 308) Lab based on the paper MC L T P C