UNIVERSITY OF KERALA - Marian Engineering College

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B.Tech Comp. Sc. & Engg., University of Kerala 44 08.502 ADVANCED MATHEMATICS AND QUEUING MODELS (R F) 3 – 1 – 0 Module I (18 hours) General linear programming problem - Slack and surplus variables - Standard form - Solution of LPP - basic solution - Basic feasible solution - Degenerate and non-degenerate solutions - Optimal solution - Solution by simplex method - Artificial variables - Big-M method - Network Analysis-Project Scheduling- Construction of Project networks- Critical Path Method (CPM)- Identification of Critical path using CPM- Estimation of Floats-Total float, Free float, Independent Float-Project Evaluation and Review Technique(PERT)-Computation of expected completion times by PERT. Module II (16 hours) Partitioned matrices and matrix factorization - LU decompositions - Vector space and subspace - Null space and Column spaces - Bases - Co-ordinate systems - Dimension of vector space - Rank - Change of basis - Inner product space - Length and orthogonality - Orthogonal sets - Orthogonal projection - Gram-Schmidt process - Least square problem - Quadratic form - Constrained optimization of quadratic forms - Singular value decomposition (proof of theorem not included) Module III (18 hours) Queuing Theory- Queues-Characteristics of Queues-Kendal’s notation-Random arrivals-Arrival and Departure Distributions-Types of Queues- Basic Queuing models- M/M/1:∞/FIFO - P n =ρ n P 0 (no proof)- Derivation of the following Characteristics (a) Probability that queue size ≥ n (b) Average number of customers in the system (c) Average length of the waiting line – Waiting time distribution (no proof) – Waiting time in the system – Waiting time in the queue - Little’s Formulae – Problems based on the above results. M/M/1:N/FIFO model – Formulae (without proof) for the average number of units in the system and in the queue and the average waiting time – Problems. M/M/c:∞/FIFO model – Standard results ( no derivation) - Problems . Reference Books 1. Linear Algebra with Applications – David C Lay, Pearson Education 2. Linear Algebra – Schaum Series 3. Linear Algebra – Kenneth Hoffmann and Ray Kunze, PHI. 4. Linear Algebra with Applications – Gareth Williams, Jones and Bartlett publications 5. Linear Algebra with Applications – Gilbert Strang, Thomson Learning 6. Linear Programming – G. Hadly, Addison Wesley 7. Operations Research – Ravindran, Philips, Solberg, Wiley 8. Operations Research – Kanti Swarup, Manmohan, Internal Continuous Assessment (Maximum Marks-50) 25 Marks - Tests (minimum 2) 15 Marks - Assignments (minimum 3) such as home work, problem solving, literature survey, seminar, term-project, software exercises, etc. 10 Marks - Regularity in the class University Examination Pattern PART A: Short answer questions 10 x 4 marks=40 marks All questions are compulsory. There should be at least three questions from each module and not more than four questions from any module. PART B: Descriptive/Analytical/Problem solving questions 3 x 20 marks=60 marks Candidates have to answer one question out of two or two questions out of four from each module. Maximum Total Marks: 100
B.Tech Comp. Sc. & Engg., University of Kerala 45 08.503 DATA BASE DESIGN 2 – 1 – 0 Module I (14 hours) Introduction to database- traditional file system- data and need for information- sequential, random and indexed sequential files- data organization- single and multilevel indexes- B trees and B+ trees- secondary storage devices- database approach–data models- schemas and instances- Data independence – 3 schema architecture – Data base languages – Data base users – Classification of data base systems – E-R modelling– Attributes and keys – E-R diagrams – Weak entities – extended E-R model- mapping ER model to relational model Module II (14 hours) Introduction to Relational model: Basic concepts: Domains Attributes, keys, tuples, relations – Relational data base schemas – relational Algebra operations, SQL in queries – views- Over view of relational calculus- Conceptual design of relational data base – Normalization theory- Functional dependencies- membership and minimal covers- Loss less decomposition of relations- First, Second, Third and Boyce – Cod normal forms – Multi valued dependencies and Fourth normal form – Join dependencies and Fifth normal form. Module III (11 hours) Security issues in database- transaction management - properties of transactions- database architectureconcurrency control- serializability (preliminary treatment only) – locking methods - time stamping methods - database recovery. Text Books: 1. Fundamentals of Database Systems – Ramez Elmasri and Shakant B. Navathe, Pearson Education. 2. Database System Concepts – Henry F. Korth and Abraham Silbershatz, McGraw Hill 3. Database systems, 3 rd Edn – Thomas Connolly and Carolyn Begg, Pearson Education Reference Books: 2. Database management systems - Alexis Leon and Mathews Leon, Vikas publishing 3. Principles of Database Systems - Jeffry D. Ullman, Galgotia Publications. 4. Introduction to database Management – M.L. Gillenson et al., Wiley 5. Fundamentals of Database Management Systems – M.L. Gillenson, Wiley Internal Continuous Assessment (Maximum Marks-50) 25 Marks - Tests (minimum 2) 15 Marks - Assignments (minimum 3) such as home work, problem solving, literature survey, seminar, term-project, software exercises, etc. 10 Marks - Regularity in the class University Examination Pattern PART A: Short answer questions 10 x 4 marks=40 marks All questions are compulsory. There should be at least three questions from each module and not more than four questions from any module. PART B: Descriptive/Analytical/Problem solving questions 3 x 20 marks=60 marks Candidates have to answer one question out of two or two questions out of four from each module. Maximum Total Marks: 100
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