23SA11 CONTEMPORARY ALGEBRA

3 0 0 3

GROUPS: Groups- Subgroups - Normal subgroups - Factor group - Cayley’s theorem – Sylow’s theorem. (9)

RINGS: Definition and examples – Subrings- Fundamental Theorem of ring, homomorphism – Ideals and Quotient Rings – More Ideals and Quotient Rings. (9)

INTEGRAL DOMAINS: Field of quotients - Euclidean Domian - Principal Ideal Domians - Unique Factorization Domains - Polynomial Rings. (9)

FIELD EXTENSIONS: Basic Theory of field Extensions - Algebraic Extensions - Splitting Fields and Algebraic Closures - Separable and inseparable Extensions - Cyclotomic polynomials and extensions. (9)

GALOIS THEORY: Basic definitions - The fundamental Theorem of Galois theory - Finite Fields - Composite and Simple Extensions - Galois Groups of Polynomials - Computation of Galois Groups over Q - Transcendental Extensions, Inseparable Extensions, Infinite Galois Groups. (9)

Total L:45

TEXT BOOKS:
1. Herstein I. N, ‘Topics in Algebra’, Wiley, 2017.
2. Dummit, D. and Foote,R. M., ‘Abstract Algebra’, Wiley, 2002.

REFERENCES:
1. Gallian, J.A, ‘Contemporary Abstract Algebra’, Brookes and Cole, 2013.
2. Artin, M. ‘Algebra’, Pearson, 2015.

23SA12 REAL ANALYSIS

4 0 0 4

SEQUENCE AND SERIES: Countable sets and Uncountabke sets - Metric Spaces - Compact Sets - Perfect Sets - Connected Sets - Convergent Sequence - Subsequences - Complete Metric Spaces - Series - Power Series - Summation by parts - Absolute Convergence. (14)

LIMITS AND CONTINUITY: Limit of Functions - Continous Functions - Continuity and Compactness - Continuity and Connectedness - Discontinuities - Monotonic Functions - Infinite limits and limits at infinity. (12)

DIFFERENTIABILITY: Derivative of a real function - Mean Value Theorem - Continuity of derivatives - L' Hospital Rule - Derivatives of Higher order - Taylor's Theorem - Differentiation of vector valued functions. (12)

INTEGRATION: Definition and existence of integral - Properties of the integral - Integration and Differentiation - Integration of vector valued functions - Rectifiable Curves. (12)

SEQUENCE AND SERIES OF FUNCTIONS: Uniform Convergence and Continuity - Uniform COnvergence and Integration - Convergence and Differentiation - Equicontinuous family of functions - The Stone-Weierstrass Theorem. (10)

Total L: 60

TEXT BOOKS:
1. Walter Rudin, ‘Principles of Mathematical Analysis’, McGraw Hill, 2019.
2. Tom Apostol, ‘Mathematical Analysis’, Narosa, 2002.

REFERENCES:
1. Royden HL, Fitzpatrick, ’Real Analysis’, Pearson, 2015.
2. Roberrt C.Bartle, Donald R.Sherbert,’ Introduction to Real Analysis’, John Wiley, 2014.

23SA13 DIFFERENTIAL EQUATIONS

3 0 0 3

ORDINARY DIFFERENTIAL EQUATIONS: Introduction – Existence and uniqueness of initial value problems for first order ODEs – Homogeneous and non-homogeneous linear ODEs - Equations with constant and variable coefficients – Variation of parameters – Singular solutions – Reduction of order – Sturm-Liouville problems - Greens’ function. (10)

SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS: System of first order ODEs – Fundamental matrix – Non-homogeneous linear systems – Linear system with constant coefficients – Picard’s theorem – Existence and uniqueness of solutions. (9)

PARTIAL DIFFERENTIAL EQUATIONS: Introduction – Classification of integrals – Linear equations of the first order - Integral surface passing through the given curve – Pfaffian differential equations – Compatible systems – Charpit’s method – Jacobi’s method. (9)

APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS: Fourier series - Classification of second order PDEs – Canonical form – Method of separation of variables – One dimensional wave equation – D’Alembert’s solution – Vibrations of a finite string – Heat conduction problem – Finite rod case. (9)

NONLINEAR SYSTEMS: Autonomous Systems - Phase plane and its phenomena – Stability for linear systems – Lyapunov’s direct method – Simple critical points of nonlinear systems. (12)

Total L:45

TEXT BOOKS:
1. Earl. A. Coddington, ‘An Introduction to Ordinary Differential Equations’, Prentice Hall, 2009.
2. I.N. Sneddon, ‘Elements of Partial Differential Equations’, Dover, 2006.
3. S.G.Deo, V.Ragavendra, Rasmita Kar, V. Lakshmikantham, ‘Text book of Ordinary Differential Equations’, Mc-Graw Hill, 2015

REFERENCES:
1. G.F. Simmons, ‘Differential Equations with Applications and Historical Notes’, McGraw-Hill, 2017.
2. William E. Boyce, Richard C. DiPrima, ‘Elementary Differential Equations and Boundary Value Problems’, Wiley, 2022.
3. Lawrence Perko, ‘Differential Equations and Dynamical Systems’, Springer, 2006. 4. Shepley L. Ross, ‘Differential Equations’, Wiley, 2007.

23SA14 PROBABILITY, STOCHASTIC PROCESSES AND STATISTICS

3 2 0 4

SAMPLE SPACE AND PROBABILITY: Sets, probability models, conditional probability, total probability theorem, Bayes’ rule, independence, counting. (6+4)

RANDOM VARIABLES: Discrete and Continuous random variables - Probability mass function and density function, distribution function. Expectation and variance. Discrete distributions: Binomial, Poisson and Geometric. Continuous Distributions: Uniform, Normal, Exponential and Weibull. (9+6)

JOINT PROBABILITY DISTRIBUTIONS AND LIMIT THEOREMS: Joint probability distribution of multiple random variables, marginal and conditional distributions, sum of independent random variables, Conditional expectation and variance. Limit Theorems - Markov and Chebyshev inequalities, Law of Large Numbers, Convergence in probability, Central Limit Theorem (9+6)

STOCHASTIC PROCESSES: Bernoulli and Poisson process, Markov chains- Discrete- Time Markov chain, Classification of states, steady-state behavior, absorption probability and expected time to absorption, period, Continuous-Time Markov chains- Birth and death process (10+7)

STATISTICAL INFERENCE: Statistical inference, prior and posterior distributions, conjugate prior distributions, Point estimation, maximum likelihood estimators. Testing of Hypotheses-problems of Testing Hypotheses, testing simple hypotheses, uniformly most powerful tests. Two-sided test, t - test, comparing means of two Normal distributions, F-distribution, Bayes test procedure. Linear statistical models - Method of least squares, regression, statistical inference in simple linear regression, Bayesian inference in simple linear regression. (11+7)

Total L : 45 + T: 30 = 75

TEXT BOOKS:
1. Dimitri P. Bertsekas and John N,Tsitsiklis, ‘Introduction to Probability’, Athena Scientific, 2008.
2. Morris H. DeGroot, Mark J. Schervish, ‘Probability and Statistics’ Pearson Education ,2018.
3. Saeed Ghahramani, ‘ Fundamentals of probability with Stochastic Processes’, Pearson Education, 2019.

REFERENCES:
1. Peter Olofsson and Mikael Andersson, ‘Probability, Statistics and Stochastic processes’ John Wiley,2012.
2. Robert V. Hogg, Elliot A. Tanis, Dale L. Zimmerman, ‘ Probability and Statistical Inference’, Pearson,2019.

23SA15 NUMBER THEORY AND CRYPTOGRAPHY

3 0 0 3

ARITHMETICAL FUNCTIONS: Divisibility-Division Algorithm, Euclidean Algorithm; Primes-Fundamental Theorem of Arithmetic: Arithmetic function-Euler totient function(6)

CONGRUENCES: Introduction to Congruence - Definition, properties, Ring of integer modulo n, Prime field, Primitive roots, Irreducible polynomial, Chinese remainder Theorem, Euler, and Fermat Theorem, Legendre, Jacobi, and Quadratic Reciprocity. (6)

CRYPTOGRAPHIC PRIMITIVES: Definitions and Illustrations: Symmetric-Key Cryptography, Classical Ciphers, Stream Ciphers, Block Ciphers LFSRs, Modes of Operation, DES, AES - Attacks (9)

PUBLIC-KEY CRYPTOGRAPHY: of PKC, RSA Cryptosystem, PKC based on the Discrete Logarithm problem -ElGamal Cryptosystem and Elliptic Curve systems. (9)

HASH FUNCTIONS AND SIGNATURE SCHEMES: Hash functions based on Cryptosystems, Message Digest,The RSA signature scheme, The Digital Signature Algorithm. The ElGamal signature scheme.(8)

KEY DISTRIBUTION AND KEY AGREEMENT: Introduction, Key transport based on symmetric encryption - Kerberos. Key agreement based on symmetric techniques - Blom’s Scheme, Key transport based on public key encryption-Needham –Schroeder protocol, Key agreement based on asymmetric techniques- Diffie-Hellman key agreement protocol, station- to- station protocol. (7)

Total L : 45

TEXT BOOKS:
1. Douglas R Stinson, ‘Cryptography Theory and Practice’, CRC Press, 2018.
2. Behrouz A Forouzan, Debdeep Mukhapadhyay, ‘Cryptography and Network Security’, Tata McGraw Hill, 2017.


REFERENCES:
1. Jonathan Katz, Yehuda Lindell,‘Introduction to Modern Cryptography’, CRC press, 2015.
2. Neal Koblitz, ‘A course in Number Theory and Cryptography’, Springer, 2012.
3. Alfred J, Menezes, Paul C, Van Oorschot and Scott A Vanstone, ‘Hand Book of Applied Cryptography’, CRC press, 2010.

23SA16 PROBLEM SOLVING AND C PROGRAMMING

3 0 0 3

PROBLEM SOLVING: Introduction to Problem Solving - Program development - Analyzing and Defining the Problem – Algorithm -Flow Chart - Programming languages - Types of programming languages- Program Development Environment. (4)

C LANGUAGE: Introduction to C Language - C Character Set - Identifiers and Keywords - Data Types – Literal Constants - Variables – l-value-r-value - Qualifiers – Modifiers - Operators and Expressions – Type conversions - Library Functions - Data Input and Output Functions – escape sequence characters – Formatted input and output.(4)

CONTROL STATEMENTS: Making Decisions : If Statement – If/else Statement - If/else if Statement – Nested if Statements – dangling else - Switch Multiple Selection Statement– Repetition : Repetition Essentials - While Loop – do-While Loop – For Loop – Nested Loops – Breaking out of a Loop Continue statement – goto Statement.(5)

FUNCTIONS: Modular Programming – Function Prototypes - Defining and Calling Functions –Function Call Stack and Activation Records - Passing Arguments to Functions – Returning a value from a function- Recursion – Recursion vs. Iteration – Scope and lifetime of variables – Memory layout of a C program - Storage Classes - Auto - Static - Extern and Register Variables.(5)

ARRAYS: Defining Array –Array Initialization - Accessing array elements - Processing arrays - Arrays as function arguments - Multidimensional arrays – Memory address calculation of an array – Row major and column major order - String Handling. (5)

POINTERS: Pointer Variable Definitions and Initializations – Passing Arguments to Functions by address – Pointer Expressions and Pointer Arithmetic - Relationship between Pointers and Arrays - Pointers and multidimensional arrays –Constant Pointer – Pointer to Constant –NULL pointer- dangling pointers - Pointers to functions - passing functions to other functions – Introduction to Stack and Heap Memory - Dynamic Memory Allocation.(8)

STRUCTURES AND UNIONS: Structure Definitions – Initializing Structures – Accessing Structure Members - Processing a structure - typedef- Structures and pointers - Passing structures to functions – Self-Referential Structures- Bit fields - Unions – Enumeration Constants.(6)

FILES: Files and Streams - Operations on Files – Types of Files, Various Read and Write Functions for Sequential-Access and Random-Access Files -Command Line Arguments.(4)

PREPROCESSOR DIRECTIVES: #include Preprocessor Directive - #define Preprocessor Directive: Symbolic Constants - #define Preprocessor Directive : Macros - Conditional Compilation.(4)

Total L : 45

TEXT BOOKS:
1. Paul J. Deitel, Harvey M. Deitel,‘C- How to program’, Pearson Education, 2021.
2. R G Dromey, ‘How to solve it by Computer’, Pearson 2019.

REFERENCES:
1. Herbert Schildt, “C The Complete Reference", Mc-Graw Hill, 2019.
2. Gottfried B, ‘Programming With C’, Mc-Graw Hill, 2019.
3. Peter Prinz and Tony Crawford, ‘C in a Nutshell’, O′Reilly, 2018.
4. Brian W. Kernighan and Dennis Ritchie, ‘The C Programming Language’, Pearson Education, 2019.

23SA17 PROFESSIONAL COMMUNICATIONS

0 0 2 1

Reading Compression : Reading for Critical Purposes (2)

Scientific Style : Clarity – Simplicity – Exactness – Brevity – Unity – Coherence-Objectivity. Formal and Informal Writing(4)

Presentation Skills. (2)

Introduction to Soft Skills. (2)

Interpersonal - Intrapersonal Communication (2)

Meetings (2)

Professional Report Writing (4)

Professional Values and Ethics – Case analysis. (4)

PRACTICALS

Short Speeches, Group Discussions, Meetings. (8)

Total P : 30

REFERENCES:
1. Course materials prepared by the faculty, Department of English.
2. Meenakshi Raman and Sangeeta Sharma, ‘Technical Communication: Principles and Practice’. Oxford University Press, 2015.
3. Dhanavel S.P., ‘English and Soft Skills’, Orient Black Swan, 2010.
4. Murphy Herta.Hildelrandt, Herbert W and Thomas Jane P, “Effective Business Communication”, Tata Mc.Graw – Hill, 2008.
5. Priyadarshi Patnaik, “Group Discussion and Interview Skills”, Indian Institute of Technology, Kharagpur, 2011.

23SA18 C PROGRAMMING LAB

0 0 4 2

1. Programs to understand the concepts of data types.
2. Familiarizing conditional, control and repetition statements.
3. Usage of single and double dimensional arrays including storage operations.
4. Implementation of functions, recursive functions.
5. Defining and handling structures, array of structures and union.
6. Implementation of pointers, operation on pointers and dynamic storage allocation.
7. Creating and processing data files.

Total P : 60

23SA21 TOPOLOGY

3 0 0 3

TOPOLOGICAL SPACES: Topological spaces- Basis- Subbasis- Order topology- Product Topology(Finite)- Subspace Topology- Closed sets and limit points - Continuous functions. (9)

PRODUCT TOPOLOGY AND CONNECTEDNESS: Product Topology (Infinite) - The Metric Topology - Connected Spaces - Connected Subspaces of the real line - Components - Path Connectedness. (8)

COMPACTNESS: Compact spaces - Compact subspaces of the real line - Limit Point Compactness - Lindelof Spaces. (10)

COUNTABILITY AXIOMS: First countability axiom - Second countablility axiom - Separation axioms - Hausdroff spaces - Regular spaces - Normal spaces - The Uryshon's lemmma. (9)

METRIZABLE SPACES: Uryshon metrization Theorem - Tietz's Extension Theorem - Tychonoff Theorem. (9)

Total L : 45

TEXT BOOKS:
1. James R Munkres, ‘Topology - A First Course’, Pearson, 2018.
2. George F Simmons, ‘Introduction to Topology and Modern Analysis’, Tata Mc-Graw Hill, 2017.

REFERENCES:
1. O.Ya.Viro,O.A.Ivanov,N.Yu.Netsvetaev,’Elementary Topology’, AMS,2008.

23SA22 Applied Linear Algebra

3 0 0 3

VECTOR SPACES: Basic definition and examples - Subspaces - bases and Dimensions - Linear transformations - The Algebra of Linear transformations. (10)

MATRICES AND LINEAR TRANSFORMATIONS: Isomorpshism- Representation of transformation by matrices- Linear functional- Annihilators- The transpose of linear transformation. (10)

EIGEN VALUE AND EIGEN VECTORS: Introduction to Eigen values, Eigen vectors, Complex Eigen Values- Diagonalizing a matrix- Orthogonal diagonalization- Applications to differential equations- Positive definite matrices - Similar matrices - Quadratic forms - Quadratic surfaces Singular value decomposition. (9)

CANONICAL FORMS: Triangular form; Nilpotent forms; Jordan forms; rational Canonical forms- Hermitian, Unitary and Normal transformations. (8)

INNER PRODUCT SPACES: Inner product, Length, angle and orthogonality - Orthogonal sets - Orthogonal projections - inner product spaces - Orthonormal basis: Gram-Schmidt process - QR Decomposition- Best Approximation, Least-squares. (8)

Total L : 45

TEXT BOOKS:
1. Hoffman, K. and Kunze, R. ‘Linear Algebra’, Prentice Hall of India, 2005.
2. Howard Anton and Chris Rorres,‘Elementary Linear Algebra’, John Wiley& Sons, 2014.

REFERENCES:
1. Herstein, I. N, ‘Topics in Algebra’ Wiley, 2017.
2. Gilbert Strang, ‘Linear Algebra and its Applications’, Thomson Learning, 2016.

23SA23 OBJECT ORIENTED PROGRAMMING

3 2 0 4

PRINCIPLES OF OBJECT ORIENTED PROGRAMMING: Procedure Oriented Programming - Object Oriented Programming Paradigm - Basic Concepts and Benefits of OOP - Object Oriented Programming Language - Application of OOP. (3)

FUNCTIONS IN C++: Function Prototyping - Call by Reference - Return by reference - Inline functions - Default, Const Arguments - Function - Overloading. Classes and Objects - Member functions - Nesting of Member functions - Private member functions - Memory allocation for Objects - Static data members - Static Member Functions - Arrays of Objects - Objects as Function Arguments - Friend Functions - Returning Objects - Const Member functions - Pointers to Members(6)

CONSTRUCTORS: Parameterized Constructors - Multiple Constructors in a Class - Constructors with Default Arguments –Dynamic Initialization of Objects - Copy and Dynamic Constructors – Destructors overloading.(3)

OPERATOR OVERLOADING: Overloading Unary and Binary Operators - Overloading Binary Operators using Friend functions - Operator Type Conversion. (4)

INTRODUCTION TO JAVA: Data Types - Declarations –Wrapper Classes - Arrays and Strings – Input/Output.-Java Classes and Methods - Constructors - Scope rules - this keyword.(5)

INHEIRTance: Defining Derived Classes - Single Inheirtance - Making a Private Member Inheirtable - Hierarchical Inheirtance - Hybrid Inheirtance - Abstract Classes - Constructors in Dervied Classes - Nesting of Classes - Composition - Aggregation - Polymorphism - Types of polymorphism. (4)

PACKAGES AND INTERFACES: Packages - Access protection - Importing packages - Interface - Defining and Implementing Interface - Applying Interface. (4)

EXCEPTION HANDLING: Fundamentals - Exception types - Uncaught Exception - Using Try and Catch - Multiple catch clauses - Nested Try statements - Throw - Throws - Java Built-in Exception – User defined Exceptions.(4)

MULTI THREADED PROGRAMMING: Java thread model - Priorities - Synchronization - Messaging - Thread class and runnable Interface - Main thread - Thread creation - Synchronization - Interthread Communication – Deadlock.(5)

I/O: I/O basics - Stream - Stream Classes - Predefined stream - Reading/Writing console Input. (3)

GUI: Applet fundamentals - GUI Components – Event Handling. (4)

Total L : 45 + T : 30 = 75

Tutorial Practices: 1. Arithmetic Operations using array of objects and dynamic data members. 2. Creation of a class which keeps track of the member of its instances. Usage of static data member, constructor and destructor to maintain updated information about active objects. 3. Usgage of a function to perform the same opeartion on more than one data type. 4. Overloading the opeartors to do arithmetic operations on objects. 5. Acquistion of the features of an existing class and creation of a new class with added features in it. 6. Implementation of run time polymorphism. 7. Use and create packages and interfaces. 8. Implementation of exception handling. 9. Implementation of Multithreading. 10. Creation of an effective GUI that handles various events performed with the appropriate actions.

TEXT BOOKS:
1. Stanley B. Lippman, Josee Lajoie and Barbara E. Moo, ‘The C++ Primer’, Addison Wesley, 2013.
2. Herbert Schildt, ‘JAVA - The Complete Reference’, Tata Mc-Graw Hill, 2018.

REFERENCES:
1. Scott Meyers, ‘More Effective C++’, Addison Wesley, 2008.
2. Bjarne Stroustrup, ‘The Design and Evolution of C++’, Addison Wesley, 2005.
3. Harvey M. Deitel and Paul J. Deitel, ‘JAVA: How to Program’, Pearson Education, 2018.
4. Horstmann and Cornell, ‘Core Java’, Prentice Hall, 2012.

23SA24 DATA STRUCTURES AND ALGORITHMS

4 0 0 4

INTRODUCTION: Primitive Data structures - Abstract Data Type - Analysis of algorithms- Best and worst case time complexities – Asymptotic notations - Growth of functions.(6)

ARRAYS: Operations and Implementation – Linear Search, non-recursive binary search - Sparse matrices – Storage - Basic sparse matrix operations. (4)

STACKS: Primitive operations - sequential implementation - Applications: Expression processing - Infix to Postfix Conversion - Evaluation of Postfix Expression - Parentheses matching - Recursive functions. (4)

QUEUES: Primitive operations – Sequential implementation - Linear queue - Circular queue- Priority queues – Double ended queues. (4)

LISTS: Primitive Operations - Singly linked lists, Doubly linked lists, Circular lists, Multiply linked lists - Applications: Addition of Polynomials - Linked Stacks - Linked queues. (7)

TREES: Terminologies – Binary tree - Sequential and linked representation - Traversals - Expression trees - Heaps and their operations - Threaded binary trees. (9)

BINARY SEARCH TRESS:Binary Search tree - Searching - Insertion and deletion of elements - Time Complexity Analysis - AVL Tree-Height - Searching - Insertion and deletion of elements - AVL rotations - Time Complexity analysis. (9))

MULTIWAY SEARCH TREES: Indexed Sequential Access – m-way search trees – B-Tree – searching, insertion and deletion - B+ trees.(5)

HASH TABLES: Hash functions - Collision handling techniques - Separate chaining, Linear probing, Quadratic probing - Analysis. (3)

GRAPHS: Terminologies - Representation using Adjacency list - Graph Traversal Algorithms: Breadth first and Depth first Search - Dijkstra's Algorithm - Time complexity Analysis. (5)

SORTING: Insertion sort, Selection sort, Bubble sort, Heap sort and Radix sort - Time Complexity analysis. (4)

Total L : 60

TEXT BOOKS:
1. Yedidyah Langsam, Moshe J Augenstein, Aaron M Tenenbaum,‘Data structures using C and C++’, Prentice Hall, 2016.
2. Sahni Sartaj, ‘Data Structures,Algorithms and Applications in C++’, Silicon Press,2013.
3. Michael T. Goodrich, Roberto Tamassia and David Mount, ‘Data Structures and Algorithms in C++’, John Wiley, 2016.

REFERENCES:
1. Thomas H Cormen, Charles E Leiserson, Ronald L Rivest, Clifford Stein,‘Introduction to Algorithms’,MIT Press, 2022.
2. Mark Allen Weiss, ‘Data Structures and Algorithm Analysis in C’, Pearson, 2017.
3. Robert L. Kruse, Bruce P Leung, Clovis L. Tondo, ‘Data Structures and Program Design in C’, Pearson Education, 2013.
4. Nell Dale, Chip Weems, and Tim Richards, ‘C++ Plus Data Structures’, Jones and Bartlett Learning, 2017.
5. Alfred V. Aho, John EHopcraft, Jeffrey D. Ullman, ‘Data structures and Algorithms’, Pearson Education, 2011.

23SA25 DATABASE MANAGEMENT SYSTEM

3 2 0 4

BASIC CONCEPTS: Introduction to databases –Characteristics of database approach - Conventional file processing – Advantages od using DBMS - Database concept and Architecture: Data Models – Instances and Schema – Three Schema Architecture - Data Independence – Components of a DBMS. (5)

CONCEPTUAL DATA MODELLING: ER DATA MODEL: Entities, Attributes, Relationships – Role and Structural constraints – Weak and Strong entity types – Entity Relationship diagrams – Generalization – Aggregation – Applications – Introduction to Network data model and Hierarchical data model. RELATIONAL MODEL: Basic concepts - constraints - Mapping ER model into Relational model.(13)

RELATIONAL QUERIES: Relational Algebra - Tuple relational calculus - structured Query Language(SQL): SQL Commands for CRUD operations - Functions in SQL - Aggregation - Categorization - Views in SQL - PL/SQL basics - Procedures - Functions - Triggers. (7)

RELATIONAL DATABASE DESIGN: Anomalies in a database - Functional dependencies - Axioms - Normal forms based on primary keys - Seconf Normal form, Third Normal form, Boyce - Codd Normal form - Examples - Multi-valued dependencies - Fourth normal form - Physical database design and tuning.(8)

FILE ORGANIZATION: Storage device characteristics - Constituents of a file - Operations on file - Sequential files - index sequential files - Primary and secondary key Retrieval - Types of indexes - Indexing using tree Structures. (5)

TRANSACTION PROCESSING AND CONCURRENCY CONTROL: Transactions, Locking techniques, Concurrent access, Deadlock handling.(4)

DATABASE SECURITY, INTEGRITY CONTROL: Security and Integrity threats – Defense mechanisms – Discretionary Access Control and Mandatory Access Control.(3)

Total L : 45 + T: 30 = 75

Tutorial Practice:
1. Creating database structures such as tables, constraints and views using DDL.
2. Practicing DML for manipulation of single, multiple tables and Report Generation.
3. Activating access rights and privileges using DCL.
4. Database programming using PL/SQL - Triggers and stored procedures.
5. Working on TCL commands to manage transactions in database.
6. Establish Database Connectivity - Applications development.

TEXT BOOKS:
1. ElmasriR and Navathe SB,‘Fundamentals of Database Systems’, Pearson Education, 2017.
2. Silberschatz A, Korth H and Sudarshan S, ‘Database System Concepts’, Mc-Graw Hill, 2019.

REFERENCES:
1. Hector Garcia-Molina, Jeffrey D. Ullman, Jennifer Widom, ‘Database Systems: The Complete Book’, Pearson Education,2011.
2. Raghu Ramakrishnan and Johannes Gehrke,’Database Management System’, Mc-Graw Hill, 2018.

23SA26 DATASTRUCTURES AND ALGORITHMS LAB

0 0 4 2

Implementation of the following:
1. Time Complexity based problems on array, matrices and strings.
2. Sparse matrix operations using arrays.
3. Stacks and queues using arrays.
4. Singly linked, doubly linked and Circular linked lists.
5. Linked Stacks, Linked queues and priority queues.
6. Binary trees.
7. Graph traversal algorithms.
8. Dictionary using Hash tables.
9. Sorting algorithms.

Total P : 60

23SA27 PYTHON PROGRAMMING LAB

0 0 4 2

INTRODUCTION: Pyhton interpreter - Program execution - Interactive prompt - IDLE User Interface.

TYPES AND OPERATIONS: Python Object types - Numeric types - Dynamic typing - String fundamentals - Lists - Dictionries - Tuples - Type objects.

STATEMENTS AND SYNTAX: Python statements - Assignments - Expressions - if Tests - while Lopps - for Loops - Iterations - Comprehensions.

FUNCTIONS AND GENERATORS: Function basics - Scopes - Arguments - Recursive functions - Anonymous functions - lambda - Generator functions.

MODULES AND PACKAGES: Python program structure - Module imports - Standard library modules - Packages - Namespaces, Pip

FILES: Opening files - Reading and writing files - Text files - BInary files.

OBJECT-ORIENTED DESIGN: Inheirtance - Polymorpshism.

STANDARD PACKAGES: Numpy - Matplotlib - Sympy - Pandas.

CASE STUDIES: Real-time applications using different Python libraries.

Implementation of the following programs with suitable Python Packages.
Test basic coding skills using data types, control statements and iteration.
Implement Pyhton data structures like lists, tuples, dictionries and sets.
General programming concepts such as functions, strings, regular expressions, reading / writing files and exceptions.
Implement object-oriented concepts.
Packing programs into reusable libraries.
File Operations.
Programs on differentiation and intergration.
Conformal mappings of standard functions.
Evaluation of real integrals using contour integration.
finding Fourier series.
Solving ordinary differential equations using Laplace transform techniques.
Evaluation of Discrete Fourier Transforms- DIT.
Solving difference equations using Z transform.

Total P : 60

TEXT BOOKS:
1. Langtangen, Hans Petter,‘A Primer on Scientific Programming with Python’, Springer, 2018.
2. Johansson, RObert, ‘Numerical Pyhton: A Practical Techniques Approach for Industry’, Apress, 2015.

REFERENCES:
1. Hans Fangohr,‘Introduction to Python for Computational Science and Engineering’, University of Southamoton, 2015.
2. Fuhrer, Solem, Verdier,‘Scientific Computing with Python 3’, Pearson, 2016.

SEMSETER III

23SA31 APPLIED GRAPH THEORY

3 0 0 3

BASIC CONCEPTS: Graphs,digraphs, subgraphs, graph models, matrix representations, Hand-shaking lemma, degree sequence, Havel-Hakimi theorem, Walk, trail, path, connectedness, distance, radius, diameter, Common families of graphs, isomorphic graphs. Trees - spanning trees, characterizations, Matrix tree theorem. (10)

CONNECTIVITY:Vertex and edge cuts, blocks, Vertex and edge Connectivity, relationship between vertex and edge connectivity. Whitney's theorem, Characterizations of 2- connected graphs , Menger's theorems. Harary;s construction of optimal k-connected graphs.Connectivity in digraphs. (8)

EULERIAN AND HAMILTONIAN GRAPHS: Eulerian trails, characterizations, Heirholzer's algorithm, Route inspection problem. Hamiltonian cycle, Gray codes, Dirac's and Ore's conditions, Travelling Salesperson problem, Nearst neighbor algorithm. (9)

MATCHING AND VERTEX COVER: Maximum Matching, Perfect matching, augmenting path, Edmond's Blossom Algorithm, Bipartite matching, Hall's theorem, job assignments. vertex cover, minimum vertex cover, Independent set, Konig's theorem. (10)

VERTEX-COLORING AND PLANARITY: Proper Vertex-coloring , chromatic number, upper and lower bounds, Brooks and Welsh - Powell theorems. Sequential and Largest degree first vertex coloring algorithms. Planarity and planarity, Euler's formula, kuratowski's theorem, Vertex coloring in planar graphs. (8)

Total L : 45

TEXT BOOKS:
1. Bondy J.A. and Murty U.S.R., ‘Graph Theory’ Springer, 2010.
2. Douglas B West, ‘Graph Theory’, Prentice Hall, 2018.

REFERENCES:
1. Balakrishnan R and Ranganathan K, ‘A Textbook of Graph Theory’, Springer, 2019.
2. Jonathan Gross and Jay Yellen,Mark Anderson, ‘Graph Theory and its Applications’, Chapman and Hall / CRC Press, 2018.
3. Thulasiraman K and Swamy M N S, ‘Graphs: Theory and Algorithms’, Wiley, 2014.

23SA32 OPTIMIZATION TECHNIQUES

3 0 0 3

LINEAR PROGRAMMING: Linear programming modeling – Solution techniques – Graphical method, Simplex method, Big M method , Two Phase method - Special cases of Simplex method. (10)

DUALITY AND SENSITIVITY ANALYSIS: Sensitivity Analysis for Graphical method and general linear programming model- Dual Problem – Primal and Dual relationship – Economic Interpretation of duality – Dual Simplex method – Post Optimal Analysis. (9)

NON-LINEAR PROGRAMMING: Elimination methods for one dimensional minimization problems – Unimodal function - Interval halving method, Fibonacci method, – Hooke and Jeeves pattern search method – Indirect search methods – Cauchy’s steepest descent method, Fletcher-Reeves conjugate gradient method. (8)

DECISION MAKING: B> Decision making under certainty and uncertainty – decision making under risk. (6)

DYNAMIC PROGRAMMING : Principle of optimality - Forward and Backward Recursion methods – Shortest route problem - Knapsack model – Work force size model. (6)

FINANCIAL APPLICATIONS : Dynamic Programming approaches to solve Financial problems - Option Pricing using Binomial Lattice - Mortgage backed securities. (6)

Total L : 45

TEXT BOOKS:
1. Hamdy A Taha, ‘Operations Research :An Introduction’, Pearson Education, 2022
2. Singiresu S Rao, ‘Engineering Optimization Theory and Practice’, John Wiley, 2019.

REFERENCES:
1. Hillier.F and Lieberman G J,‘Introduction to Operations Research’, Tata Mc-Graw Hill, 2021.
2. Cornuejols and Reha Tutuncu, ‘Optimization Methods in Finance’, Cambridge University Press, 2018.
3. D.Bertsimas and Tsitsiklis, ‘Introduction to Linear ‘Optimization’, Athena Scientific, 1997.

23SA33 COMPLEX ANALYSIS

3 0 0 3

ANALYTIC FUNCTIONS AND FUNDAMENTAL THEOREMS: Analytic functions, harmonic conjugates, elementary functions, Mobius transformation, conformal mappings, Cauchy’s theorem and Integral formula, Morera’s Theorem, Cauchy’s theorem for triangle, rectangle, Cauchy’s theorem in a disk. (10)

ZEROS OF ANALYTIC FUNCTIONS: The index of a closed curve, counting of zeros. principles of analytic continuation. Liouville's theorem, fundamental theorem of algebra. (8)

SERIES: Series, uniform convergence, power series, radius of convergences, power series representation of Analytic function, Relation between Power series and Analytic function, Taylor's series, Laurent's series. (8)

RESIDUES AND POLES: Rational Functions, singularities, poles, classification of singularities, characterization of removable singularities, poles. Behavior of an analytic functions at an essential singular point, conformal mapping. (9)

COMPLEX INTEGRATION : Entire and meromorphic functions, residue theorem, evaluation of definite integrals, argument principle, Rouche’s Theorem, Schwartz lemma, Open mapping and Maximum modulus theorem and applications, convex functions, Hadmard’s Three circle theorem. (10)

Total L : 45

TEXT BOOKS:
1. Ahlfors, V., ‘Complex Analysis’, Mc-Graw Hill, 2013.
2. Conway, J.B.,‘Functions of One Variable’, Narosa, 2007.


REFERENCES:
1. Brown, J.W. and Churchill, R.V., ‘Complex Variables and Applications’ Mc-Graw Hill, 2008.
2. Ponnusamy. S and Silverman. H, ‘Complex Variables with Applications’, Birkhauser, Boston, 2006.

23SA34 MACHINE LEARNING

3 2 0 4

INTRODUCTION: Basics of Machine learning – Types – Convex set - Convex functions - Convex optimization - Loss functions in machine learning - Gradient descent - variants. (5)

SUPERVISED LEARNING:Regression - Linear - Polynomial - Multiple regression - Evaluation measures - Bias - variance tradeoff - over-fitting - under fitting - Regularization - hyper parameter tuning. (8)

CLASSIFICATION:Linaer models - Logistic regression - Bayesian Classifier - Decision theory - maximum A posteriori estimation - Maximum Likelihood Estimation - Linear Discriminant Analysis - Support Vector Machines - Linaer, Soft margin, Linaerly non-separable data, Kernel functions , Decision trees: Introduction - Purity measures - Entropy, information gainl, gain ratio, Gini index - ID3 - K nearst neighbor classifier - Model selection & Evaluation measures. (17)

NEURAL NETWORKS: Perceptron - activation functions - Multilayer perceptron - Back Propagation - Training Algorithm. (8)

UNSUPERVISED LEARNING: Clustering –Types - K-means clustering– EM - Mixture of Gaussians –Spectral clustering - Cluster validity measures – dimensionality reduction- Principal components analysis (PCA) -Linear Discriminant Analysis (LDA) - Independent components analysis (ICA) - Applications : image segmentation – Image compression – Outlier analysis (7)

Total L : 45 + T: 30 = 75

Tutorial Practices:
1. Download the datasets from UCI machine learning repository / www.kaggle.com for classification and clustering.
  a. Mail spam
  b. Breast cancer data
  c. Iris data
  d. MNIST dataset
2. Implement the following Classification algorithms on the above suitable datasets.   a. Naïve Bayes
  b. LDA / QDA
  c. SVM
  d. K nearest neighbor
  e. Multi layer Perceptron
3. Do tenfold cross validation experiments and statistical validation using t-test and ANOVA.
4. Apply clustering for image segmentation and image compression.
5. Apply Spectral clustering on data sets and visualization through plots
6. Apply PCA / LDA / Factor analysis on Iris data set, reduce the dimension and visualize the data .
7. Apply semi supervised learning techniques on data sets for the following tasks: to fill missing values / classification

TEXT BOOKS:
1. Alpaydin Ethem, ‘Introduction to Machine Learning’, Massachusetts Institute of Technology Press, 2020.
2. Christopher M Bishop,‘Pattern Recognition and Machine Learning’, Springer, 2016.

REFERENCES:
1. ShaiShalev-Shwartz and Shai Ben-david,‘Understanding Machine Learning’, Cambridge University Press, 2017.
2. Trevor Hastie, Robert Tibshirani and Jerome Friedman, ‘The Elements of Statistical Learning’, Springer, 2013.
3. kevin Patrick Murphy,‘Probabilistic machine Learning’, MIT Press, 2022.
4. Tom M.Mitchell,‘Machine Learning’, McGraw Hill Educatio, 2017.
3. Richard O Duda, Peter E Hart and David G Stork, ‘Pattern Classification (Digitized)’, John Wiley, 2016.

23SA35 SCIENTIFIC COMPUTING LAB

0 0 2 1

1. Solution of algebraic and transcendental equations- Newton Raphson method, method of false position, Graeffe’s root squaring Method.
2. Solving linear system of equations by direct method and iterative method- Gauss elimination method, Crout’s method , Gauss - Seidel method.
3. Computing Eigen value and Eigen vectors.
4. Interpolation with unequal intervals and equal intervals.
5. Numerical Differentiation and Integration
6. Taylor’s series method, Euler’s method, Modified Euler’s method Fourth order Runge Kutta method for solving first order differential equations’
7. Numerical solutions of Solution of one dimensional heat equation by explicit and implicit methods – One dimensional wave equation and two dimensional Laplace and Poisson equation’
8. Solving LPP using simplex method and two phase method.’

Total P : 30

TEXT BOOKS:
1. Steven C. Chapra and Raymond P. Canale, ‘Nmerical Methods for Engineers with Software and Programming Applications’, Mc-Graw Hill, 2015.

REFERENCES:
1. CurtisF. Gerald,and PatrickO. Wheatley, ’Applied Numerical Analysis’, Pearson, 2011.
2. Yousef Saad. ‘Numerical methods for large eigenvalue problems’, University Press, 2011.

23SA36 MINI PROJECT & SEMINAR

0 0 4 2

Mini – project is to be done during the summer vacation at the end of the second semester and a seminar is to be conducted during the third semester.

SEMSETER - IV

23SA40 PROJECT WORK

0 0 24 12

Every student shall undertake a project work during the fourth semester. The project work shall be undertaken in an industrial / research organization or in the college in consultation with the faculty guide and the Head of the Department. In case of the project work at industrial / research organization, the same shall be jointly supervised by a faculty guide and an expert from the organization.

PROFESSIONAL ELECTIVES

23SA61 Algebraic Topology

3 2 0 4

ALGEBRAIC TOPOLOGY: Homotopy of Paths- The Fundamental Groups- Circle , group of Sn, Covering spaces- Retractions of fixed points- The fundamental theorem of Algebra. (9+6)

SEPARATION THEOREMS IN PLANE: The Jordan Separation Theorem—Invariance of domain-Jordan Curve Theorem- Imbedding graphs in a plane- Winding number of simple closed curve.(10+7)

CLASSIFICATION OF SURFACES: Fundamental Groups of Surfaces-Homology of Surfaces- Cutting and pasting- The classification theorem- Constructing compact surfaces. (10+7)

AXIOMATIC APPROACH TO DIGITAL TOPOLOGY: Axioms of Digital Topology, Relation between the suggested and classical Axioms, Deducing the properties of ALF spaces from the axioms. (8+5)

ABSTRACT CELL COMPLEXES: Topology of complexes, Cartesian complexes and combinatorial coordinates, AC complexes compared with other Locally Finite Spaces. (8+5)

Total L : 45 + T: 30 = 75

TEXT BOOKS:
1. James R. Munkres, ‘Topology- A First Course’, Pearson, 2018.
2. Allen Hatcher, ‘Algebraic Topology’, Cambridge University Press, 2002.

REFERENCES:
1. Herbert Edlesbrunner and John Harer, ‘Computational Topology– An Introduction’, AMS, 2010.
2. Vladimir A. Kovalevsky, ‘Geometry of Locally Finite Spaces: Computer Agreeable Topology and Algorithms for Computer Imaginary’, House Dr. Baerbel Kovalevski, 2008

23SA62 ARTIFICIAL INTELLIGENCE

3 2 0 4

INTRODUCTION: The foundations of AI - The History of AI - Intelligent agents - Agent based system. (2)

PROBLEM SOLVING: State Space models - Searching for solution - Uninformed search - Heuristic: Functions - properties - Informed search - Greedy best first search - A* search - Local Search algorithms: Hill-climbing search - Genetic Algorithm - Adversary based search : Minimax – Alpha Beta pruning – Imprefect real time descisions: Cutting-off search - Stochastic games : Expectinax - Constraint satisfaction problem: Inference - Backtracking search.(16)

KNOWLEDGE REPRESENTATION AND REASONING: Knowledge representation - Logics - bivalent logic - inference - Fuzzy logic: membership - Fuzzy rules and reasoning - Fuzzy inference.(8)

UNCERTAIN KNOWLEDGE AND PROBABILISTIC REASONING: uncertainty - Probabilistic reasoning - Semantics of Bayesian network - Exact inference in Bayesian network- Approximate inference in Bayesian network - Probabilistic reasoning over time – Inference in temporal models - Hidden Markov Models – Dynamic Bayesian Networks.(10)

DECISION-MAKING: Basics of utility theory- Decision Networks - Sequential decision problems - Markov decision process - Value iteration - Policy iteration - Decisions in Multi agent system: Single move games - Group decision making.(9)

Total L : 45 + T: 30 = 75

Tutorial Practices:
1. Search Techniques: A* algorithms for 8 - puzzle and Missionaries and Cannibals problem, Hill climbing, genetic algorithm and Constraint satisfication techniques.
2. Simple games - minimax and expectimax.
3. Logic based excerises, Fuzzy Inference System.
4. Decision making: Implementing HMM models, sequential and multi agent decision making.

TEXT BOOKS:
1. Stuart Russell and Peter Norvig, ‘Artificial Intelligence: A Modern Approach’, Pearson Education, 2020.
2. David Pool and Alan Mackworth, ‘Atificial Intelligence: Foundations of Computational agents’, Cambridge University Press, 2017. 3. Timothy Ross, ‘Fuzzy Logic with Engineering Applications’, John Wiley and sons, 2016.


REFERENCES:
1. Christopher M.Bishop, ‘Pattern Recognition and Machine Learning’, Springer, 2016.
2. Daphne koller and N Friedman,‘Probabilistic Graphical Models - Principles and Techniques’, MIT press,

23SA63 BIG DATA AND MODERN DATABASE SYSTEMS

3 2 0 4

OBJECT AND SPATIAL DATABASES:
Object Oriented Databases - Complex data types - Structured types and Inheritance – Query Processing in Object databases - Spatial Databases : Geometric Information System – Spatial Data Types – Spatial Queries - Spatial indexing techniques. (6)

PARALLEL AND DISTRIBUTED DATABASES:
Architecture of parallel databases – Parallel query evaluation, Parallel Query optimization – Distributed DBMS Architecture, Distributed Database Design, Distributed Query Processing.(5)

DATA MODELING FOR BIG DATA: Big Data and Challenges, Big Data models, NoSQL data models, Principles of NoSQL models, BASE properties, CAP Theorem. (5)

NOSQL DATABASES: Document and Graph Databases: Document Oriented Stores - MongoDB - Graph databases:Neo4J. (8)

NOSQL DATABASES: Key Value and Columnar Databases: Key-Value Stores (in-memory): Redis, Column Oriented Store: Cassandra - Hbase - BigTable. (8)

BIG DATA PLATFORM: Hadoop and HDFS - Map-reduce - SPARK - Real time Streaming. (8)

DATABASE INTEGRATION: Data warehousing, Virtual Data Integration - Schema directed data integration - Schema mapping and information preservation - Applications (5)

Total L : 45 + T: 30 = 75

Tutorial Practices:
1. Design applications using object relational databases.
2. Designing and quering spatial databases.
3. Designing No-SQL databases: MongoDB, Redis, Cassandra, HBASE, Neo4J.
4. Parallel programming using Map-Reduce -Hadoop.
5. Big Data Analytics using Spark.
6. Application building using data integration tools.

TEXT BOOKS:
1. M.Tamer Ozsu, Patrick Valduriez, ‘Principles of Distributed Database Systems’, Springer, 2019.
2. Tomsaz Wiktorski, ‘Data-intensive Systems: Principles and FUndamentals using Hadoop and Spark (Advanced Information and Knowledge Processing)’, Springer, 2019.
3. Pramod J. Sadalage and Martin Fowler, ‘NoSQL Distilled - Brief Guide to the Emerging World of Polyglot Persistence’, Pearson Education, 2013.

REFERENCES:
1. Elmasri Ramez and Navathe SB, ‘Fundamentals of Database Systems’, Pearson, 2017.
2. Anhai Doan, Alon Halevy, Zachary Ives, ‘Principles of data integration’, Morgan Kaufmann, 2012

23SA64 CALCULUS OF VARIATIONS AND TRANSFORMS

3 2 0 4

CALCULUS OF VARIATIONS: Functional - Variation of a functional - Euler-Lagrange equation - Necessary and sufficient conditions for extrema - Variational methods for boundary value problems in ordinary and partial differential equations.(8+5)

INTEGRAL EQUATIONS: Introduction - Linear integral equation of the first and second kind of Fredholm and Volterra type - Solutions with separable kernels – Eigen values – Eigen functions - Resolvent kernel – Construction of Green’s function for BVP. (9+6)

LAPLACE TRANSFORM: Definition - Transforms of Standard Functions - Transform of unit step and Dirac delta functions – Transforms of derivatives and integrals –Derivative and integrals of Transforms- Transforms of Periodic functions - Inverse Laplace transform- Convolution Theorem. Solving ordinary linear differential equations with constant coefficient and solving integral equations using Laplace transform. (10+7)

FOURIER TRANSFORM: Fourier integrals - Fourier transform- Fourier sine and cosine transform - Transforms of standard functions - Properties, Convolution theorem (Statement only) – Discrete Fourier and Fast Fourier Transforms – Discrete Convolution – Periodic sequence and circular convolution – Discrete Fourier Transform – decimation–in-time algorithm – Decimation-in-frequency algorithm – Computation of inverse DFT. (10+7)

Z-TRANSFORM: Z - transform of standard functions, inverse Z-transform – properties of Z – transform – Difference equations – Modeling and Solution of difference equations. (8+5)

Total L : 45 + T: 30 = 75

TEXT BOOKS:
1. Ram P. Kanwal, ‘Linear Integral Equations: Theory and Technique’, Academic Press, 2014.
2. I.M. Gelfand and S. V. Fomin, ‘Calculus of Variations’, Dover, 2017.
3. Ewin Kreyszig, ‘Advanced Engineering Mathematics’, Wiley, 2018.

REFERENCES:
1. Dennis G. Zill, ‘Advanced Engineering Mathematics’, Jones & Bartlett, 2018.
2. Michael D. Greenberg, ‘Advanced Engineering Mathematics’, Pearson, 2013.
3. Roland E. Thomas and Albert J. Rosa, ‘The Design and Analysis of Linear Circuits’, John Wiley, 2011.
4. robert Weinstock, ‘Calculus of variations with Applications to Physics and Engineering’, Dover, 2012.

23SA65 CLASSICAL MECHANICS

3 2 0 4

THE MECHANICAL SYSTEMS: Introductions, basic properties Generalized coordinates- Constraints - Virtual work - Energy and momentum. (9+6)

LAGRANGE’S EQUATIONS: Introduction to Lagrange’ s equations, Derivation of Lagrange’s equations - Examples - Integrals of the motion(10+7)

HAMILTON’S EQUATIONS: Introduction, Hamilton’s principles, Hamilton’s equations – Other variational principles.(10+7)

HAMILTON – JACOBI THEORY: Hamilton’s principal function - The Hamilton – Jacobi equation - Separability.(8+5)

CANONICAL TRANSORMATIONS: Differential forms and generating functions - Special transformations - Lagrange and Poisson brackets. (8+5)

Total L : 45 + T: 30 = 75

TEXT BOOKS:
1. Donald T. Greenwood, Classical Dynamics, Dover Publication, 2012.
2. Herbert Goldstein, Charles Poole, John Safko, Classical Mechanics, Pearson Education, 2002

REFERENCES:
1. David Morin, Introduction to Classical Mechanics with problems and solutions, Cambridge University press, 2008.
2. R. Douglas Gregory, Classical Mechanics, Cambridge University press, 2006.

23SA66 COMPUTATIONAL FINANCE

3 2 0 4

SIMPLE MARKET MODEL: Basic notions and Assumptions, No-Arbitrage Principles, one step Binomial model, risk and return, Forward contracts, Call and Put options. (7)

RISK-FREE ASSETS: Time Value of Money- Simple interest, periodic compounding, streams of payments, continous compounding, Comparsion of compounding methods. Money market - Zero-Coupon bonds, coupon bonds. (7)

PORTFOLIO THEORY: Risk and return - Expected return, standard deviation as risk measure. Two Seccurities - Risk and expected return on a portfolio, feasible set. Several Securities- Risk and Expected return, minimum variance portfolio, efficient frontier, market portfolio, Captial Asset Pricing Model.(11)

BASIC OPTIONS THEORY: Definitions - Put-call purity. Bounds on option prices- European option, calls on Non-dividend paying stock, American options. variables determining option prices. Binomial models - Single step, two step, several steps, flow of information, filtration. Option pricing- single step, two step, Cox -Ross -rubinstein formula American claims, martingale property. (12)

CONTINOUS TIME MODEL: Limitations of discrete models, Continuous time limit - choice of N-step Binomial model, Black Scholes model. (8)

Tutorial Practices:
1. Problems using Capital Asset Pricing model.
2. Problems using Auto Correlation.
3. Plot time series data and find outliers.
4. Monte carlo Simulation of Options pricing.
5. Finding minimum variance portfolio.
6. Finding Optimal portfolio.
7. Implementation Cox-Ross Rubinstein Formula

Total L : 45 + T: 30 = 75

TEXT BOOKS:
1. Capinski M. and Zastawniak T., ‘Mathematics for Finance: An Introduction to Financial Engineering’, Springer, 2011.
2. Sheldon M. Ross,‘An Elementary Introduction to Mathematical Finance’.
3. David Ruppert, ‘Statistics and Data Analysis for Financial Engineering’, Springer-Verlag, 2011

REFERENCES:
1. Simon Benninga, ‘Financial Modeling’, MIT Press, 2014.
2. EdwinJ. Elton, Martin J. Gruber, Stephen J. Brown and William N. Goetzmann,‘Modern portfolio Theory and Investment Analysis’, John Wiley & Sons, 2014.

23SA67 DATA MINING

INTRODUCTION: Motivation for Data Mining - Importance - Definition - Kinds of data for Data Mining - Data Mining functionalities - patterns - Classification of data Mining Systems - majoe issues in Data Mining- Overview of Data Mining techniques. Data Preprocessing: Types of data, data cleaning-Smoothing , Handling missing values - Data reduction - Feature subset selection - Sampling methods - Data transformation - Data discretization - Chi square and Information Gain. (9)

DATA WAREHOUSE AND OLAP TECHNOLOGY: Overview - need for Data Warehouse- multidimensional data model- Data Warehouse architecture - Data warehousing Schemas - Data Warehousing to data mining. (6)

MINING FREQUENT PATTERNS, ASSOCIATIONS AND CORRELATIONS: Basic concepts,Efficient and Scable frequent item set mining methods - Apriori, FP-Growth, Eclat. CLASSIFICATION AND PREDICTION:: Overview of Classification techniques - Ensemble learning - bagging, boosting, cascading, stacking - CLUSTERING - Hierarchical - Density-based. (10)

MINING DATA STREAMS: Challenges - Characteristics of streaming Data, Issues and Challenges, Streaming data Mining Algorithms, Any time stream Mining.(6)

SEQUENCE MINING: Characteristics of Sequence Data, Problem Modeling, Sequential pattern Discovery, Time COnstraints, Applications in Bioinformatics, Multivariate Time Series(MVTS) Mining: Importance of MVTS data - Sources of MVTS data - Mining MVTS data.(8)

APPLICATIONS AND TRENDS IN DATA MINING: Spatial Data Mining - Graph Mining - Web Mining - Text Mining. (6)

Total L : 45 + T: 30 = 75

Tutorial Practices:

Implementation of data mining techniques using WEKA.
Implementationof Assciationrule mining using Apriori algorithm and FP Growth algorithm.
Classification rules Decision Tree Classifier, Ensemble of Classifiers.
Implementation of Clustering algorithms.
Case studeis using R programming.

TEXT BOOKS:
1. Jiawei Han, Micheline Kamber, ‘Data Mining – Concepts and Techniques’, Morgan Kaufmann Publishers, 2012.
2. Tan, Steinbach and Kumar, ‘Introduction to Data Mining’, Pearson Education, 2014.

REFERENCES:
1. Trevor Hastie, Robert Tibshirani and Jerome Freidman, ‘The Elements of Statistical Learning: Data Mining, Inference, and Prediction’, Springer Series in Statistics, 2011.
1. Ian Witten, Frank Eibe and Mark A Hall, ‘Data Mining: Practical Machine Learning Tools and Techniques”’ Elsevier, 2011.

23SA68 DESIGN AND ANALYSIS OF ALGORITHMS

3 2 0 4

INTRODUCTION: Fundamentals of algorithmic problem solving - Methods of specifying an algorithm - Proving the correctness. (4)

ANALYSIS OF ALGORITHM: Propertires of Asymptotic notation - analysis of recursive algorithms: recursion Tree method - Master Theorem.(4)

DIVIDE AND CONQUER: Binary search - Merge Sort - Quick sort - Large Integer mutliplication - Strassens's matrix multiplication - Closest pair. (6)

GREEDY METHOD: Minimum cost spanning tree: Kruskal's and Prim's, Topological sorting, Huffman codes - Optimal caching - Activity Scheduling. (7)

DYNAMIC PROGRAMMING: Principles of dynamic programming - 0/1 Knapsack problem - longest common subsequece problem - All pairs shortest problem - optimal binary search trees - travelling salesman problem. (8)

STRING MATCHING: The Naive Method, Rabin - Karp Algorithm, The Knuth - Morris - Pratt Algorithm.(4)

NETWORK FLOW: Flow networks and Flows - Network with multiple sources and working with flows - Ford - Fulkerson Method - Augmenting paths - Max-Flow min-cut theorem. (5)

NP AND COMPUTATIONAL INTRACTABILITY: Class P - Efficient certification and NP, NP hard and NP complete - backtracking: n- queens problem, Graph colouring problem, Hamiltonian cycle, Branch and bound: Assignment problem, Travelling salesman problem, 0/1 Knapsack probelm. (7)

Total L : 45 + T: 30 = 75

Tutorial Practices:

Implementation of the following problems:

1. Problem solving using different algorithmic techniques.
2. Strassen's Matrix Multiplication.
3. Primsminimum cost spanning tree.
4. Kruskal's minimum cost spanning tree using min heap data structure, union and find operation.
5. Application of all pairs shortest path problem, longest common Subsequence.
6. N-queens problem using backtracking.
7. Assignment Problem using branch and Bound.

TEXT BOOKS:
1. Thomas H. Cormen, Charles E. Leiserson, and Ronald LRivest, ‘Introduction to Algorithms’, MIT Press, 2022.
2. Jon Kleinberg and Eve Tardos, ‘Algorithm Design’, Pearson Education, 2013.

REFERENCES:
1. Anany Levitin, ‘Introduction to Design and Analysis of Algorithms’, Pearson, 2014.
2. Michael T. Goodrich and Roberto Tamassia, ‘Algorithm Design, Foundations, Analysis, and Internet Examples’, Wiley, 2014.
3. Parag H Dave, Himanshu B dave ,‘Design and Analysis of Algorithms’, Pearson,2014.

23SA69 DIGITAL IMAGE PROCESSING AND COMPUTER VISION

3 2 0 4

DIGITAL IMAGE FUNDAMENTALS: Image Sampling and Quantization, Digital Image Representation, Image Types, Pixel neighborhood. (3)

IMAGE ENHANCEMENT: Gray-Scale Modification, Histogram processing, Image Shaerpening, Image Smoothing - Image Restoration - noise Models, Noise removal using spatial filters, Color Image Enchancement. Image Transforms - Fourier Transform, Discrete Cosine Transform, Discrete Wavelet Transforms, Filtering in Frequency domain.(8)

EDGE DETECTION: First order derivative, Second order detection, Color Edge detection, Pyramid edge detection, Edge linking and boundary detection. (6)

DIGITAL MORPHOLOGY:Binary Dilation, Erosion, Opening and Closing, Hit-or-Miss Transform, Basic Morphological Algorithms.(5)

GREY-LEVEL SEGMENTATION: Baiscs of Grey-Level Segmentation, The Use of Regional Thresholds, Moving Averages, Cluster-Based Thresholds, Multiple Thresholds, Region-based segmentation, Watershed Transform.(7)

IMAGE RESTORATION: Image Degradations, The Inverse Filter, The Wiener Filter, Structured Noise, Motion Blur, The Homomorphic Filter, Least Square Filters, Generalized Inverse & Iterative Methods, Recursive filtering, Bayesian Methods. (8)

IMAGE ANALYSIS AND CPMPUTER VISION: Feature Extraction - color, texture and shape features, Dimensionality Reduction, Classification with machine learning and deep learning algorithms, Performance Measures.(8)

Total L : 45 + T: 30 = 75

Tutorial Practices:
1. Basic image processing techniques like sampling and quantization
2. Implementation of Image segmentation and edge detection.
3. Implementation of Histogram equalization.
4. Implementation of 2-D DFT and DCT.
5. Implementation of feature extraction.
6. Implementation of image filtering methods in spatial and frequency domain.
7. Image restoration.
8. Implementation of image classification and clustering.
9. Developing simple image analysis applications.

TEXT BOOKS:
1. Umbaugh, S. E., "Digital Image Processing And Analysis Applications with Matlab and CVIPTOOLS", CRC press, 2018.
2. Milan Sonka, Va clav Hlava C, Roger Boyle,"Image Processing, Analysis and Machine Vision", Cengage Learning, 2015.

REFERENCES:
1. Richard Szeliski,"Computer Vision: Algorithms and Applications", Springer-Verlag,2022.
2. Richard Hartley and Andrew Zisserman,"Multiple View Geometry in Computer Vision", Cambridge University Press, 2014.
3. R.C. Gonzalez and R.E. Woods, "Digital Image Processing", Addison-Wesley,2017.

23SA70 EPIDEMIC MODELS

3 2 0 4

BASICS OF EPIDEMICS: The epidemic in a closed population – Initial growth-the final size. Heterogeneity: Differences in infectivity, differences in infectivity and susceptibility (8+5)

STRUCTURED POPULATIONS: The concept of state-i-states, p-states, recapitulation and problem formulation.(8+5)

THE BASIC REPRODUCTION RATIO: The definition of R0, general h-state, on conditions that simplify the computation of R0, sub models for the kernel, extended example, pair formulation models. Partially vaccinated populations, the intrinsic growth rate r, some generalities, separable mixing (15+11)

MACROPARASITES: Introduction, counting parasite load, the calculation of R0 for life cycles, seasonality and R0, a pathological mode.(8+5)

CONTACT: Introduction, Contact duration, consistency conditions, effects of subdivision, network models.(6+4)

Total L : 45 + T: 30 = 75

TEXT BOOKS:
1. O.Diekmann, J.A.P. Heesterbeek, “Mathematical Epidemiology of Infectious Diseases: Model building, Analysis and Interpretation”, John Wiley, 2000.
2. Roy M. Anderson and Robert M. May, “Infectious diseases of humans; dynamic and control” Oxford university Press, 1992.

REFERENCES:
1. Diekmann O., Heesterbeek, J.A.P. and Britton, T. Mathematical tools for understanding infectious disease dynamics. Princeton, Univ. Press, 2012.

23SA71 GAME THEORY

3 2 0 4

INTRODUCTION: Basic concepts -Theory of rational choice – Interacting decision makers (2)

STRATEGIC GAMES AND NASHEQUILIBRIUM: Strategic games: Examples –Nash equilibrium: concept and examples -Best response – Dominated actions –Symmetric games and symmetric equilibria- Illustrations: Cournot’s and Bertrand’s models of duopoly, Electoral competition, War of Attrition , Auctions, Accident Laws.(8+6)

MIXED STRATEGY NASH EQUILIBRIUM: Introduction, Strategic games with randomization- Mixed strategy Nash equilibrium: concept and examples - Dominated Actions -Formation of Players’ beliefs - Illustrations: Expert diagnosis, Reporting a crime.(6+4)

EXTENSIVE GAMES WITH PERFECT INFORMATION: Strategies and outcomes – Nash equilibrium – Sub game perfect equilibrium –Backward induction - Illustrations: Stackelberg’s model of duopoly, Buying votes, Ultimatum game.(6+4)

GAMES WITH IMPERFECT INFORMATION: Bayesian games – Examples – Strategic information – Transmission – Agenda Control with imperfect Information – Signaling games - Education as a signal of ability.(6+4)

REPEATED GAMES: Nash equilibrium in repeated games, finitely and infinitely repeated Prisoner's Dilemma - – Sub game – Perfect equilibria and the one – deviation – Property – General results – Finitely replaced games – Variation on a theme: Imperfect observability.(6+5)

BARGAINING: Rubinstein Bargaining Model with Alternating Offers -Nash Bargaining Solution- Relation of Axiomatic and Strategic Model- Illustration: Trade in market.(5+3)

AUCTION AND MECHANISM DESIGN: Introduction - The Vickery auction- Sponsored Search auction- Social Choice theory- VCG mechanism.(6+4)

Total L : 45 + T: 30 = 75

TEXT BOOKS:
1. Martin J. Osborne, ‘An Introduction to game theory’, Oxford University Press, 2004.
2. Nisan N., Roughgarden T.,Tardos E., Vazirani V., ‘Algorithmic Game Theory’, Cambridge University Press, 2007.

REFERENCES:
1. Thomas L.C, ‘Games, Theory and Applications’, Dover Publications, 2011.
2. Ken Binmore, ‘Playing for Real: A Text on Game Theory’, Oxford University Press, 2007.
3. David Easley, Jon Kleinberg, ‘Networks, Crowds, and Markets: Reasoning About a Highly Connected World’, Cambridge University Press, 2010.

23SA72 GEOMETRY OF LOCALLY FINITE SPACES

3 2 0 4

AXIOMATIC APPROACH TO DIGITAL TOPOLOGY: Axioms of Digital Topology, Relation between the suggested and classical Axioms, Deducing the properties of ALF spaces from the axioms.(8+5)

ABSTACT CELL COMPLEXES: Topology of complexes, Cartesian complexes and combinatorial coordinates, AC complexes compared with other Locally Finite Spaces.(10+7)

COMBINOTORIAL HOMEOMORPHISM: Definition of combinatorial homeomorphism, balls and spheres, generalized boundary and boundary of space, orientation of AC complexes, combinatorial manifolds, block complexes, consistency of the (m,n)-adjacencies. (10+7)

MAPPINGS AMONG LOCALLY FINITE SPACES: Connected –Preserving Mappings (CPM), the combinatorial homeomorphism, properties of manifolds and block complexes.(8+5)

HOMOLOGY: Homology of groups, matrix reduction, relative homology, exact sequences, co-homology.(9+6)

Total L : 45 + T: 30 = 75

TEXT BOOKS:
1. Vladimir A. Kovalevsky, ‘Geometry of Locally Finite Spaces: Computer Agreeable Topology and Algorithms for Computer Imaginary’, House Dr. Baerbel Kovalevski,2008.
2. Herbert Edlesbrunner and John Harer, Computational Topology An Introduction’, AMS,2010.

REFERENCES:
1. James R. Munkres, ‘Topology- A First Course’, Pearson, 2018.
2. Allen Hatcher, ‘Algebraic Topology’, Cambridge University Press, 2002.

23SA73 INFORMATION RETRIEVAL AND WEBSEARCH

3 2 0 4

INTRODUCTION: Overview of IR Systems - Historical Perspectives - Goals of IR - The impact of the web on IR - The role of artificial intelligence (AI) in IR (3)

TEXT REPRESENTATION: Statistical Characteristics of Text: Zipf's law; Porter stemmer; morphology; index term selection; using thesauri. Basic Tokenizing, Indexing: Simple tokenizing, stop-word removal, and stemming; inverted indices; Data Structure and File Organization for IR - efficient processing with sparse vectors. (8)

RETRIEVAL MODELS: Similarity Measures and Ranking - Boolean Matching – Extended Boolean models – Ranked retrieval - Vector Space Models -, text-similarity metrics - TF-IDF (term frequency/inverse document frequency) weighting - cosine similarity, Probabilistic Models. (10)

QUERY PROCESSING: Query Operations and Languages- Query expansion; Experimental Evaluation of IR: Performance metrics: recall, precision, and F-measure, PR Curve, Precision @ k, R-Precision, MAP, NDCG. (5)

TEXT CATEGORIZATION AND CLUSTERING: Categorization: Rocchio; Naive Bayes, kNN; Clustering: Agglomerative clustering; k-means; Expectation Maximization (EM); Dimension Reduction: LSI, PCA.(6)

INFORMATION FILTERING TECHNIQUES: Introduction to Information Filtering, Relevance Feedback - Applications of Information Filtering: RECOMMENDER SYSTEMS: Collaborative filtering and Content-Based recommendation of documents and products.(4)

WEB SEARCH: IR Systems and the WWW - Search Engines: Spidering, Meta Crawlers; Link analysis: Hubs and Authorities, Google PageRank, Duplicate.(4)

INFORMATION EXTRACTION AND INTEGRATION: Extracting data from text; Basic Techniques: Named Entity(NE) Recognition, Co-reference Resolution, Relation Extraction, Event Extraction; Extracting and Integrating specialized information on the Web, Web Mining and Its Applications.(5)

Total L : 45 + T: 30 = 75

Tutorial Practices:
1. Building a Web Crawler.
2. HITS/PageRank for ranking of Web Pages.
3. Spam Detection in personal mails.
4. Building a Recommender System.
5. Designing a Personalized Search Engine.
6. Identifying near duplicates in Web pages - Plagiarism Checker.
7. Designing a Desktop Search Engine.

TEXT BOOKS:
1. Christopher D. Manning, Prabhakar Raghavan and Hinrich Schütze, ‘Introduction to Information Retrieval’, Cambridge University Press, 2012.
2. B.Croft, D. Metzler, T. Strohman, ‘Search Engines: Information Retrieval in Practice’, Pearson Education, 2015.

REFERENCES:
1. Stefan Büttcher, Charles L. A. Clarke, Gordon V. Cormack, ‘Information Retrieval – Implementing and Evaluating Search Engines‘, The MIT Press, 2016.
2. Ricardo Baeza-Yates and Berthier Ribeiro-Neto, ‘Modern Information Retrieval’, Pearson Education, 2010.
3. Francesco Ricci, Lior Rokach, Bracha Shapira, Paul B. Kantor, ‘Recommender Systems – Handbook’, Springer, 2015.

23SA74 MATHEMATICAL MODELING

3 2 0 4

INTRODUCTION TO MODELING: Modeling process, Overview of different kinds of model. (2)

EMPIRICAL MODELING WITH DATA FITTING: Error function, least squares method; fitting data with polynomials and Splines. (4)

CAUSAL MODELING AND FORECASTING: Introduction, Modeling the causal time series, forecasting by regression analysis, prediction by regression. Planning, development and maintenance of linear models, trend analysis, modeling seasonality and trend, trend removal and cyclical analysis, decomposition analysis. Modeling financial time series. Econometrics and time series models. Non seasonal models: ARIMA process for univariate and multivariate.(10)

PORTFOLIO MODELING AND ANALYSIS: Portfolios, returns and risk, risk-reward analysis, asset pricing models, mean variance portfolio optimization, Markowitz model and efficient frontier calculation algorithm, Capital Asset Pricing Models (CAPM).(12)

DISCRETE-TIME FINANCE: Pricing by arbitrage, risk-neutral probability measures, valuation of contingent claims, and fundamental theorem of asset pricing, Cox-Ross-Rubinstein (CRR) model, pricing and hedging of European and American derivatives as well as fixed-income derivatives in CRR model, general results related to prices of derivatives.(5)

MODELING WITH BIOINFORMATICS: Introduction,Biological data- types, mode of collection, documentation and submission. Sequence alignment- Definition, significance, dot matrix method, dynamic programming- Global and local alignment tools, scoring matrices and gap penalties. Multiple sequence alignment: Iterative methods. (12)

INFORMATION FILTERING TECHNIQUES: introduction to Information Filtering, Relevance Feedback - Applications of Information Filtering: RECOMMENDER SYSTEMS: Collaborative filtering and Content-Based recommendation of documents and products.(10)

Total L : 45 + T: 30 = 75

Tutorial Practices:
1 Least square method for fitting data
2. Modeling financial time series
3. ARIMA process
4. Markowitz model for portfolio modeling
5. Capital asset pricing models
6. CRR model
7. Sequence alignment by using dynamic programming technique
8. Multiple sequence alignment.

TEXT BOOKS:
1. Giordano F R, Weir M D, and Fox W P, ‘A First Course in Mathematical Modeling’. Brooks/Cole, Belmont, 2014.
2. Capinski M. and ZastawniakT,’Mathematics for Finance: An Introduction to Financial Engineering’, Springer, 2011.
3. Mount. DW, ‘Bioinformatics Sequence and Genome Analysis’, Cold Spring Harbor Laboratory, Press, 2006.

REFERENCES:
1. Hamdy A. Taha, ‘Operation Research- An Introduction’, Pearson Education, 2022.
2. Christoffersen. P, ‘Elements of Financial Risk Management’, Academic Press,2012.
3. G.Polya, ‘ How to Solve it: : New Aspect of Mathematical Method’, Princeton University Press, 2018.

23SA75 MOBILE TECHNOLOGY

3 2 0 4

INTRODUCTION: Introduction to mobile applications - Importance of mobile applications - Strategies and Challenges - Software and Hardware requirements for developing mobile applications - Types of Mobile applications - benefits of creating mobile applications - Marketing and advertising mobile applications - Mobile devices overview and classification. (3)

MOBILE USER INTERFACE DESIGN: Mobile applications users - Social aspect of mobile interfaces - Accessibility - Design patterns - Designing for the various mobile platform - Adaptive Mobile Websites - Dedicated Mobile Websites. (4)

MOBILE APPLICATION DEVELOPMENT: Introduction to Android Platform – Android and MVC architecture - Application life cycle - UI design for Android - UI fragments - Different types of layouts – Widgets – List view – Fragment navigation – Dialogs - Intents.(14)

CELLULAR CONCEPT: transmission - Frequencies for radio transmission - Regulations - Signals , Antennas, Signal propagation ,Path loss of radio signals , Additional signal propagation effects - Multi-path propagation – Cell Concept - Factors determining cell size and shape (10)

DATABASE: Creating database - Room architecture - Accessing database - Querying database. (3)

Advanced Features: Using Resources and Media - Audio playback - Retained Fragments - Creating options menu - Ancestral navigation - Saving and loading data to local files - Andriod file system - Creating and Implementing context menu - Image handling - Background Services - tracking device location - Jetpack compose - UI and Layouts. (14)

ANROID SECURITY MODEL: Android architecture - Dalvik VM - Permissions - User Management - Device Security. (7)

Tutorial Practices:
1. Android SDK installation and study
2. Defining Layouts
3. Single Activity Application, Application with multiple activities, using intents to Launch Activities
4. Application using GUI Widgets
5. Application with Notifications
6. Application studying background services.
7. Application tracking mobile devices. 8. Creating and Saving Shared Preferences and Retrieving Shared Preferences
9. Usage of SQLite Databases for storage
10. Working with Retrofit library in Android Applications
11. Android Automated Testing Frameworks
12. Study of Anroid Jetpack components.
13. Case Study: Dagger Framework for Android
14. Case Study: Cross platform applications.

Total L : 45 + T: 30 = 75

TEXT BOOKS: 1. Chris Stewar, Bryan Sills, Kristin Marsicano and Brian Gardener, "Android Programming: The big Nert Ranch guide", Addison Wesley, 2022.
2. Jeff McWherter and Scott Gowell, "Professional Mobile Application Development", John Wiley, 2012.
3. Nikolay Elenkov, "Anroid Security Internals: An in-depth guide to Android's Security Architecture", No Strach Press, 2014.

REFERENCES: 1. Ronan Schwarz, Phil Dutson, James Steele and Nelson To, "The Android Developer's Cookbook - Building Applications with the Android SDK", Addison Wesley, 2014.
2. Mark Murphy, "the Busy Coder's Guide to Android Development", Commons Ware, 2019.

23SA76 OPERATING SYSTEMS

3 2 0 4

INTRODUCTION: Abstract view of an operating system - Operating Systems Objectives and Functions – Evolution of Operating Systems - Dual-mode operation - System calls- Structure of Operating System. (3)

PROCESS DESCRIPTION AND CONTROL: Process concepts - Process Creation – Process Termination – Process states - Process Description – Process Control (3)

PROCESS AND THREADS: Relationship between process and threads – Thread States – Thread Synchronization Types of Thread – Multithreading model. (4)

PROCESS SCHEDULING: Scheduling basics - CPU-I/O interleaving- (non-)preemption - context switching- Types of Scheduling – Scheduling Criteria - Scheduling Algorithms – Algorithm evaluation – Real-time scheduling. (5)

PROCESS SYNCHRONIZATION: Concurrent Process – Principles of Concurrency – Race Condition - Mutual Exclusion – Critical section problems – Software support – Hardware Support – Operating System Support: Semaphore, Monitor – Classical problems of synchronization – Synchronization examples.(4)

DEADLOCK: Principles- Characterization – Methods for handling deadlock - Deadlock prevention, Avoidance, Detection, and recovery.(4)

MEMORY MANAGEMENT: Memory hierarchy –Memory Management requirements - Memory partitioning: Fixed partitioning, Dynamic partitioning, Buddy systems – Simple paging – Page table structures – Simple Segmentation – segmentation and paging(6)

VIRTUAL MEMORY MANAGEMENT: Need for Virtual Memory management – Demand Paging –Copy on write -Page Fault handling - Page replacement - Frame allocation- Thrashing - working set model.(5)

IO MANAGEMENT AND DISK SCHEDULING: Organization of I/O function – Evolution of I/O function – Types of I/O devices – Logical Structure of I/O functions – I/O Buffering – Disk I/O – Disk Scheduling algorithms – RAID - Disk Cache.(4)

FILE SYSTEM MANAGEMENT: Files – Access methods - File system architecture – Functions of file management –Directory and disk structure -Mounting - File sharing –File system implementation – Directory implementation - File Allocation – Free space managment.(4)

VIRTUALIZATION: Requirements for Virtualization - Type 1, Type 2 Hypervisors – Para virtualization- Memory Virtualization - I/O Virtualization - Virtual machines on Multicore CPUs–Virtualization in Multiprocessor environment.(3)

Total L : 45 + T: 30 = 75

Tutorial Practices:
1. Practicing UNIX Commands
2. Writing SHELL Scripts
3. Writing programs using UNIX System Calls
4. Process Creation and Execution
5. Thread Creation and Execution
6. Process / Thread Synchronization using semaphore
7. Developing Application using Inter Process communication (using sharedmemory, pipes or message queues)
8. Implementation of Memory Management Schemes
9. Implementation of file allocation technique (Linked, Indexed, Contiguous).

TEXT BOOKS:
1. Silberschatz A, Galvin, PB. and Gagne, G. ‘Operating System Concepts’, John Wiley & Sons, Inc.,2018.
2. William Stallings, ‘Operating Systems: Internals and Design Principles’, Pearson Education, 2017.
3. Andrew S Tanenbaum, ‘Modern Operating System’, Prentice Hall, 2018.

REFERENCES:
1. Elmasri, E., Carrick A.G. and Levine, D. ‘Operating Systems: A Spiral Approach’, McGraw Hill, 2014.
2. McHoes, AM and Flynn, I.M. ‘Understanding Operating Systems’, Cengage Learning, 2016.
3. Dhamdhere D M, ‘Operating Systems: A Concept-based Approach’, McGraw-Hill, 2015.

23SA77 PREDICTIVE ANALYTICS

3 2 0 4

DATA WRANGLING: DataIngest, Data Cleaning - Exploratory data analysis - Univariate data – Bivariate data, Multivariate data. (5+3)

LINEAR REGRESSION: Coefficient of determination, Significance test, Residual analysis, Confidence and Prediction intervals.(5+3)

MULTIPLE LINEAR REGRESSION: Coefficient of determination, Interpretation of regression coefficients, Categorical variables, heteroscedasticity, Multi-co linearity outliers, Auto regression and Transformation of variables, Regression, Model Building.(10+7)

LOGISTIC AND MULTINOMIAL REGRESSION: Logistic function, Estimation of probability using Logistic regression, Variance, Wald Test, Hosmer Lemshow Test, Classification Table, Gini Co-efficient.(5+3)

DECISION TREES: Introduction, CHI-Square Automatic Interaction Detectors (CHAID), Classification and Regression Tree(CART), Analysis of Unstructured data.(5+3)

FORECASTING: Moving average, Exponential Smoothing, Casual Models. (5+3)

TIME SERIES ANALYSIS: Moving Average Models, ARMA, ARIMA models , Multivariate Models.(5+3)

CASE STUDIES : Application of predictive analytics in retail, direct marketing, health care, financial services, insurance, supply chain, Social media analytics– Customer Analytics - Risk Analytics - Analytics for Retail and Ecommerce, etc- Working with data from different sources: spread sheets, databases, and the cloud -Model Development- Model Validation. (5+5)

Total L : 45 + T: 30 = 75

TEXT BOOKS:
1. Daniel T. Larose, Chantal D. Larose, ‘Data Mining and Predictive Analytics’, Wiley,2015
2. Douglas C. Montgomery, Cheryl L. Jennings, Murat Kulachi, ‘Introduction to Time Series Analysis and Forecasting’,Wiley, 2015.
3. Max Kuhn, Kjell Johnson, ‘Applied Predictive Modeling’, Springer, 2014.

REFERENCES:
1. Richard A. Johnson, Irwin Miller and John Freund, ‘Probability and Statistics for Engineers’, Pearson Education, 2014.
2. Ronald E. Walpole, Raymond H. Meyers, Sharon L. Meyers, ‘Probability and Statistics for Engineers and Scientists’, Pearson Education, 2014.
3. Thomas W.Miller, ‘Modeling Techniques in Predictive Analytics with Python and R A guide to Data Science’, Pearson Education, 2014.

23SA78 STATISTICAL LEARNING

3 2 0 4

THEORETICAL FOUNDATIONS : Review of Statistical Inference, Review of Probability, Testing of Hypothesis – Introduction to Function Spaces – Vector Spaces - Metric Spaces – Cauchy Sequence – Complete Metric Space – Normed Space, Inner Product Space – Banach Space - Hilbert Space – Sobolev – Examples - Mercer Kernels - Reproducing Kernel Hilbert Space (RKHS), Concentration of Measure Measures of Complexity - Rademacher Complexity.(10)

LINEAR REGRESSION: Simple, Multiple, Other Considerations in the Regression Model – Resampling Methods Cross-Validation, Bootstrap– Linear Model Selection & Regularisation – Subset Selection , Shrinkage Methods – Ridge, Lasso, Dimension Reduction Methods (8)

NON-LINEAR REGRESSION : Polynomial Estimators, Step Functions, Basis Functions, Regression Spline Smoothing Splines, Local Regression, Generalised Additive Models. (4)

LINEAR CLASSIFICATION: Review of Classification Models, Logistic Regression, Linear Discriminant Analysis, Quadratic Discriminant Analysis, Comparison of Classification Methods. (6)

TREE BASED METHODS: Regression Trees, Classification Trees, Bagging, Random Forests, Boosting(9)

SUPPORT VECTOR MACHINES: Maximal Margin Classifier – Support Vector Classifiers - Support Vector Machines – Non-linear Decision Boundaries – SVMs with more than 2 classes.(4)

UNSUPERVISED LEARNING: Principal Components Analysis – Clustering Methods – K-Means Clustering, Hierarchical Clustering.(4)

Total L : 45 + T: 30 = 75

Tutorial Practices:

Solve the following problems using R

1. Simple Regression, Multiple Regression, Ridge Regression and Lasso Regression.
2. Non-linear Regression, Splines and Additive Models
3. Linear Classification,
4. Tree based methods
5. Support Vector machines
6. Clustering Methods

TEXT BOOKS:
1. Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani, “An introduction to Statistical learning”, Springer, 2013.
2. Trevor Hastie, Robert Tibshirani, Jerome Friedman, “Elements of Statistical Learning: Data Mining, Inference and Prediction”, Springer,2013

REFERENCES:
1. Vladimir N Vapnik, “Statistical learning theory”, Wiley, 1998.
2. Robert Schapire, Yoav Freund, “Boosting : Foundations and Algorithms”, The MIT Press, 2012

23SA79 STOCHASTIC DIFFERENTIAL EQUATIONS

3 2 0 4

MATHEMATICAL PRELIMINARIES: Probability spaces - Random variables - Stochastic processes – Brownian motion.(7+4)

ITO STOCHASTIC CALCULUS: Ito Integrals - Construction of its integrals - Properties.(9+6)

THE ITO FORMULA AND THE MARTINGALE REPRESENTATION THEOREM: one-dimensional Ito formula - The multi-dimensional Ito formula – The Martingale representation theorem.(9+6)

STOCHASTIC DIFFERENTIAL EQUATIONS: Construction of stochastic differential equations - an existence and uniqueness result- weak and strong solutions.(10+7)

METHOD OF SOLVING STOCHASTIC DIFFERENTIAL EQUATIONS: Linear stochastic differential equations - Reducible stochastic differential equations - Some explicitly solvable equations.(10+7)

Total L : 45 + T: 30 = 75

TEXT BOOKS:
1. Peter E Kloeden and Eckhard Platen,’Numerical Solution of Stochastic Differential Equations’, Springer, 2018.
2. Bernt Oksendal , ‘Stochastic Differential Equations - An Introduction with Applications’, Springer, 2016.

REFERENCES:
1. Sasha Cyganowski, Peter Kloeden and Jerry Ombach, ‘From Elementary Probability to Stochastic Differential Equations with Maple’, Springer, 2002.

23SA80 TOPOLOGICAL DATA ANALYSIS

3 2 0 4

COMPLEXES: Topological spaces, Continuity, Connectedness, Surfaces, Homeomorphisms, Homotopy, Isotopy, Simplices, Simplicial Complex, Euler Characteristics.(6+4)

HOMOLOGY: Simplical Homology, Chain Complexes, Cycles and boundaries, Homology groups and Betti numbers, The homology of a ball, reduced homology, Induced maps, matrix reduction: Euler - Poincare formula, Boundary matrices, Smith normal forms, reduction algorithm, Relative homology groups; Excision, Maps between vector spaces, Excat Sequences: Chain Complexes and Chain maps, The snake or zig-zag, Connecting homomorsphism, mayer - Vietoris sequence, cohomology. (12+8)

MORSE THEORY: generic smooth functions, Morse Functions, Morse lemma, Gradient vector field on a manifold, Attaching cells, transversality, Integral lines, Stable and unstable manifolds, Morse-Smale functions, Morse Smale complexes, Morse inequalities, Floer homology, Relation between Morse Theory and Homology.(10+7)

PERSISTENT HOMOLOGY: The elder rule, Filtrations, Persistence, diagrams, Matrix reduction, Pairing lemma, Sparse matrix representation, Extended persistence, Spectral sequence, Stability, Bottleneck distance, Tame functions, Wasserstein distance, Lenght and total curvature of a curveusing stability, Bipartite graph matching for computing bottleneck distance. (10+7)

DATA-STRUCTURES: Piecewise-linear functions, Scalar data analysis: Contour tree andReeb graph, Vector data analysis. (7+4)

Total L : 45 + T: 30 = 75

TEXT BOOKS:
1. Herbert Edlesbrunner and John Harer,"Computational Topology - An Introduction", AMS, 2010.
2. James R.Munkers, "Topology - A First Course", Pearson, 218.
3. James R.Munkers, "Elements of Algebraic Topology", CRC Press, 2018.

REFERENCES:
1. John M.Lee,"Introduction to Topological Manifold",Springer,2011.
2. Gunther Rote and GertVegter, "Computational Topology - An Introduction (Effective Computational Geometry for Curves and Surfaces (Chapter 7))",Springer, 2006.

23SA81 MEASURE AND INTEGRATION

3 2 0 4

MEASURE ON THE REAL LINE: Camtor=like sets - Lebesgue outermeasure- Measurable sets - Regularity- Measurable functions - Borel and Lebesgue Measurability - hausdroff measures on real line. (8+5)

INTEGRATIN OF FUNCTIONS OF A REAL VARIABLE: Integration of Non-negative functions - The general Integral- Integration of Series - Riemann and Lebesgue Integral.(10+7)

DIFFERENTIAtION: The four derivatives - Continous non differentiable Functions - Functions of Bounded Variation - Lebesgue's Differentiation Theorem - Differentiation and Integration - The Lebesgue Set.(10+7)

ABSTRACT MEASURE SPACES: Measures Spaces, Integrationwith respect to a measure, The L^p space, The inequalities of Holder and Minkowski, Completness of L^p.(9+6)

CONVERGENCE: Convergence in Measure - Almost Uniform Convergence - Convergence Digrams - Counter examples. (8+5)

Total L : 45 + T: 30 = 75

TEXT BOOKS:
1. De Barra G.,"Measure Theory and Integration", New Age International, 2022.
2. Royden HL, "Real Analysis", Pearson, 2015.

REFERENCES:
1. Halmos P.R., "Measure Theory", Graduate Text in Mathematics, Springer, 2008.
2. Rana I.K., "An Introduction to Measure and Integration", Narosa Publishing House, 2007.

23SA82 FUNCTIONAL ANALYSIS

3 2 0 4

FUNDAMENTALS OF NORMED SPACES: Normed spaces- Continuity of linear maps - Hahn Banach theorems.(8+5)

BOUNDED LINEAR MAPS ON BANACH SPACES: Banach Spaces - Uniform boundedness priciple - Closed graph Theorem - Open mapping theorem.(10+7)

SPACES OF BOUNDED LINEAR FUNCTIONALS: Bounded inverse theorem - Spectrum of a bounded operator - Duals and transposes duals of L^p (a,b) and C[a,b].(10+7)

COMPACT OPERATORS ON NORMED SPACES: Weak and weak* convergence - Reflexivity - Compact linear maps - Spectrum of Compact Operator.(9+6)

GEOMETRY OF HILBERT SPACES: Inner product spaces - orthogonal sets - Approximation and optimization - Projection and Riesz representation theorem.(8+5)

Total L : 45 + T: 30 = 75

TEXT BOOKS:
1. Limaye B.V., "FUnctional Analysis", New Age International, 2014.
2. Kreyzig E., "Introduction to Functional Analysis with Applications", John Wiley, 2007.

REFERENCES:
1. Conway J.B., "A Course in Functional Analysis", Springer, 2007.
2. Goffman. C and Pedrick. G, "A First Course in Functional Analysis", Prentice Hall, 2002.

23SA83 LOGIC FOR COMPUTER SCIENCE

3 2 0 4

PROPOSITIONAL LOGIC (PL): Propositional FOrmulae - Interpretations - Logical Equivalence - Satisfiability, Validity and Consequence Semantics of PL - Soundedness and Complteness - Hilbert System H - Dervied rules in H - Soundness and Completeness of H - Consistency.(8)

RESOLUTION AND DECISION DIAGRAMS: Conjuctive Normal Form - Clausal FOrm - Resolution Rule - Soundness and Completeness of Resolution - Definition of Binary Decision Diagrams(BDD) - Reduced BD Ordered BDD - Apply Operators to BDD's - Restriction and Qunatification. (7)

FIRST-ORDER LOGIC FOR (FOL): Relations and Predicates - Formulae in FOL - Interpretations - Logical Equivalence - Semantics of FOL - Soundness and Completion of Semantic table - gentenz System G - Equivalence of H and G.(8)

NORMALFORMS AND RESOLUTION: PCNF and Clausal Form - Herbrand's Theorem - Ground Resolution - Substitution - Unification - General Resolution - Soundness and Completness of General Resolution.(7)

UNDECIDABILITY: Undecidability of FOL - Decidable cases of FOL - Finite and Infinite Models - Complete and Incomplete Theories.(5)

TEMPORAL LOGIC: Introduction - Syntax and Semantics - Models of Time - Linear Temporal Logic - Semantic Taleaux - Binary Temporal Operators - Deductive System L - Soundness and Completeness of L.(5)

PROGRAM VERIFICATION: Correctness Formulae - Deductive System HL - Program Verification - Program Synthesis - Formal Semantics of Programs - Soundness and Completeness of HL.(5)

Total L : 45 + T: 30 = 75

Tutorial Practices:
From Formulae in Logic Programming - Horn Clauses - SLD - Resolution - SLD - Normal forms - Search Rules in SLD - resolution - PROLOG.
SAT SOLVERS: A linear solver - A cubic solver - Davis-Putnam Algorithm - DPDLL ALgorithm - Example of DPLL - Improving DPDLL _ Complexity of SAT.
Concurrent Programs - Deductive Verification - Programs as Automata - Model Checking of Invariance properties - Model Checking of Liveness Properties - Expressing an LTL Formula as an Automation - Model Checking Using the Synchronous Automation - Branching - TIme Temporal Logic - Symbolic Model Checking.


TEXT BOOKS:
1. Mordechai Ben- Ari, "Mathematical Logic for Computer Science", III Edition, Springer, 2012.
2. Huth m and Ryan M, "Logic in Computer Science: Modelling and Reasoning about systems", Combridge University Press,2005.

REFERENCES:
1. JeanH. Gallier, "Logic for Computer Science: Foundation of Automatic Theorem Proving", Second Edition, Dover Publications, 2014.
2. I.M.Copi, D.Cohen, P.Jetli, M.Prabakar, "Introduction to Logic", Pearson Education, 2006.
3. Matt Kaufmann, Panagiotis Manolios and J Strother Moore Kluwer, "Computer- Aided Reasoning: An Approach", Academic Publishers, 2000.