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Maharishi Arvind Institute of Science and Management
MCA Batch 2002-2003
[II Semester Syllabus]


Combinatorics: Permutations and combinations, Recurrence relations, Generating functions, Decision tables.

Graphs: Incidence and degree, Handling lemma, Isomorphism, Bgraphs and union of graphs, Connectedness, Walk, Path, Circuits, and Components. Connectedness algorithms, Shortest path algorithms, Euler graph, Fleury's algorithm, and Chinese postman problem. Hamiltonian graphs - necessary and sufficient conditions, Traveling salesman problem, Bipartite graphs.

Trees: Properties of trees, Pendant vertices in a tree, Center of a tree, Rooted and binary trees, Spanning trees - Spanning tree algorithm. Fundamental circuits, Spanning tree of weighted graph, Cut-sets and cut-vertices, Fundamental cut-sets, Connectivity and separativity, Network flows, Max Flow Min Cut theorem.

Planer graphs: Combinatorial and geometric duals, Kuratowski's graph, Detection of planarity, Thickness, and Crossings.

Matrix representation of graphs: Incidence, Adjacency matrices and their properties.

Colorings: Chromatic number, Chromatic polynomial, The six and five color theorems. The four color problem.

Directed graphs: Binary relations, Directed graphs, and Connectedness, Directed Trees, Arborescence, Polish method, and Tournaments.

Counting of labeled trees: Cayley's theorem, Counting methods, Polya's theorem.

Applications of graphs in Computer Science.

Recommended Book(s):
Graph Theory with Applications to Engineering... - Narsingh Deo.


Introduction to data processing: Data structures - Elements, Fields, Records, and Files. Data collection, Preparation, Verification, Editing and Checking.

Business files: Records - fixed and variable length, Record layout, Information of permanent and semi-permanent nature. Master file and transaction files, File organization - Sequential, Relative and Indexed. File creation and handling, Addition and deletion of records, Updation of master file with the help of transaction file(s). Processing modes - batch and online with examples. File and data security, Backups and file recovery procedures.

COBOL: COBOL as a hight level business data processing language , Character set, Words, Verbs, Data names, Reserved words, Paragraphs, Sections, Divisions. Inbuilt documentation, Execution of COBOL programs, Evolution of different versions.

COBOL syntax: Coding sheet, Development of simple program illustrating program structure and COBOL language. Compiling, Debugging, Testing and Executing COBOL programs.

Structured programming objectives: Program development in modules, Debugging and maintenance, Program design - Top down approach. HIPO flowcharts and pseudo codes.

COBOL implementation of structure programming: Basic control logic structure, Coding standards, Program organization - Modular development and Subroutines, Interlinking and Nesting. Indenting and Formatting.

Procedure functions facilities for I/O operations. Table handling, Indexed tables - SEARCH. Externally stored data manipulation, Sequential file processing, Verbs, and Procedures for SORT, MERGE, SEARCH and ORDER. Direct access files - Query facilities, Relative, Random and Indexed sequential files. Report writer - General format of a report.

Business data processing organization: I/O control, Access control, Process control, Passwords and other security aspects, Job scheduling, Computer logs. Documentation, Management of computer resources, Centralized traditional data processing department, Emerging scene of distributed data processing, System audit, Implementation of data processing systems, Review of data processing services, Budgeting and control of costs.

Recommended Book(s):
Information System Through COBOL - Philippakis & Kazmier.


Basic concepts of data structures: Abstract and system defined data types, Data objects, Data abstraction, Notion of an algorithm - Complexity measures, Rate of growth, Basic timing analysis of an algorithm. Ordering notion, Detailed timing analysis, Space complexity.

Arrays and their representations: Single and multidimensional arrays, address calculation using row and column major ordering.

Stacks and queues: Representation and manipulation of Stacks and Queues using arrays, Usage of stacks and queues. Recursion, Circular queues, Conversion from infix to postfix and prefix form, Polish expressions.

Pointers and their usages: Continued v/s linked storage.

Linked list: Singly and doubly linked lists, Operations on lists, Circular linked lists, Representation of sparse matrices using generalized list structure and polynomial representation using linked lists.

Storage management and garbage collection: Memory allocation strategies, Dynamic storage management - Reclamation and Compaction, Boundary tag method.

Trees: Tree - Binary and N-ary trees, Representation of trees, Tree traversal algorithm, Threaded trees and advantages, Conversion of general trees to binary trees, B-tree applications, Decision trees, Game trees and expression parsing.

Symbol tables: Decision tables - Static symbol tables, Hash tables, Binary search trees, Dynamic symbol tables.

Graphs and their representation: Matrix representation, List structure, Graph traversal algorithm, Applications of graphs.

String and their features: String representation and manipulation using arrays and lists. String matching algorithms - Brute Force, Knuth-Morris-Prat, and Boyer-Moore strategies.

Sorting and searching: Sequential, Binary and hashed searching, Internal and external sorting techniques. Bubble sort, Insertion sort, Shell sort, Merge sort and Quick sort comparisons.

Recommended Book(s):
Introduction to Data Structures - Trembley & Sorenson


Prerequisite: Mathematical foundation of computer science, Probability and statistics.

(a) Numeric Computration:
Computer arithmatic: Floating point numbers - Operations, Normalizations, and their consequences.

Iterative methods: Zeros of single transcendental equations and zeros of polynomials using Bijection, False position, Newton-Raphson etc. Convergence of solution.

Simultaneous linear equations: Solution of simultaneous linear equation - Gauss elimination method and pivoting, Ill conditioned equations and refinement of solutions, Gauss Seidal iterative method.

Numerical differentiation and integration: Solution of differential equations - Runge-Cutta method, Predictor-Corrector method, Automatic error monitoring and stability of solutions.

Interpolations and approximations: Polynomial interpolation - Newton, Lagrange methods. Difference tables, Approximation of function by Taylor series and Chebychev polynomials.

(b) Statistical Computation:
Frequency charts: Different frequency charts.

Regression analysis: Lease square fit, Polynomial and Curve fitting, Linear regression and Non-linear regression algorithms. Multiple regression algorithms.

Time series and forecasting: Moving averages, Smoothening of curves, Forecasting models and methods.

Statistical quality control methods: Factor analysis, ANOVA, Test of signinficance, Chi-Square (?) Test, F-test applications to medicine, psychology and agriculture etc.

Recommended Book(s):
Computer Oriented Numerical Methods - Rajaraman V.
Numerical Analysis - Bansal, Bhargav, Agarwal.


Introduction: System definition and concepts, Characteristics and types of systems, Real-life business sub-system, System models, System boundaries, Real-time and distributed systems, Basic principle of successful systems.

Overview of systems analysis and design: Feasibility analysis, Design, Implementation, Testing and Evaluation. Introduction to SDLC (System Development Life Cycle) and its various phases.

Project selection: Source of project request, Managing projects, Review and selection, Preliminary investigation.

Feasibility study: Technical and economical feasibility, Cost-benefit analysis.

System requirement specification and analysis: Fact finding techniques, Data flow diagrams, Data dictionaries, Process Organization and Interactions, Decision trees and tables.

Detailed design: Modularization, Module specification, File design, System development involving databases.

System control and quality assurance: Design objectives, Reliability and Maintenance. Software design and documentation tools, Top down and Bottom up approaches. Units and integrated testing, Testing practices and Plans. Systems controls, Audit trails and Security.

System administration and training, Conversion and Operation plans.

Hardware and software selection, Hardware acquisition, Memory, Resources, Peripherals, Benchmarking, Vendor selection, Software selection - Operating Systems, Languages, Language processors, Performance and Acceptance criteria.

Recommended Book(s):
System Analysis and Design - Awad Elias M.

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