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NAGPUR -10, MAHARASHTRA, INDIA. 
NAGPUR
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ATLANTA COMPUTER INSTITUTE
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NAGPUR
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Email: atlantaworld@gmail.com
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University Syllabus Course For BCA

Atlanta Computer Institute Nagpur conducts Tuition Classes for BCA First Year (  Part 1 ) , BCA  Second Year (   Part 2  ) and BCA Final Year ( Part 3 ) for all universities in India . The Following syllabus is of Nagpur University.  Final Year Projects Training is also given to  BCA  Students.
 
 
BCA Bachelor of Computer Applications   Part 1

 BCA Part 1 ( First Year ) 

SUBJECT-III     ANALYTIC COMPUTATION


Paper-1 :  DISCRETE   MATHEMATICAL  STRUCTURE

Unit-1:   Fundamental

Sets  and subsets, operation on sets, Sequences, division  in the  integers, matrices, Mathematical   structure. Logic-  proposition   and   logical operations,  Conditional  Statement, Methods   of proof,  Mathematical   induction.

Unit-2  :  mathematical   logic

Statement     and   notation, connectivities,  Normal   Forms, The   theory  of Inference  for the Statement     calculus. The  predicate   calculus, Inference   theory  of  the predicate  calculus

Unit-3   Counting

Permutation, combinations, the  pigeon hole principle, recurrence  relations   and  digraphs-product  sets and  partitions, relations and  Digraphs, paths  in relations and    digraphs, properties of relations  , equivalence  relations, computer    representation    of relations   and   Digraphs, manipulation    of  relations, transitive   closure   and   warshall’s  algorithm.Functions- definition   and   introduction , function   for  computer  science, permutation functions,      growth  of  functions

Unit-4  :  graph  theory

 Basic concept of    graph theory, euler   paths  and  circuits,Hamiltonian  paths and  circuits. Other relation  and  structure – partaily  Ordered  sets,Lattices,Finite  Boolean  algebras, functions  of Boolean  algebras, Boolean   function   as  Bollean   polynomials. Tress -  introduction ,undirected   trees, minimal   spanning  ttrees.

Unit-5 :  Semigroups  and  groups

Binary    Operations   revisited, Semigroups, products   and  quotient s  of Semigroups,groups,product s  and   quotients   of  groups. Introduction to compatibility   Theory-Languages  , Finite   state  Machines, semigroups,Machines and  languages

 

Paper-2:Computer oriented statistical methods

Unit-1:   Introduction

Definition  of statistics, importance    and  scope  of  statistics,limitation of  Statistic,  distrust  of  statistics.  Statistical   data  collection-  primary  and  secondary   data, methods  of  collecting  primary   data  Sources  and secondary  data, Census  and  sample  investigation.  Presentation   of  statistical  data-  classification   , Tabulation, frequency  distribution, graphic  representation   of  a  frequency  distribution,average  or measure  s of  central   tendency or  measures  of  locations, requisites  for  an  ideal  measure of  central  tendency-Arithmetic :   Mean, median,mode,eometric mean  and Harmonic  Mean, weighted   Average, Relationship amongst   different  averages.

 Unit-2:    Measures   of  Dispersion, Skeewness  and  kurtosis

Meaning      and   significance  of  dispersion, methods  , of  measuring  dispersion- range,quartile, mean  deviation,    standard  deviation, coefficient  of  skweness, kurtosis, coefficient  of  dispersion, coefficient  of  variation. Co relation   and  regression-definition   of  correlation, scatter diagram, karl pearson  coefficient  o  correlation, limits for  correlation  coefficient, definition  of  regression, lines  of  regression, regression  curves, regression  coefficients,properties  of regression coefficients, correlation   analysis vs.  regression  analysis.

Unit-3:   probability

Introduction , definitions  of  various    terms, mathematical   or  classical   probability, statistical   or  empirical    probability,  mathematical  tools, sets    and  elements of  sets, operation s   on sets,axomatic approach  to probability, probability  function ,  mathematical    law  of  addition  of probability and  conditional  probabilities, independent  events, bayes   theorem, geometric    probability.

Unit-4  Random  variables    and    distribution   functions

Definition  of   random  variable  , distribution  function, properties   of  distribution  function,disctrete   random   variable,probability   mass    function,discrete    distribution function , continuos   random  variable,  continuous   density  function, continuous  distribution   function.Mathematical   expectation  and  Generation   function  -  definition    of   mathematical    expectation  , addition  &  multiplication   theorem   of   expectation , co-variance  , expectation &  variance   of  a linear   combination  of  random  variables, moment  generating   function,   cumulants.

Unit-5:    Theoreitical   discrete   distributions

Introduction  , bernouli  distribution ,  binomial  distribution,poisson  distribution, geometric  distribution  . theoretical   continuous  distributions- introductuion, normal  distribution, gama distribution, cauchy’s  distribution  and   central  limit  theore

 

Paper-3   OPERATION   RESEARCH

Unit-1   :   Introduction   to Operation   Research   (OR)

Origin  and  Development  of  OR,  nature  of OR,  characteristics,  of OR, classification  of problems  in  OR, MODELS IN OR ,phases of  OR, uses  and  limitations  of OR, methodologies  in  OR, APPLICATIONS IN OR   Linear   programming  - concept   of linear   programming   model, mathematical  formulation  of the  problem, graphical  solution   methods   linear   programming   methods -  simplex  method, big Methods, dual  simplex  method,two   methods   phase .Duality   in linear  programming -  formulation of  dual  problem, application of duality

Unit-2:   Transportation  problem :     Mathematical   models for transportation  problem , types. Assignment   problem-zero  one    programming   model  for assignment   problem. Types of assignment  problem. Hungerian  method , branch  and bound  techinique  for assignment  problem . Game  Theory-terminologies  of  game  theory, Two   person  Zer0 –sum games,  the maximin-minimax principles, games   without  saddle  points –mixed strategies , graphical solution of 2xn and xn  gamrs , dominance property.

Unit-3  Decision   Theory:    Introduction  , decision under   certainty   decision  under  risk, decision   under  uncertainity,  decision tree    Network  Scheduling   by  cpm / pert -  Introduction , basic  concept, constaints  in  network, critical  path  ethod ( CPM), PERT network , PERT   calculations.  Time –cost –Trade _off  Aspects   in Network   technique , advantages of  network ( PERT/CPM)

Unit-4 :  Inventory  control  :  Introduction,inventory  control , selective  control  techniques, types  of  inventor,economic lost size problem, problem of EOQ  with   shortage , Inventory  control techniques- uncertainity   demand, inventory     control techniques- stochastics problem, inventory  control  with   price  breaks.

Unit-5   quening  Theory:   introduction  , terminologies  of  quening   system,   characteristics  of queuing  system, characteristics  of  queuing system, poisons   process    and   exponential   distribution , classification   of  queues, definition of transient  and steady  states, poisson   queues, non-poissons queuing  System , cost  -profit  models  in  queuing control.

 

 

 

 

 

 

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