## BCA Bachelor of Computer Applications Part 1

*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 Part 1 ( First Year )

**SUBJECT-III ANALYTICCOMPUTATION **

**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.

BCA Bachelor Of Computer Application, BCCA, Bachelor of Commerce & Computer Application BE IT/CS, Information technology/Computer Science MCA, Master of Computer Application MCM, Master of Computer Management Diploma , Polytechnic Others,