B.Sc. (M.S.C.)

MATHEMATICS (B.A. and B.Sc.) - Paper III – Mathematics

Unit A: Rings & Fields:
Definition and examples of a ring. Simple properties. Types of rings. Integral domain, skew field, field. Examples. Homomorphism of rings, properties, ideals Maximal ideal, Prime ideal. Quotient rings. Theorem. If R is a commutative ring with identity and M is an ideal of R, then

2. M is a maximal ideal if & only if R/M is a field. 3. M is a prime ideal of a ring R ff & only ff R/M is an integral domain. Definition of Euclidean Ring. Examples. The ring of Gaussian integers. Polynomial rings. Ring of polynomials over a field. Division algorithm.

Unit B : Linear Algebra :
Vector space definition and examples of subspace, quotient spaces, linean dependence and independence, basis, dimension, finite dimensional vector spaces invarience of the number of vectors in basis. Linear transformations, kernel of a linear transformation, rank and nullity of a linear transformation. Rank and nullity theorem.

Algebra of linear transformations introduction of addition and scalar multiplication and multiplication of Linear transformations. Characteristic roots, characteristic equation. Matrix of Linear transformation relative to a basis, change of the representation of the matrix wfth the basis. Similar matrices. Eigen values, eigen vectors, Cayley Hamilton Theorem. Inverse of matrix using Cayley Hamitton Theorem. Elemantary transformation and matrices, invarience, rank reduction to normal form, computation of inverses of matrices.

System of Homogeneous and non homogeneous linear equation consistence conditions, general solution. Inner product spaces norm of a vector space. Schwart inequality. Orthogonal vectors. Orthonormal vectors. Bessel inequality. Perseval's equation. Gram Schmidt orthogonalization process. Real quadratic forms, reduction of quadratic forms under general linear and orthogonal groups of Linear transformation. Sylvesters Law of Inertia definite, semi definite norms. Necessary and sufficient conditions for definiteness general reduction of 2nd degree equation in 2 and 3 variables.

Reference Books
1. Hoff man and Kunz : Linear Algebra
2. Herstein, I.N. : Topics in Algebra.
3. Telugu Adademi.
4. L. Nagamuni Reddy.
5. V Krishna Murthy & J.L. Arora Linear Algebra.
6. Sharma & Vasistha Linear Algebra.
7. A first course in abstFact algebra Fraleigh Telugu translation by Telugu Akademi.
8. Bhattacharya and Jain Rings and Fields.
9. Surrjeet Singh and Zammenuddin Modern Algebra.
10. A.G. Gardner Grop Theory

With Mathematics Combinations

Paper III - Applied Statistics I

Paper IV - Applied Statistics II

Without Mathematics Combinations

Paper III - Statisticial Applications Examination

Paper IV - Electives

Statistics (B.Sc. and B.A.) (with Mathematics Combination) - Paper III - Applied Statistics I

1. Sampling : simierandam sampling with and without replacement, estimates of population means and their standard errors. Stratified random sampling - Proportional and Neyman's optional allocations, Estimates of population means and their standard errors.

2. Designs: Principles of experimentation. Linear models leadingto C.R.D., R. B. D.

3. Index Numbers : Construction and uses of Index number - simple and weighted index numbers - Tests for ideal index numbers. Cost of living index numbers, whole sale price index loess. Base shifting and splicing, fixed and chain baso index numbers.

4. Time Series : Comportments of time series, determination of trend by Iraphical, semiaverages, least square and moving average methods. Determi nation of seasonal indices by simple averages, ratio to moving average, ratio to trend and link relatives methods.

5. Statistical Quality Control : Basis of control charts, construction and uses of charts for X, R, P np and C.- Vital Statistics : Rates and Raties, Fertility and mortality rates, construction and uses of complete life tables. Notion of abridged life tables population growth (Bogestic Growth).

Suggested Books
Telugu Akademi Books:
1.Anuvarthitha Sankyakha Sastramu;
2. Pratimpa Sidhentham;
3. Sankya Vileshanamu;
4. Vyapara Ganithamu];
5. Applied Statistics by V.K. Kapoor and S.G. Gupta;
6. Fundamental of Statistics, Vol. 2 by Goon Gupta and Das Gupta;
7. Sampling Techniques by Coachran;
8. Calculus of Finite Difference and Numerical Analysis by H.C. Saxena (X).

List of Practicals
1. Simple random Sampling - Estimation of the Population mean, population total and their standard errors.
2. Stratified random sampling - Estimation of the population mean, population total and their standard errors.
3. Determination of trend moving Averages.
4. Estimation of trend Least squares method.
5. Seasonal indices simple averages.
6. Calculation of simple indix numbers.
7. Computation of weighted index numbers.
8. Cost of living index numbers.
9. X, R charts.
10. P, Np, and C charts.
11. Fertility rates.
12. Mortality rates.
13. Construction of complete life tables.
14. Analysis of CRD. 15. Analysis of RBD.

Statistics (B.Sc. and B.A.) (with Mathematics Combination) - Paper IV - Applied Statistics II

A. Elements of Sampling and Experimental Designs
1. Principles of Experimentation. Completely Randomised design. Randomised block design and Latin Square design and their relative merits (2 questions)
2. Fedtorial experiments, Description and analysis of 2 2 and 23 factorial experiments. (1 question)
3. Random numbers and their uses - Drawing of random samples from Binomial and Poison Normal Populations. (1 question)
4. Systematic sampling and the nation of I.P.S. Sampling (1 question)
5. Variance and cost functions and their uses.
6. Sampling versus census planning, organisation and execution of sample surveys, Pilot surveys sampling and non-sampling errors. some large scale surveys conducted in India. (2 questions)

Short Notes (1 question)

List of Practicals
1. Analysis of C.R.D. (Missing Plot Technique)
2. Analysis of R.B.D. (Milssing Plot Technique)
3. Analysis of L.S.D.
4, Analysis of 2 2 - Facatoriai experiment
5. Analysis of 21 - Factorial experiment.
6. Drawing of Random Sample for Binomial population.
7. Drawing of Random Sample from Poisson population.
8. Drawing of Random Sample from Normal population.
9. Drawing of a Systarnatic Sample of estimation of population mean, total and their standard errors.
10. Drawing of P.P.S. Sample and estimation of population total and standard error.

Suggested Books
l.-Prayoga Rachana Vislesana
2. Sample surveys Siddanthalu Telugu Akademi Books
3. Applied Statistics by V.K. Kapoor and S.C. Gupta
4. Fundamentals of Statistics Vol. II by Goon, Gupta & Das Gupta.
5. Experimental Designs by Cocharan and Cox.
6. Sampling theory and Methods by M.N. Murthy
7. Sampling theory and Methods by P.V. Sukhathme and B.V. Sukhathme
8. P.P.S. Sampling Drawing of A.P.P.S. Samples by the cumulative total method and estimation of population total and its standard.

B. Optimazation Methods
1. Definition and scope of operations research, different types of models their consturction (1question)
2. Definition and formulation of linear programming problem (LPP) with illustrations - concepts of optimal solutions, graphical method of solution, the simplex algorithen of solving the L.P.P. (only simple cases) concepts of degeneracy and dual LPP (2 questions)
3. Transportation problem: Methods to obtain the initial basic feasible solution - The North West Corner Rule, the row minima method, the column minima method, vogel's approximation method, the U.V method of obtaining, optimal solution - transportation problem as a particular case of LPP ( 2 questions).
4. Elements of game theory : Rectangular games - Rectangular games with saddle points mixed stratagies, principle of dominance, solution by graphical method (2 questions).

List of Practicals
1. L.P.P. Graphical Method (Maximization type)
2. L.P.P. Graphical Method (Minimization type)
3. L.P.P. Simplex Method (Maximization type)
4. L.P.P. Simplex Method (Minimization type)
5. Transportation problem : North West Corner Rule
6. Transportation problem: Vogels' approximation method
7. Transportation problem (U.V Method)
8. Game theory (Saddle point)
9. Game theory (Metehod of deminen)
10. Game theory (2 x h game - graphical method)

Suggested Books
1. Goeal and Mithal : Operations Research.
2. Meurice Sasieni Arther Yaspan and Lawrence Fiedman : Operation Research Methods and Problems.

C. Elements of Computer Programming
The College with Computer Facility only have to operate this paper
1. Introduction to Computer Programming - algorithms Flowcharts and decision tables.
2. Digital computers, Block diagram of a Computer Generations (First, Second, Third and Fourth)
3. Number Systems: Binary, Octal and Hexadecimal systems Conversion from one representation to another. (2 questions from items 1 to 3)

Basic
4. Constants vasibles, expermissions, REM, READ, DATA, RESTORE, INPUT, PRINT, STOP End.
5. Control statement Co. To. Computer, Co. To, IF, THE'M, For-NEXT. substripted variable - DIM statement.
6. Library Functions, user defined functions and subroutines.
7. Matrix comments : CON, IND, INV TRN. etc. (3 questions from item 4 to 7)

Fortran
8. Constants, Variables, expressions Arithmetic statement READ, PRINT, FORMAT Statements Stop, END.
9. Control statement GO, TO mpted GO TO Arithmetic logical IF, DO LOOP.
10. Library functions, Arithmetic statement function, FUNCTION subprogramme, Subroutine subprogramme COMMON AND EQUIVALENCE Statements. (2 questions from items 8 to 10 short Notes: 1 question)

N.B.: Training Practical Aspects on the above items on Computers

Books Suggested

1. P.S. Grover : Computer Programming in BASIC
2. Hirsch : Self taught in Basic Programming;
3. S.D. Sharma: Computer Programming in FORTRAN
4. V. Rajaraman: Computer Programming in FORTRAN
5. P.S. Grave- Computer Programming in FORTRAN
6. RVS. Rao : Computer Programming in FORTRAN
7. P.V. Ratnam & P.S. Raju - FORTRAN Programming

Fortran : List of Practicals : Programme based on BASIC
1. INPUT READ
2. IF THEN GO TO
3. FOR NEXT AND SUBSCRIBED VARIABLES
4. SOB routines and user defined functions
5. READ IF GO TO
6. DO LOOP and SUB subscripted variables
7. Arithmatic statement functions
8. Function Sub. Programme
9. SUBROUTINE Sub-Programme
10. COMMON AND EQUIVALENCE
11. Miscellaneous

Without Mathematics Combinations

Paper III - Statisticial Applications Examination

B.A / B.Sc. Statistics (without Mathematics Combination) - Paper III - Statisticial Applications Examination

1. Tests of significance - concepts of Null hypothesis, level of significance, Type I and Type 11 errors - Large sample tests for proportions mean and standard deviations. Small sample tests using test for mean difference of two means, Correlation coefficient Tests based on X2 and F Non Parametric tests Signtest, Median Test and Run Test (descriptive way) (two questions)

2. Need and definition of Index numbers - simple and Weighted index no. - construction of whole sale price index and consumer price index numbers. Standard tests of index numbers. Base shifting and splicing of index numbers. (1 question)

3. Time Series : Notion of time series components of time series - Methods of determining trend and seasonal variations (1 question)

4. Vital Statistics : Measurement of mortality and fertility. Various birth and death rates. Concept of Life Tables (I question)

5. Statistical Quality Control : Control charts, Basis of Control Charts, Control charts for variables and attributes, Uses of X R p np and C charts (2 questions) Short notes : 1 question

Note :
Mathematical derivations are not necessary

Suggested Books
1. Anuvarthitha Sankhyaka Sastramu;
2. Vyapara Ganithamu Telugu Akademi Books;
3. Prathirupa Sidhantamu
4. Applied Statistics by S.C. Gupta, VK. Kapoor

List of Practicals
1. Large Sample tests for proportions, means and S.D.S.;
2. Small sample tests for means, variances & Correlation;
3. Signtest, Median test and Run test;
4. Computation of simple index numbers;
5. Calculation of Weighted index numbers;
6. Estimation of Trend Moving overages and least squares method;
7. X R Charts;
8. P np and C Charts;
9. Fertility rates;
10. Mortality rates.

B.A / B.Sc. Statistics (without Mathematics Combination) - Paper IV
Any one of the following

(a) Elements of Sampling and Design of experiments

(b) Elements of Numerical Analysis and operations research,

(c) Demography

B.A / B.Sc. Statistics (without Mathematics Combination) - Paper IV - (a) Elements of Sampling and Design of Experiments

1. Sampling versus census Planning Organisation and execution of sample survey, Pilot Survey sampling and non-sampling errors - some large scale surveys conducted in India (1 question)

2. Random number tables and drawing of random samples - Simple Random Sampling (with and wihout replacement) Stratified Random sampling. Systematics sampling and multistage sampling (in a descriptive way only) (2 questions)

3. National Income Statistics : Concept of National Income, Methods of estimation, Features of National income estimates. (I question)

4. Principles of Design of Experiments. Randomisation, Replication and Local Control Description of completely randomised. Design Randomised Block, Design Latin Square, Design and factorial experiments and their relative merits. (3 questions) Short notes : 1 question

Note : Mathematical derivations are not necessary.

Suggested Books
1. Sample Surveys Siddanthalu
2. Prayoga Rachana Visleshana
3. Anuvarthitha Sankhyaka Sstramu
4. Applied Statistics by S.C. Gupta & VK. Kapoor
5. Fundamentals of Statistics Vol. 11 by Gran Gupta & Das Gupta
6. Experimental Designs by Cochran and Co.

List of Practicals
1. Drawing of Random Samples from Normal Population
2. Simple Random Sampling Estimation of the population mean population total and their standard errors.
3. Estimation of National Income
4. Analysis of CRD
5. Analysis RBD
6. Analysis of LSD
7. Analysis of 22 experiment
8. Analysis of 21 experiment.

B.A / B.Sc. Statistics (without Mathematics Combination) - Paper IV - (b) Elements of Numerical Analysis and Operations Research

1. Numerical differentiation - Finding dy/dx, dy² / dx ² of Newtons forward formulae Finding dy/dx, dy² / dx ² of of Newtons backward (1 question)

2. Numerical Integration - Trapezoidal Rule, Simpson's 1/3 rule, Simpson's 3/8 rule and Weddles rule. (question)

3. Definition and scope of operations research and diff erent types of models. Difinition and formulation of Linear programming. Problem with illustrations Graphical method. (1 question)

4. Transportation problem (1) North west Corner rule (2) Rowminima, Column minima Method (3) Minimax Maximum method and (4) Vogel's approximation method of finding initial basic feasible solution only (2 questions)

5. Game Theory Rectangular games, Rectangular games with saddle points. Solution by graphical method. (1 question)

6. Elements of Sequencing problem with jobs with two machines and their solution (1 question) Short notes (1 question)

Note
: Mathematical derivations are not necessary

Suggested Books
1. Numerical Analysis - Telugu Adademi Books;
2. Vyapara Ganitham Telugu Academic Books;
3. Operations Research by Kanthiswaroop, Gupta & Manmohan;
4. Operations Research Methods and problems by Maurice Sasieni, etc.;
5. Operations Research by Goel and Mittal;
6. Linear Programming by S.I. Gauss.

List of Practicals
1. Numerical differentiation
2. Numerical integration
3. LPP Graphical Methods (Maximisation and Minimization types)
4. Transportation problem North west corner Rule solution
5. Transportation problem Vogels approximation method
6. Transportation problem U.V. Method
7. Game Theory Saddle point
8. Game Theory Graphical method solution.

B.A / B.Sc. Statistics (without Mathematics Combination) - Paper IV - (c) Demography

1. Introduction of Demography Nature and scope. Brief history of the development of Demographic work in India. (1 question)
2. Evolution of Indian Census 1872-1981 rates and ratios Standardisation of rates (1 question)
3. Age sex pyramid sex ratio basic characteristics of population of India and A.P. (1 question)
4. Techniques of measuring Mortality factors effecting mortality
5. Techniques of measuring Fertility - Factors effecting fertility (1 question)
6. Life tables Components of FIT and its uses. (1 question)
7. Population growth models - linear, exponential. (1 question)

Short notes on all the above (1 question)

Books for reference
1. B.D. Misra : The study of Population;
2. D.J. Bogue : Principles of Demography
3. Sarma RV.S. : Statistical Techniques in Population studies (Telugu Akademi)

List of Practicals

1. Calculation of crude death rate (CDR) crude birth rate (CBR) Sex ratio (SR) Child women rate (CWR);
2. Drawing of Age sex pyramid;
3. Measures of Mortality - Infant mortality Standardized Mortality rate;
4. Measures of Fertility General fertility rate (GFR) Age specific fertility rate (ASFR) Total fertility rate (TFR);
5. Gross reproduction rate (GRR) and net reproduction rate (NRR);
6. Life tables;
7. Growth models linear;
8. Growth models exponential the end.

Computer Science

IInd Year

Paper III - Programming in C++ and Data Structures

IIIrd Year

Paper IV - Business Data Processing

Paper IV - PC Software and Database Management Systems

IInd Year

B.Sc Course Structure and Scheme of Examination

1

Programming in C++ and Data Structures

2.

Programming in C++ and Data Structures Lab

Second Year B.Sc Breakup of marks for Practical

Each student has to answer one question.
The breakup of marks is as follows

1.

Programming in C++ and Data Structures

1. Alogrithms/Problem Solving (10 marks)
2. Programming (10 marks)
3. Result (10 marks)

2.

Viva Voce

10 marks

3.

Record

10 marks

Paper II: Programming in C++ and Data Structures

Unit I
Introduction to C++ - Basics - Procedural Abstraction and Functions

Unit II
I/O Streams - Classes and Abstract Data Types - Flow of Control - Tools for defining ADTs

Unit III
Arrays - Strings and Three Dimensional arrays - Pointers and Dynamic Arrays - Recursion

Unit IV
Templates and Abstraction - Pointers and Linked Lists - Inheritance

Unit V
Data Structures - Linked Lists - Stacks - Queues (Creation, Insertion and Deletion of Nodes) - Trees (Creation, Insertion and Deletion of nodes, in order, preorder and post order traversal) - graphs (adjacency lists, adjacency matrix, depth first search methods)

Laboratory-II: C++ and Data Structures Laboratory

1. Abstract Data Types for Rational numbers and for Complex Numbers (See Example 5 and 6 Page 50-508 for Book 1)

2. Multi Dimensional Arrays (Two Dimensional Grading Problem Page 613 of Book1)

3. Palindrome Testing Program (Page 629 of Book 1)

4. Multipath Inheritance and Virtual Functions Examinations Database (See Page 534 of Book 3)

5. Multilevel Inheritance - Product Company Modeling (see Page 544 of Book 3)

6. Hierarchy Inheritance - Vehicle Database (Page 549 of Book 3)

7. Template Functions for Bubble Sort

8. Program to Demonstrate use of class template that needs a list of values (For details see Programming Examples on Page 766 of Book 1)

9. User Defined Template arguments - Student Record (See Page 609 of Book 3)

10. Overloading of Operators +=, -+, /+ for complex classes.

11. Inheritance of Class Template - Union of sets (see Page 617 of Book 3)

12. Program to perform stack operations such as push() and pop() functions using an array method

13. Program to perform queue operations such as qstore(), qdelete() functions using an array method

14. Program to create the circular queue by using the operations qstore(), qdelete() functions using an array method

15. Program to create the linear linked list and display the list in LIFO method

16. Program to add new companion to a linked list or delete existing components in it.

17. Program to construct a linear linked list and to display the list in FIFO method.

18. Program to convert an infix expression to post fix expression using a stack

19. Program to construct to double linked list and add or delete an item

20. Program to create a binary tree and to display the contents of the tree using the tree traversal methods

21. To implement binary search and calculate the search time.

22. Stream computations with files - student files - creating - writing – reading

Suggested Text Books for Second Year

Prescribed Text Books

1.

Problem Solving with C++

Walter Switch

Addission Wesley

2.

Data Strucutres, Algorithms and Application in C++

Sartanj Sahni

McGraw Hill

Reference Text Books

3.

Mastering C++

R Venugopal, Rajkumar & T Ravishankar

Tata McGrawHill

4.

Data Structures using C++

Yedidjah Langsan, Moshej Augenstin, Aaron M Tanenbaum

Prentice-Hall

COMPUTER SCIENCE - Paper IV - Business Data Processing
Unit I: Introduction to Data Processing concepts, data preparation, transcription, validation, storage and retrieval. Structure of COBOL Programs Four divisions of COBOL, Structured Programming Concepts. Identification, Environment and Data Divisions, Record and Data item descriptions

Unit II : Procedure Division - Data movement verbs, Accept and Display arithmetic verbs, structured programming constructs such as Perform and IF, Table handling, other miscellaneous verbs.

Unit Ill : File Processing - File structure, operations on files, batch processing of sequential files, sorting and merging. Direct access devices, indexed sequential files, relative files.

Unit IV: Overview of systems analysis and design, business system concepts, system development life cycle, project selection, feasibility study.

Unit V : Systems requirements specification and analysis, system design objectives, design, testing and implementation, performance and acceptance criteria.

COMPUTER SCIENCE - Textbooks

1. Philippakis As and Kazmier LJ Information Systems through COBOL McGraw-Hill. 1978.
2. Lee Introduction to Systems Analysis, NIC Galgotia

COMPUTER SCIENCE - Practical Ill - COBOL and D Base/Fox Base/ Fox Pro

COBOL: At least 10 experiments (Programs) on the following :
Structural programming, sequential file creation, file extension, sorting and merge of files, accessing records in a sequential file, operations on direct access fit's, file creation, inserting records, deleting records, start reading from a specified location, Updating files.

D Base or Foxbase or Fox Pro : At least 8 experiments on the following
Building a data base, searching a database, sorting a data base editing and modifying data bases, creating and printing formatted reports, managing numbers and dates, managing multiple data files, designing and developing programs in Dbase/Foxbase/Foxpro. At least 4 experiments on usage of other PC packages such as Lotus etc.

COMPUTER SCIENCE - Practical IV : Project Work
Design and implementation of one of the computer applications

COMPUTER SCIENCE - Paper IV - PC Software and Database Management Systems

Unit I : Introduction to MS-DOS, files, directories, system commends, redirection, pipes, batch files. Wordprocessing (e.g. Word Star) - Features of word processing, creation and editing, global search and replace, formatting block operation mail merge, spell checking.

Unit II: Unix-Login, Unix Commands, System calls, Redirection, pipes File Systems and Operation, Elements of shell programming, sorting.

Unit III : Spread Sheats (Lotus-123) - Worksheet, constants and formulas Library functions, Graphic output, macros, applications.

Unit IV : Relational Database, Structure, storage organisation, relational algebra, Normal forms.

Unit V : D base-III - creation and editing of Dbase files, queries, sorting and indexing, report generation, Dbase-111 programming.

COMPUTER SCIENCE - Textbooks
1. PC Software, made simple Taxali, TMH Press 1994.
2. Richard W. Brightman, Teffrey M. Dimsdale Using Micro Computers, Galgotia, 1987.
3. C.J. Date An introduction to Database ststem