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NATIONAL UNIVERSITY Syllabus Department of Statistics Four Year B. Sc. Honours Course Effective from the session: 2009–2010 National University Subject: Statistics Syllabus for Four Year B.Sc Honours Course Effective from the Session: 2009-20 10 Year wise course and marks distribution Socond Year (Honours) Subject Code 7375 Subject Title Numerical Mathematics Sampling Technique Lab 1 Numerical Mathematics Lab 2 Sampling technique Probability Distribution Viva Voce Agricultural Economics Money, Banking and Public Finance Calculas-II Math Lab (Practical) 9999 English (Compulsory) 3663 3664 3665 3666 3667 3696 7228 7241 7373 Marks 100 100 50 50 100 50 50 100 100 50 100 Credits 4 4 2 2 4 2 2 4 4 2 Non-Credit Marks: 100 Course Code 3663 Course Title: Numerical Mathematics Credits: 4 Class Hours: 60 Exam Duration: 4 Hours Differences of a polynomial, Finite difference operator. Factorial notation. Difference equations. Newton’s forward and backward Interpolation formula. Central difference formula. Gauss, Stirling’s and Bessel’s, Lagrange’s interpolation formulae. Interpolation with unequal interval of the argument. Inverse interpolation. The accuracy of the interpolation formulae, Numerical differentiation. Numerical Integration: General quadrature formula. Numerical integration by different formulae. The accuracy of quadrature formula. Numerical integration for unequal intervals of the arguments. Stirling’s formula for N!. Numerical solution of equations by various methods, convergence of these methods and their inherent errors. Simultaneous equations in several unknowns. Double interpolation. Function of two variables. Double interpolation by applying single interpolation formula. Books Recommended: i) James B.Scasborough ii) Freeman, H. iii) Mallick, S .A iv) Hilderbrand : Numerical Mathematical Analysis : Finite Diferences for Actuarial Statisticw. : Numerical Mathematics (in English) Shankhik Ganit (in Bangla) : Introduction to Numerical Analysis Course Code 3664 Marks: 100 Course Title: Sampling Technique Credits: 4 Class Hours: 60 Exam Duration: 4 Hours Introduction: Basic concept of sample survey, relative advantages, disadvantages and suitability of complete and sample enumeration. Uses of sample survey. Role of sampling theory. Requirements of a good sample design. Preliminaries in sample survey : Units, Population, Sampling units, Sampling frame related problems. Basic principles of sample survey. Various steps involved in a sample survey. Pilot survey, Random or probability sampling and Non-random or purposive sampling. Quota sample. Mixed sample. Population values and estimates in sample survey: Bias and its effect. Precision and accuracy of estimates. Different type of errors associated with sampling such as sampling error & non sampling errors and complete enumeration. Various methods of data Collection. Questionnaire and schedule. Preparation of questionnaire. Open and closed questionnaire. Different types of random sampling. Simple random sampling: Advantages and disadvantages, Drawing of samples with and without replacement sampling, estimates and standard errors. Simple random sampling for proportion-estimate and standard errors. Determination of sample size for specified precision. Introduction to other probability sampling schemes. Stratified random sampling: Reasons for stratification. Formation and number of strata. Stratified random sampling, estimator, standard error. Allocation of samples to strata. Cluster Sampling: Reasons for clustering, formation of clusters, size of clusters. Simple cluster sampling with equal size clusters-estimates and standard error, comparison with simple random sampling. Two stage sampling. Systematic sampling : Use, limitation, estimates, bias, standard error and efficiency. Comparisons with simple random sampling. Systematic sampling for populations with linear trend. Methods for dealing with population with linear trend or periodic variation. Ratio and Regression Estimate: Ratio and Regression estimate, Ratio estimation examples. Estimate, Bias, Mean square error, approximate variance, condition for unbiased ratio estimation, Unbiased ratio type estimate. Regression estimation, example, properties and limitation, bias and approximate variance, estimate of the variance, Bias of the linear regression estimate. Comparative merits and demerits of ratio and regression estimate. Books Recommended: (i) Cochran, W.G. : Sampling Technique (ii) Islam, M.N. : An Introduction to sampling Methods. Book (iii) Kish, L. :World. Survey Sampling (iv) Hansen, Hurwitz and Mandow : Sample Survey Methods and Theory Vol-1 & (v) Sukhatme, P.V Vol-2 : Sampling Theory of Surveys with Application (vi) Daroga Singh : Sampling Technique Course Code Course Title: 3665 Marks: 50 Credits: 2 Lab 1. Numerical Mathematics Numerical Mathematics: Problems with operators and polynomials. Uses of interpolation formulae for equal and unequal interval. Newton’s forward and Backword, sterling’s, Basel’s formulae, Lagrange’s interpolation formula. Newton’s divided difference formula, Inverse interpolation, Numerical Solution of equation, Numerical integration. Double interpolation. Course Code Course Title: 3666 Marks: 50 Credits: 2 Lab 2. Sampling technique Sample survey: Drawing of sample by SRS, Stratified sampling, systematic sampling, cluster sampling with equal size. Estimation of parameters in each case. Estimation of variance of the estimates of the parameters, determination of precision of estimates. Relative efficiency of different sampling scheme. Estimate of parameters by ratio and regression methods and their standard errors. Course Code 7241 Marks: 100 Credits: 4 Course Title: Money Banking public finance Class Hours: 60 Exam Duration: 4 Hours 1. Money : Definition, functions, importance, types of money. 2. Value of money : Meaning, quantity theory of money, cash transaction and cash balance approach, concept of inflation and deflation. 3. Commercial. Banking : Functions, Balance sheet, liquidity and profitability. Multiple credit creation of commercial banks. Commercial Banks of Bangladesh. 4. Central Banking : Objective, Functions, Credit Control of central bank. Bangladesh Bank. 5. Specialized Banking : Objective, Importance. Role of BSB, BSRS, BKB, Islami Bank, Grameen Bank. 6. Public Finance : Definition, Nature and Scope, Distinction between public finance and private finance, Role of public finance in developing countries. 7. Public Revenue : Sources, tax & fees, impact & incidence of taxes, direct & indirect taxes, value added tax. 8. Public Expenditure : Need for public expenditure & its increasing importance. 9. Budget : Concept of budget. Distinction between revenue and capital budget, public debt. Sectoral allocation. Study of the budgets of Bangladesh (last five years). 10. Characteristics of the Economy of Bangladesh : Obstacles & preconditions of economic development. Agricultural resources, its importance and problems. 11. Population in Bangladesh : Its growth, structure & distribution Problem, family planning, unemployment problem. 12. Industry in Bangladesh : Importance of industrialization, structure of industry. Problems & prospect of industries. Books Recommended : 1. Crowther : Outline of Money 2. Luckett : Money & Banking 3. Musgrave : Theory of public Finance 4. Due : Government Finance. 5. Faaland & Parkinson : Bangladesh : A Test case of Development. 6. A. R. Khan 1989 : The Strategy of Development in Bangladesh Macmillan, Course Code 7228 Marks: 50 Course Title: Agricultural Economics Credits: 2 Class Hours: 40 Exam Duration: 2.5 Hours 1. Introduction : Definition of Agricultural Economics, need for a separate study. 2. Structure and characteristics of traditional agriculture : Basic features of traditional agriculture, development in traditional agriculture. 3. Contribution of agriculture to economic development : Product contribution; factor contribution, market contribution and their relative importance; Importance of agriculture for industrial development. 4. Types of farming : Commercial, cooperative and collective farming; share cropping, subsistence farming Vs. Capitalist farming. 5. Agricultural Finance : Importance of agricultural credit, sources of agricultural credit, institutional and non institutional; functions of rural money markets if the LDCs. 6. Land reform : Definition, objectives of land reform, features of past and modern land reforme, difficulties of implementing land reform. 7. Marketing : Role of agricultural marketing, marketing functions and market structure, market intelligence, imperfections of agricultural marketing in LDCs. 8. Role of government: Rationale for government intervention in agriculture, protections of farmes’s income, price support and input subsidy- a comparative study. Books Recommended : 1. Ghatak and lngersent : Agriculture and Economic Development. 2. Hill and Ingersent : Economic Analysis of Agriculture. 3. Mellor : Economics of Agricultural Development. 4. Southworth and Johnson : Agricultural Development. 5. Barkat, Zaman & Raihan : Political Economy of Khas land 6. ‰mq` G wU Gg AvwRRyj Bmjvg : AvaywbK K…wl A_©bxwZ Course Code 7373 Course Title: Calculus- II Marks: 100 Credits: 4 Class Hours: 60 Exam Duration: 4 Hours Vector valued functions of a single variable: Limits. Derivatives and integrals. Tangent lines to graphs of such functions. Arc length from vector viewpoint. Arc length parametrization . Curvature of space curves: Definition. Curves of zero curvature. Curves of constant nonzero curvature. Cartesian equations and parametric equations. Radius of curvature. Centre of curvature. Functions of several variables: Limits and continuity. Partial derivatives. Differentiability, linearization and differentials. The chain rule. Partial derivatives with constrained variables. Directional derivatives, gradient vectors and tangent planes. Extreme values and saddle points of functions of several variables. Lagrange multipliers. Taylor’s formula. Multiple Integration: Double integrals and iterated integrals. Double integrals over nonrectangular regions. Double integrals in polar coordinates. Area by double integrals. Triple integrals and iterated integrals. Volume as a triple integral. Triple integral in cylindrical and spherical coordinates. General multiple integrals. Jacobians. Topics in Vector Calculus: Scalar and vector fields, Gradient, divergence and curl, and their properties. Line integrals, Independence of paths. Green’s theorem. Surface integrals. Stokes’ theorem. The divergence theorem. Evaluation: Final exam (Theory ; 4 hours ): 100 marks. Ten questions will be set, of which any six are to be answered. Books Recommended : 1. Howard Anton- C a l c u l u s 5 / E (a n d f o r w a r d e d i t i o n ) Course Code 7375 Marks: 50 Course Title: Math Lab (Practical) Credits: 2 Getting started. Problem solving using Mathematica /Maple (Problems will be selected from courses studied in the first and second years of their studies). Students are 3696 M a r k s : 50 Credits: 2 required to work on theirTitle Course Viva-voce assignments in MMT 201 in the lab Viva-voce on courses studied in the first and second years. sessions.C o u r s e Code Course Code Course Title: 9999 Marks: 100 English (Compulsory) Non-Credit Class Hours: 60 Exam Duration: 4 Hours Aims and objectives of this course: To develop students’ English language skills, to enable them to benefit personally and professionally. The four skills listening, speaking, reading and writing will be integrated to encourage better language use. 1. Reading and understanding 54=20 Students will be expected to read passages that they might come across in their everyday life, such as newspapers, magazines, general books etc. Simple stories will also be included to give students a familiarity with different uses of the language. [N.B. : 5 Questions are to be answered. Each question will carry 4 marks. There may be division in each question] a) Understanding different purposes and types of readings b) Guessing word-meaning in context. c) Understanding long sentences d) Recognizing main ideas and supporting ideas. e) Answering comprehension questions. f) Writing summaries. 2. Writing 40 a) Writing correct sentences, completing sentences and combining sentences. 5 b) Situational writing : Posters, notices, slogans, memos, advertisements etc. 4 c) Paragraph writing : Structure of a paragraph; topic sentences; developing ideas; writing a conclusion; types of paragraphs (narrative, descriptive, expository, persuasive); techniques of paragraph development (such as listing, cause and effect, comparison and contrast). 8 Or, d) Newspaper writing : Reports, press releases dialogues etc. e) Writing resume©s. Or, 8 f) Writing letters : Formal and informal letters, letters to the editor, request letters, job applications, complaint letters etc. g) Essay : Generating ideas; outlining; writing a thesis sentence; writing the essay: writing introductions, developing ideas, writing conclusions; revising and editing. 15 3. Grammar 25 a) Word order of sentences. b) Framing questions. c) Tenses, articles, subject-verb agreement, noun-pronoun agreement, verbs, phrasal verbs, conditionals, prepositions and prepositional phrases, infinitives, participles, gerunds. (Knowledge of grammar will be tested through contextualised passages). d) Punctuation. 4. Developing vocabulary : Using the dictionary, suffixes, prefixes, synonyms, antonyms, changing word forms (from verb to noun etc.) and using them in sentences. 10 5. Translation from Bengali to English. 15=5 6. Speaking skills : Speaking skills should be integrated with writing and reading in classroom activities. The English sound system; pronunciation skills; the IPA system; problem sounds, vowels, consonants and dipthongs; lexical and syntactic stress. (Writing dialogue and practising it orally students can develop their speaking skill. Dialogue writing can be an item in writing test.)