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Here are all the subjects you will be studying for the B Sc degree
in Mathematical Statistics. Remember that you have two sets of Electives.
You must choose one course from the first set and two courses from
the second set. The degree is only available as a complete degree program at the bachelors level. 1. Section 1 BUS/COM2 - Business Communication Part I: Writing Skills Language as skill of communication Phonetics Modifiers Sentence connectives The participle The gerund Punctuation and capitalization Vocabulary Use of abbreviations Correct usage Letter writing Part II: Communication Skills Verbal communication Oral presentation Technical written communication Forms pf technical writing Report writing Advertising Collection of short essays Collection of short stories BUS/INF1 - Computer Usage Evolution of the computer Computer fundamentals Concept of information and data processing Importance of software Basics of Word Processing Spreadsheet applications using Excel Microsoft Access Microsoft Power Point BUS/INF2 - Introduction to Computer Science Computer basics History generators and classification of computers Number systems Data representation Boolean algebra and logic circuits Memory unit Input/output Classification of programming languages Operating systems Basic operational concepts Numerical analysis Algorithms and flowcharts Programming languages Computer graphics Management information systems BUS/INF3 - Introduction to Computer Business Environment Introductory concepts Data processing Data structure file organization and maintenance Programming Operating systems E-commerce and Internet System analysis and design Computer based information systems Database Viewing and editing in dBase III Plus Printing reports and labels in dBase III Plus References CBR/BUS1 - Mathematics (Mathematics I, II & III) Part I: College Algebra Indices, logarithms and suds Ratio, proportion and variation Simultaneous linear equations and quadratic equations Arithmetic progression, geometric progression and harmonic progression Permutation and combination Binominal theorem Exponential series and logarithmic series Simple interest compound interest and annuity Partnership Stocks and shares' Determinants Vectors and matrices Set theory Rectangular Cartesian co-ordinates in a plane Equations of straight lines Circle Parabola Ellipse Hyperbola Part II: Differentiation Real numbers Functions and graphs Continuity and limit Differentiation Successive differentiation Tangents and normals Mean value theorem Mean value theorem Maxima and minima intermediate forms Partial differentiation Equality of repeated derivatives Concavity and points of inflection Curvature and evolutes asymptotes Singular points Curve tracing Envelopes Partial differentiation Equality of repeated derivatives Concavity and points of inflection Curvature and evolutes Asymptotes Singular points Curve tracing Envelopes Part III: Integration Table of standard results Methods of integration Integration of algebraic relational functions Integration of trigonometric functions Integration of irrational functions Definite integral as the limit of a sum Areas of plane regions Rectification Lengths of plane curves Volumes and surfaces of revolution Center of gravity Moment of inertia Differential equations of the first order and first degree Equations of first order but not of the first degree Trajectories of a family of curves Linear equations References CBR/STAT01 - Introduction to Statistics Classification and tabulation Measures of central value Measures of dispersion Skewness moments and Kurtosis Correlation analysis Regression analysis Association of attributes Index numbers Time series analysis Interpretation and extrapolation Log and antilog tables CBR/STAT02 - Introduction to Probability Probability theory random variables Some probability distribution functions Two-dimensional random variables Random processes Correlation functions Spectral density of random processes Linear systems with random inputs CBR/BUS2 - Introduction to Differential Equations Equations of the first order and of degree higher than one Linear equations of second and higher order Simultaneous equations Euler's homogeneous linear differential equations Method of variation of parameters Total differential equations Laplace transform Co-ordinate geometry The plane and the straight line The sphere Electives 1: Select one course from - FB/CBR2 - Mechanics, Heat and Waves Physical measurements Elasticity Surface tension Viscosity Gas laws and specific heats of gasses Conduction and thermal conductivity Propagation of light Photometry S H M and wave motion Sound Vectors Gravitation Hygrometry References BUS/INF4 - Programming Introduction to programming; Overview of C programming; Types, operators and expressions; Managing input and output operations; Control flow; Arrays; User defined functions; Structure and union; Pointers; File handling in C. BUS/PS02 - Business Psychology Principles, practices and problems; Techniques. Tools and tactics; Employee selection principles and techniques; Psychological testing; Performance appraisal; Training and development; Leadership, motivation and job satisfaction; Job organization; Working conditions; Safety, violence and health in the workplace; Stress in the workplace; Consumer psychology CBR/STAT20 - Discrete Mathematics Brief survey of discrete mathematics; Mathematical logic; Boolean algebra and logic circuits; Set theory; Matrices; Number theory; Relation; Functions; Posits and lattices; Combinations; Group theory; Rings and fields; Graph theory; Trees; Probability and automata. 2. Section 2 CBR/STAT03 - Sampling and Distributions Varying probability sampling Simple random sampling Estimation of the sample size Stratfield sampling Ratio estimators Regression estimators Systematic sampling Cluster sampling Varying probability sampling Two phase and repetitive sampling Two-stage sampling Non-sampling errors Bayesian approach for interference in finite populations The bootstrap method Small area estimations Imputation methods. CBR/STAT04 - Vector Analysis Multiplication of vectors by scalars and addition of vectors Geometry with vectors Geometry Scalar product Applications to metric geometry Vector product and scalar triple product Geometry with Cartesian co-ordinates Statics with vectors Vector valued functions of scalar variables Differential operators Integral transformation CBR/STAT05 - Mathematical Modeling The probability paradigm The binomial model and random variables Continuous random variables and the Gaussian model Statistics The Poisson model Modeling random signals References CBR/STAT06 - Probability and Inference I Probability Discrete distributions Continuous distributions Multivariate distributions The normal distribution relation between interference and probability applications of probability and interference CBR/STAT07 - Ordinary Differential Equations Elementary differential equations Equations of first order and first degree Trajectories Linear equations with constant coefficients Homogeneous linear equations and Cauchy-Euler equations Equations of the first order but not of the first degree and singular solutions Extraneous loci Ordinary simultaneous differential equations Number integration Picard's interactive methods Existence and uniqueness theorems Independence of solutions of linear differential equations Wronshian and its equations Exact differential equations and equations of special forms Linear equations of second order Simultaneous equations of the form dx/R = dy/Q=dz/R Total differential equations Riccati's equations Integration in series Series solutions of linear differential equations Legendre polynomials and functions Legendre functions of second kind Bessel functions Hermite polynomials Laguerre polynomials Hyper-geometric functions Partial differential equations' Linear partial differential equations of order one Non-linear partial differential equations with constant coefficients Partial differential equations of order two with available coefficients Monge's methods References CBR/STAT08 - Sequences and Series Sets and statements The real number Neighborhoods and limit points of a set Sequences Infinite series with positive terms Infinite series with positive and negative terms Real functions-limit and continuity functions Real functions - the derivative Reimann integrability CBR/STAT09 - Linear Algebra A system of vectors Matrices Elementary row operations An introduction to determinants Vector spaces Linear mappings Matrices from linear mappings Eigenvalues, Eigenvectors and diagonalization Euclidean spaces Quadratic forms 3. Section 3 CBR/STAT10 - Probability and Inference II Estimation Bayesian methods Tests of statistical hypotheses Theory of statistical inference Quality improvement through statistical methods CBR/STAT11 - Variance Analysis Introduction General theory for testing and confidence intervals One-way analysis of variance Multiple comparison methods Simple linear and polynomial regression the analysis of count data Basic experimental designs Analysis of covariance Factorial treatment structures Split plots, repeated measures, random effects and sub-sampling Multiple regression - matrix formation Unbalanced multifactor analysis of variance Confounding and fractional replication in 2n factorial systems Non-linear regression References CBR/STAT12 - Multivariable Analysis Vector and matrix algebra Groups, Jacobian of some transformations, functions and spaces Multivariable distributions and their functions Basic multivariable sampling distributions Tests of hypotheses of mean vectors Tests concerning covariance matrices and mean vectors Discriminant analysis Principal components Canonical correlations CBR/STAT13 - Time Series Analysis Introduction Simple descriptive techniques Fitting time-series models Fitting time-series models in the time domain Forecasting Stationary processes in the frequency domain Spectral analysis Invariance processes Linear systems State-space models and the Kalman filter Non-linear models Multivariate time-series modeling Some more advanced topics Examples and practical advice Electives 2: Select two courses from - CBR/STAT14 - Matrices Fundamental concepts Algebra of matrices Rank of a matrix Vector spaces of n-tupelos and their transformations Systems of linear equations Quadratic forms and congruence of matrices Quadratic forms in the real field Hermitian matrices and forms Orthogonal matrices - unitary matrices Characteristic roots and characteristic vectors of a matrix Orthogonal and unitary reductions of quadratic forms Similarity of matrices References CBR/STAT15 - Numerical Analysis Numerical methods Linear programming Transportation and assignment problems Flow charts and computer programs Program to find root of a polynomial using iterative method Program to find root of a polynomial using bisection method Program to find root of a polynomial using Newton-Raphson method Program to find root of a polynomial using Regula-Falsi method Solution of simultaneous linear equations using Gauss-Seidel method Solving the differential equations using Euler's method Solving the differential equations using Euler's modified method Solving the differential equations using Runge-Kutta II method Solving the differential equations using Runge-Kutta VI method Numerical integration using Simpson's and Trapezoidal rule Newton's forward interpolation formula Newton's backward interpolation formula Largrange's interpolation formula Problem for Gauss iteration Problem for Gauss-Jordan iteration Problem for Jacobi iteration CBR/STAT16 - Computational Mathematics Discrete time-space models Steady state discrete models Poisson equation models Non-linear 3D models Epidemics, images and money High performance computing Message passing interface Classical methods for Ax = d Krylov methods for Ax = d CBR/STAT18 - Probability for Scientific and Engineering Data analysis Probability theory Discrete random variables and their distribution functions Continuous random variables and their distribution functions Multivariable probability distributions Sampling distribution theory Point and interval estimation Inferences about population means Inferences about population proportions Linear regression and correlation Multiple linear regression Single-factor experiments - analysis of variance Design and analysis of multifactor experiments Statistical quality control CBR/STAT19 - Scientific Computing Scientific computing Systems of linear equations Linear squares Eigen-value problems Non-linear equations Optimization Interpolation Numerical integration and differentiation Initial value problems for ODE's Boundary value problems for ODE's Partial differential equations Fast Fourier transform Random numbers and simulation |
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