# BSc. Statistics (Regular)

The programme provides instruction in statistical theory and methods, and their application to the collection, collation, presentation, analysis and dissemination of data. It is designed to provide practical training and to enhance the knowledge and skills of a statistician. In addition, the course seeks to meet the need of those who have developed an interest in the subject from several years of relevant working experience and who are desirous of acquiring further knowledge in the field. More specially, the programme seeks to equip students with the knowledge and skills to perform professional duties as statisticians, and to work more effectively with other specialists on statistical activities and programmes such as censuses, surveys, quality control and other statistically related projects and activities. The programme emphasizes the acquisition of practical and problem solving skills to enable students to relate what they learn to what is done in practice so as to enable them to ply more meaningful roles in solving current developmental problems at local, national and international levels.

**Content of Courses for each Semester**

**Year 1 Semester 1**

**MATH 171: Calculus I (3, 0, 3)**

Real Numbers; Ordering Real Numbers, Absolute value and distance, Algebraic Expressions Exponents(Indices), Radicals(Surds) Logarithms, and Complex Numbers: Algebra of complex Numbers, Exponents of i. **Functions:** Definition and Types. Basic Types; Polynomials, Rational, Exponential and Trigonometry. Properties of Functions; Zeros, Even and Odd, Periodicity, Inverse and Fixed Points. Sequence and Finite Series. The Binomial Theorem: Positive integer exponents, Integer and Rational exponents. **Limits of functions**. Differentiation of Functions. Integration of Polynomials, Trigonometric (cosine and sine only) and Exponential. Applications of Derivatives: Maxima and Minima, Linear approximations and Related rates

**MATH 173: Logic and Set Theory (3, 0, 3)**

**Introduction to number systems and logic: **Overview of the natural numbers, integers, real numbers, rational and irrational numbers, algebraic and transcendental numbers. Brief discussion of complex numbers; statement of the Fundamental Theorem of Algebra. Ideas of axiomatic systems and proof within mathematics; the need for proof; the role of counter- examples in mathematics. Elementary logic; implication and negation; examples of negation of compound statements. Proof by contradiction. **Sets, relations and functions: **Union, intersection and equality of sets. Indicator (characteristic) functions; their use in establishing set identities. Functions; injections, surjections and bijections. Relations, and equivalence relations. Counting the combinations or permutations of a set. The Inclusion-Exclusion Principle. **The integers: **The natural numbers: mathematical induction and the well-ordering principle. Examples, including the Binomial Theorem. **Elementary number theory: **Prime numbers: existence and uniqueness of prime factorisation into primes; highest common factors and least common multiples. Euclid’s proof of the infinity of primes. Euclid’s algorithm. Solution in integers of ax+by = c. Modular arithmetic (congruences). Units modulo n. Chinese Remainder Theorem. Wilson’s Theorem; the Fermat-Euler Theorem. Public key cryptography and the RSA algorithm. **The real numbers: **Least upper bounds; simple examples. Least upper bound axiom. Sequences and series; convergence of bounded monotonic sequences. Irrationality, Decimal expansions. Construction of a transcendental number. **Countability and Uncountability: **Definitions of finite, infinite, countable and uncountable sets. A countable union of countable sets is countable. Uncountability of R. Non-existence of a bijection from a set to its power set. Indirect proof of existence of transcendental numbers.

**MATH 175: Vectors and Mechanics (3, 0, 3)**

Vectors in Euclidean Spaces, especially in dimensions 1,2 and 3. Position Vector. Dot (Scalar) Product, Cross (Vector) Product of Vectors. Composition and Resolution of Vectors. Application of Vectors to Geometry: Vector equations of lines and planes. Vector-valued functions Differentiation of vector-valued functions. Application of vectors to Mechanics: Kinematics, Statics and Dynamics in euclidean space.

**MATH 177: Computing for Mathematics I (2, 1, 3)**

General overview of the principles of Computing; Data & Programs or Algorithms. The role of Algorithms, the origins of computing machines and its social repercussions. Data storage (bits and their storage). Main memory and mass storage. Representation of information as bit patterns. The binary system- (storing of integers and fractions). Data manipulation, Computer architecture, machine language and program execution. Operating Systems: The history of Operating Systems, its architecture, coordinating the Machine’s Activities and Handling competition among processes. Algorithms -The concept of an algorithm (representation, discovery, iterative and recursive structures). The efficiency and correctness of algorithms. Introduction to Data Abstractions: Basic data structures, related concepts and implementation of some Data structures. Computer Graphics Overview and modeling, spreadsheets.

**BIO 155: Biology for Mathematics (2, 0, 2)**

Cell structure, Basic Physiology and Anatomy

**CHEM 155: Physical Chemistry (2, 0, 2)**

Introduction to Physical chemistry: Definition, Structure of Science, Classifications; The Scientific Method: Laws, Hypotheses, Theories and Models. States of Matter I: Classification; Structure and Properties of matter; Types of systems; State variables and Equations of state. Thermodynamics I: The First Law, Heat Capacity, Enthalpy and Thermo-chemistry. Chemical Kinetics I: Elementary Chemical Kinetics, Basic Laws, Effect of Temperature and the Arrhenius equation.

**ECONS 151: Elements of Economics I (2, 0, 2)**

The purpose of this course is to introduce students without prior knowledge of Economics to the fundamental concepts and the use of analytical techniques which will be helpful in the study of economic problems. It is also intended to provide students not intending to specialize in the subject with knowledge of principles which can be in related disciplines. The course covers the nature and scope of economics, consumer choice, determination of prices in different market conditions, Production Theory and Theory of Distribution.

**ENGL 157: Communication Skills l (2, 0, 2)**

Oral and written Communication skills ability to express ideas in good English. Correction of common deficiencies in English grammar. Comprehension and critical reading skills.

**PHY 153: Electromagnetism (2, 0, 2)**

*Electrostatics*: Currents and the conservation of charge. Lorentz force law and Maxwell’s equations. Gauss’s law. Application to spherically symmetric and cylindrically symmetric charge distributions. Point, line and surface charges. Electrostatic potentials; general charge distributions, dipoles. Electrostatic energy. Conductors. *Magnetostatics*: Magnetic fields due to steady currents. Ampere’s law. Simple examples. Vector potentials and the BiotSavart law for general current distributions. Magnetic dipoles. Lorentz force on current distributions and force between current-carrying wires. *Electrodynamics:* Faraday’s law of induction for fixed and moving circuits. Ohm’s law. Plane electromagnetic waves in vacuum, polarization. Electromagnetic energy and Poynting vector. *Electromagnetism and relativity*: Review of special relativity; tensors and index notation. Charge conservation. 4-vector potential, gauge transformations. Electromagnetic tensor. Lorentz transformations of electric and magnetic fields.* *Maxwell’s equations in relativistic form. Lorentz force law.

**Year 1 Semester 2**

**MATH 172: Calculus II (3, 0, 3)**

Integration: Indefinite Integral and Definite Integral. Application of Integration to Areas and Volumes. Integration by Substitution, Integration by Parts, Integration by Resolution to Partial Fractions. Approximate Integration. Co-ordinate Geometry: Equations of Lines and Circles, Conic Sections, Parabola, Ellipse and Hyperbola. Parametric Representation of Curves.

**MATH 174: Discrete Mathematics (3, 0, 3)**

Multinomial coefficients. Complex Numbers. Demoivre’s Theorem. Finite Difference Equations. The Z-transform approach to solution. Duality, Consistency. Difference Equations with Characteristics Polynomials, which have complex roots. Boolean Algebra. Basic Boolean Functions. Digital Logic Gates Minterm and Maxterm Expansions. Elements of proof Theory. Relations in a Set. Partial Ordering. Zorn’s Lemma.

**MATH 176: Linear Algebra I (3, 0, 3)**

Matrices and Determinants. Systems of Linear Equations. Vector Spaces and Subspaces, Basis Dimension and Co-ordinates. Algebra of Linear Transformations and Representation by Matrices. Eigenvalues and Eigen-vectors; Similar Matrices, Change of Basis. Cayley-Hamilton Theorem.

**ENGL 178: Computing for Mathematics II (3, 0, 3)**

*Advanced spreadsheet functions:* Conditional and Logical functions, Counting and Totalling cells conditionally, And, Or, Not, and Lookup functions. *Views, scenarios, goal seek, solver*: Goal seeking and solving, Advanced solver features, Scenarios, and Views. *Using spreadsheet to manage lists*: Excel lists, Listing terminologies, Sorting data, Subtotals, Filtering a list, Advanced filtering, Criteria tips, Multiple criteria, Calculated criteria, Data consolidation, Pivottables, Modifying a pivottables, Managing pivottables, Formating a pivottable, Banding, and Slicers. *Charts*:* *Introduction to charting, Creating charts, Formating charts, Changing the chart layout, and Sparklines. *Templates*: Introduction to templates, and Create custom templates. *Drawing and formatting*: Inserting, Formating, and Deleting Objects. *Excel *tools: Reviewing, Auditing, and Proofing tools.

**STAT 166: Probability and Statistics (3, 0, 3)**

General introduction, including the uses and applications of statistics, types of data and their collection methods, stages of statistical investigation; Descriptive analysis of data including exploratory data analysis; Introductory study of probability theory: Sets and sample space, random experiments and outcomes, measure of probability of events, mutually exclusive and independent events, conditional probability and Bayes‘ theorem, Some basic rules/theorems of probability; Counting techniques and application to problems; Random variables and probability distributions; moments

**ECONS 152: Elements of Economics II (2, 0, 2)**

A survey of national income- its measurement and determinants, fluctuations in economic activity and trends in Ghana’s national income, index number, international trade and national economy, the role of Government.

**ENGL 158: Communication Skills II (3, 0, 3)**

Communication skills oral presentation, formal speech making, conducting Interviews and meetings. Communication process, skill in communication, channels in communication in an organisation, preparation of official documents such as letters memos, reports minutes and proposals.

**Year 2 Semester 1**

**MATH 265: Mathematical Methods I (3, 0, 3)**

Partial differentiation of function of several variables. Differentiation of implicit functions, theorem and applications. Jacobians. Differentiation of a vector function of several Variables. Total Differential, Tangent Plane to Surface. The tangent vector. Curvilinear Co-ordinates. Plane polar, cylindrical and spherical Co-ordinates. Multiple integrals. Line integrals, multiple surface and volume integral. Gradient, divergence and curl. The Theorems of Green, Gauss, and Stokes.

**MATH 267: Abstract Algebra I (3, 0, 3)**

**Groups: **The Integers modand symmetries. Definitions and Examples. Subgroups. Centre of a Group. **Cyclic Groups: **Definitions, Cyclic Subgroups. Generators and Relations. The method of Repeated Squares. Cauchy Theorem.**Permutation Groups: **Definitions and Notations. Dihedral Groups. **Cosets and Lagrange’s Theorem: **Cosets. Lagrange’s Theorem. Fermat’s and Euler’s Theorem. **Isomorphisms: **Definitions and Examples. Direct Products. **Homomorphisms and Factor Groups:**Factor Groups and Normal Subgroups. Group Homomorphisms. The Isomorphism Theorems. **Matrix Groups and Symmetry: **Matrix Groups. Symmetry. **The Structure of Groups: **Finite Abelian Groups. Solvable Groups. **Group Actions: **Groups Acting on Sets. The Class Equation. Burnside’s Counting Theorem. **TheSylow’s Theorems: **The Sylow Theorems. Examples and Applications. **Applications of Groups: **Privative Key Cryptography. Public Key Cryptography. Algebraic Coding Theory: Error- Detecting and Correcting Codes, Linear Codes, Parity-Check and Generator Matrices and Efficient Decoding.

**MATH 277: Real Analysis I (3, 0, 3)**

*Limits and convergence: *Sequences and series in R and C. Sums, products and quotients. Absolute convergence; absolute convergence implies convergence. The Bolzano-Weierstrass theorem and applications (the General Principle of Convergence). Comparison and ratio tests, alternating series test. *Continuity: *Continuity of real- and complex-valued functions defined on subsets of R and C. The intermediate value theorem. A continuous function on a closed bounded interval is bounded and attains its bounds. *Differentiability: *Differentiability of functions from R to R. Derivative of sums and products. The chain rule. Derivative of the inverse function. Rolle’s theorem; the mean value theorem. One-dimensional version of the inverse function theorem. Taylor’s theorem from R to R; Lagrange’s form of the remainder. Complex differentiation. *Power series: *Complex power series and radius of convergence. Exponential, trigonometric and hyperbolic functions, and relations between them. Direct proof of the differentiability of a power series within its circle of convergence. *Integration: *Definition and basic properties of the Riemann integral. A non-integrable function. Integrability of monotonic functions. Integrability of piecewise-continuous functions. The fundamental theorem of calculus. Differentiation of indefinite integrals. Integration by parts. The integral form of the remainder in Taylor’s theorem. Improper integrals.

**MATH 275: Linear Algebra II (3, 0, 3)**

Annihilating polynomials. Linear functionals, dual spaces, multilinear forms. Determinant by multilinear form, uniqueness properties. Inner product spaces. Orthogonalization process. Best approximation. Adjoints, and Hermitian unitary and normal transformations. Hermitian, bilinear and quadratic forms, reduction to a canonical form.

**MATH 279: Mathematical Programming (2,1,3)**

Quick review of Computer Organization; Arithmetic of the Computer: Floating - Point Format, Representation and Operations in the Computer; Algorithmic Design and Development; Introduction to Computer Programming Techniques: Coding in a High Level Language using MATLAB and if possible one symbolic mathematical application like MATHEMATICA, MAPLE, DERIVE or any other package designed for scientific computing.

**STAT 265: Probability Distributions (3, 0, 3)**

Review of probability spaces and measure, properties and concept of random variables and probability distributions; Some useful discrete and continuous probability distribution functions, moment-generating functions, probability generating function, characteristics functions and limit theorems; Joint probability distributions; Random walks and Poisson processes; Basic concepts of statistical inference, introduction to sampling techniques and sampling distributions of sample means, proportions and variances.

**ENGL 263 Literature in English I (1, 1, 1)**

Literature as Poetry: What is a poem, and its characteristics? Difference between a poem and song. The figure of speech and the literary device. Practical Appreciation. Texts to be studied: selected African and English poems. Literature as Drama: What is a play, and its characteristics: Drama and theatre. Shakespeare. The Modern Play. Texts to be studied: One Shakespeare play and one modern African Play.

**Year 2 Semester 2**

**STAT 268: Abstract Algebra II (3, 0, 3)**

**Rings: **Rings. Integral Domains and Fields. Ring Homomorphisms and Ideals. Maximal and Prime Ideals. **Polynomials: **Polynomial Rings. The Division Algorithm. Irreducible Polynomials. **Integral Domains: **Fields of Fractions. Factorization in Integral Domains. **Lattices: **Lattices. Boolean Algebra. **Applications of Ring: **An application to software Design. The Algebra of Electric Circuit.

**MATH 278: Real Analysis II (3, 0, 3)**

**Uniform convergence: **The general principle of uniform convergence. A uniform limit of continuous functions is continuous.** **Uniform convergence and term-wise integration and differentiation of series of real-valued functions.** **Local uniform convergence of power series.

**Uniform continuity and integration:*** *Continuous functions on closed bounded intervals are uniformly continuous. Review of basic facts on* *Riemann integration (from Analysis I). Informal discussion of integration of complex-valued and R^{n}-valued functions of one variable; *R ^{n} as a normed space, d*efinition of a normed space. Examples, including the Euclidean norm on

*R*

^{n}and the uniform norm on C[a, b]. Lipschitz mappings and Lipschitz equivalence of norms. The Bolzano-Weierstrass theorem in R

^{n}.

**Differentiation from R**Definition of derivative as a linear map; elementary properties, the chain rule. Partial derivatives; continuous partial derivatives imply differentiability. Higher-order derivatives; symmetry of mixed partial derivatives (assumed continuous). Taylor’s theorem. The mean value inequality. Path-connectedness for subsets of R

^{m}to R^{n}:^{n}; a function having zero derivatives on a path-connected open subset is constant.

**Metric spaces:**Definition and examples. Metrics used in Geometry, Limits, continuity, balls, neighbourhoods, open and closed sets.

**The Contraction Mapping Theorem:**The contraction mapping theorem. Applications including the inverse function theorem (proof of continuity of inverse function, statement of differentiability). Picard’s solution of differential equations.

**MATH 266: Mathematical Methods II (3, 0, 3)**

Improper Integrals. Integrals depending on a Parameter. Differentiation and Integration under the Integral Sign. Gamma and Beta Functions; Stirling’s Formula. Basic Properties and use of the Laplace Transform. Fourier Series. Fourier Transforms.

**MATH 276: Numerical Analysis I (2, 1, 3)**

**Mathematical Preliminaries and Error Analysis:*** *Round-off Errors and Computer Arithmetic, Algorithms and Convergence. **Solutions of Equations in One Variable***: *The Bisection Method, Fixed-Point Iteration, Newton’s Method and Its Extensions, Error Analysis for Iterative Methods, Accelerating Convergence, Zeros of Polynomials and Müller’s Method. **Methods for solving Systems of Equations:*** *Linear Systems equations by Direct Methods, Pivoting Strategies, Matrix Inversion and Determinant of a Matrix, Matrix Factorization, Special Types of Matrices(symmetric, positive definite, diagonal matrices, diagonally dominant), Iterative methods (Jacobi, Gauss-Seidal), Relaxation Techniques for Solving Linear Systems. **Interpolation and Polynomial Approximation: **Interpolation and the Lagrange Polynomial, Data Approximation and Neville’s Method, Divided Differences, Hermite Interpolation, Cubic Spline Interpolation, Parametric Curves. **Numerical Differentiation and Integration:*** *Numerical Differentiation, Richardson’s Extrapolation, Elements of Numerical Integration, Composite Numerical Integration, Romberg Integration, Adaptive Quadrature Methods, Gaussian Quadrature, Multiple Integrals, Improper Integrals

**STAT 266: Statistical Inference (3, 0, 3)**

Estimation: Point and interval estimation of parameters (mean, proportion and variance), properties of point estimators, methods of point and interval estimation; Hypothesis Testing: Basic concepts, significance tests for parameters including analysis of variance (ANOVA); Non-parametric tests (Chi-square tests, tests for independent and paired samples); Type I and II errors and power function, Neyman-Pearson Lemma and likelihood ratio test for most powerful critical region.

**MATH 286: Differential Equations I (3, 0, 3)**

Introduction: Methods of deriving Differential Equations. Ordinary Differential Equations of first order. Separable, Homogeneous, Linear, Exact, Integrating factors and methods of isoclines. Linear differential equations of the second order with constant coefficients. Systems of first order equations. Solution of ordinary equations of first order Using methods of variation of parameters. Reduction of nth order equation to a system of first order equations

**ENGL 264: Literature in English II (1, 1, 1)**

Literature as Poetry: What is a poem, and its characteristics? Difference between a poem and song. The figure of speech and the literary device. Practical Appreciation. Texts to be studied: selected African and English poems. Literature as Drama: What is a play, and its characteristics: Drama and theatre. Shakespeare. The Modern Play.

**Year 3 Semester 1**

**MATH 365: Differential Equations II (3, 1, 3)**

Existence and uniqueness of solution of differential equations. Solution of certain linear differential equations of second order in series (for example, Legendre’s equation and Bessel’s equation). Special functions (recurrence relations); Legendre polynomials, Bessel functions, Hermite and Chebychev polynomials, Laguerre and Hypergeometric functions

**MATH 379 NUMERICAL ANALYSIS II (2, 1, 3)**

*Numerical Solutions of Nonlinear Systems of Equations: *Fixed Points for Functions of Several Variables, Newton’s Method, Quasi-Newton Methods, Steepest Descent Techniques, Homotopy and Continuation Methods, The Conjugate Gradient Method. *Initial-Value Problems for Ordinary Differential Equations: *Euler’s Method, Higher-Order Taylor Methods, Runge-Kutta Methods, Error Control and the Runge-Kutta-Fehlberg Method, Multistep Methods, Variable Step-Size Multistep Methods, Extrapolation Methods, Higher-Order Equations and Systems of Differential Equations, Stability, Stiff Differential Equations

**STAT 361: Statistical Computing and Data Analysis I (2, 2, 3)**

The topics includes: Database management and use of statistical packages; Graphical techniques; importing graphics into word-processing documents (e.g, LaTeX); Microsoft Excel, Access and Power Point; Data analysis and automating tasks in spreadsheet using macros; Programming in Visual Basic for Applications(VBA), Report development in spreadsheet; Simulation and sampling.

**STAT 363: Demographic Statistics (3,1, 3)**

Scope, uses and sources of demographic and socio-economic data; methods of enumeration; demographic concepts and measures; current and cohort methods of description and analysis; rates and ratios; standardization; construction of life tables. Measurement of fertility, mortality and nuptiality. Determinants of age structure and the intrinsic growth rate. Survey data; interpretation of demographic statistics, tests of consistency and reliability. Population projection, and discuss their effects upon education and manpower planning; Use of microcomputer to interpret demographic data.

**STAT 365: Sample Survey Theory and Methods I (3,1, 3)**

Introduction: Uses, scope and advantages of sample survey, types of surveys, and organization and management of surveys; Basic concepts of sampling: Types of sampling designs (probability and non-probability sampling); sampling unit, sampling size and sampling frame, errors in surveys, and bias arising from non-response; Data collection methods; History of censuses in Ghana, organization of censuses and sample surveys – stages in the planning and execution of censuses and surveys, scope and cost of census and survey, construction of questionnaire, pre-testing of questionnaire and pilot surveys, field operations, coding of collected data, processing of data, control tabulations, etc.; Evaluation of census data (post enumeration surveys); Non-probability sampling methods; Simple random sampling: estimation of population means, proportions and totals; properties of estimates; determination of sample size.

**STAT 367: Introduction to Regression Analysis (3,1, 3)**

Basic concepts of regression and correlation analysis; Correlation coefficient and scatter diagram; Estimation of parameters of simple and multiple regression models by the least squares method, inferential analyses on regression parameters; Use of qualitative variables; Residual analysis for testing model assumptions and adequacy; Correlation analysis of response and predictor variables, concept of multicolinearity; Use of statistical packages for regression and correlation analyses (SPSS, R, Strata, SAS, Excel, etc.).

**STAT 369: Stochastic Processes I (3,1, 3)**

Definitions and context for the theory of stochastic processes; Random walks with and without reflecting/absorbing barriers. Markov Chains: definition, the transition matrix, continue-time chain, and the Chapman-Kolmogorov equations; Classification of states; The existence and uniqueness of a stationary distribution; Applications, in particular to Bonus-Malus Systems, simulation of Markov chains; Properties of some standard probability distributions (introduction to Poisson Processes); The Theory of Recurrent Events; Poisson Processes, Markov Processes; Renewal Processes.

**Year 3 Semester 2**

**STAT 362: Statistical Computing and Data Analysis II (2,2, 3)**

Application of statistical packages (e.g. SPSS, R, Strata, SAS, Splus, Strata, Minitab, Genstat, Excel, etc.) in statistical data analysis. This will include statistical reporting using software packages for statistical computations, numerical and graphical summaries; confidence intervals, parametric and non-parametric tests; regression and time series analyses; Analyzing data from comparative studies.

**MATH 366: Partial Differential Equations (2,2, 3)**

Definition of a Partial Differential Equations (PDE). Equations of the First Order, Cauchy Problem, Characteristics, Method of Lagrange, Classification of Second Order Equations. Laplace and Poisson Equations, Boundary Value Problems, the Sturm-Liouville Problem, Separation of Variables, Fundamental Solution of Potentials and their Properties, Harmonic Functions, Green’s Function, Uniqueness Theorems. The Wave and Heat Equations, Methods of Eigen Functions, Expansions.

**STAT 364: Non-Parametric Statistics (3,1, 3)**

Non-parametric statistics is about estimation and hypothesis testing when the form of the underlying distribution is unknown. The topics include: General nature of nonparametric tests: comparisons with classical parametric methods, emphasis on assumptions and interpretation, ranks and runs; Goodness of fit tests analysis contingency table for measures of association; Tests for randomness; *-sample tests: Tests of randomness, Kolmogorov-Smirnov test, Wilcoxon's rank sum, Kruskal-Wallis, Friedman tests, Sign, Wilcoxon Signed-rank, Kendall's **Spearman's rank correlation coefficient tests; Confidence intervals based on ranks; Efficiency of nonparametric procedures and robustness considerations.*

**STAT 366: Sample Survey Theory and Methods II (3,1, 3)**

Random sample designs: The definitions, notations and description of selection with stratified sampling, systematic sampling, cluster sampling, multi-stage sampling, and probability proportional to size (pps); Properties estimates of population means, proportions and totals; determination of sample size; Ratio and regression estimation; Criteria for choosing sampling designs; Variance estimation with complex sample designs: Taylor series method, repeated replications, jackknife repeated replications, use of appropriate software to calculate standard errors; Students would be required to conduct surveys on some socio-economic issues using sample designs and submit reports for assessment.

**STAT 368: Time Series Analysis I (3,1, 3)**

Topics will include the following: Basic concepts of time series modelling; Descriptive techniques for time series; Stationary time series, removal of trend and seasonal differences, moments and autocorrelation; Index Numbers: Uses and types of price indexes; Simple autoregressive and moving average models, moments and autocorrelations, the conditions of stationarity and invertibility; Mixed (ARMA) models and the AR representation of MA and ARMA models; Fitting and testing time series models; Forecasting, methods of forecasting, scientific forecasting, basic forecasting models, forecasting criteria; Model building and identification.

**STAT 370: Stochastic Processes II (3,1, 3)**

Martingales and martingales convergence theorem; Brownian motion: distributional results, reflection principle, stopping times and hitting times, diffusion processes; Conditional Expectation: precise definition, properties of the conditional expectation operator, deriving results using the conditional expectation; Stochastic differential equations and the Radon-Nikodym Theorem. Branching Processes: generating functions, definitions, extinction probabilities, martingales recuperated from branching processes and intro to more complicated examples.

**Year 4 Semester 1**

**STAT 461: Project Report Writing (1,2, 2)**

The topics include the following: Principles of conducting research; Types of approaches to research: Qualitative and quantitative; Selecting research topic; Research proposal; Literature search; Methods of data collection; Analysis of research data; Writing and presentation of research report. After this, students will be given research topics from various areas in Statistics to write on and submit reports as their project works.

**STAT 463: Introduction to Measure and Probability Theory (3,1, 3)**

Measure and integration: Measurable functions, measures, measure space; integration, monotone convergence theorem, Fatou's lemma; convergence theorems; Radon Nikodym theorem; Lebesgue decomposition; Probability Theory: Probability as a measure; probability space; random variables; distribution functions and characteristic functions. Sums of random variables, independence. Modes of convergence of sequences of random variables. Borel-Canteli lemmas and the zero-one laws, laws of large numbers and central limit theorem.

**STAT 465: Survival Analysis (3,1, 3)**

Topics include Types of survival data; survivor and hazard functions; censoring; estimating the survivor and hazard functions; comparing survivor functions using non-parametric tests; parametric models for the hazard function; Cox proportional hazards regression models.

**STAT 467: Design and Analysis of Experiments I (3,1, 3)**

The nature of experimental investigation: experimental objective, statistical objectives of design – elimination of sources of bias and random errors; Principles experimentation: randomization, replication and blocking, covariates, orthogonality, balance, logical control or error, sequential design; Elementary concepts of design of experiments: factors, factor levels plots, treatments, single factor and multiple factor experiments, fixed, rand and mixed effects models; Completely randomized design: Randomization process, the model and its specification, estimation effects, partitioning of the total sum of squares, expected mean squares, analysis of variance and its underlying assumptions, test of treatment effects, methods of multiple comparisons; Randomized block design: situations for its use, compare and contrast with completely randomized design, the model and its specification, estimation effects of additivity and interaction, partitioning of total sum of squares, analysis of variance and its test of treatment and block effects, Turkey’s test of additivity, treatment of missing observation.

**STAT 469: Operations Research I (3,1, 3)**

Basic concepts and historical background of operations research (OR); Decision Theory: techniques of decision theory, for example, minimax/maximin criterion, minimax regret criterion, decision trees, expected values, etc.; Linear programming (LP) as resource allocation tool: Formulation of LP problems, solution methods of LP models, duality theory and economic interpretations, post optimality (sensitivity) analysis of LP model; Application transportation and assignment problems; Integer programming methods; Unconstrained and constrained optimisation problems and methods of solution.

**STAT 471: Applied Time Series Analysis (3,1, 3)**

Probability models for time series, stationary processes, the autocorrelation function; pure random process, MA and AR processes; mixed models, integrated models; the general linear process, continuous processes. Model identification and estimation, estimating the auto covariance and autocorrelation functions; fitting AR and MA processes; estimating the parameters of mixed and integrated models; the Box-Jenkins seasonal model; residual analysis. Forecasting, univariate and multivariate procedure; prediction theory. Spectral theory, the spectral density function; Fourier analysis and harmonic decompositions; periodogram analysis; spectral analysis, effects of linear filters; estimation of spectra; confidence intervals for the spectrum. Use of statistical packages for graphical and numerical analysis

**STAT 473: Further Topics in Regression Analysis (3, 1, 3)**

Analysis of the general linear regression model: homoscedasticity and heteroscedasticity assumption concepts, detection and effects of multicollinearity, residual analysis model selection and validation, stepwise variable selection procedures, use of dummy variable and transformations; Non-linear regression models (logistic, poisson regression, ridge, etc. regression models), the use of indicator variables, odds ratio analysis of binary data, measurement of association in two-way tables; Applications involve the use of a statistical software package, like SPSS, R, SAS, or STATA for data analysis.

**STAT 475: Mathematics of Finance (3,1, 3)**

Topics to be covered include: Rates of interest and discount including nominal and effective interest rates; Simple and compound interests; Present and future values of stream of cash flows; Annuities and perpetuities; Amortization of loans and sinking funds; Break-Even Analysis; Investment appraisal techniques: payback technique, accounting rate of return, net present value (NPV), internal rate of return (IRR), and discounted-payback period (DPP); Determination of yields on investment funds: money-weighted rate of return and time –weighted rate of return; Introduction to the operation of certain financial securities such as forwards contracts, *futures* contracts, stocks, treasury bills and fixed deposits, bonds, options, hedging; Capital rating, Stochastic interest rate models; Index Numbers.

**ACTS 475: Loss Models I (3,1, 3)**

Principles of general insurance, economics of insurance; Models for loss severity, Insurance claim number models: the Poisson distribution, the negative binomial distribution; parametric models, effect of policy modifications and tail behaviour. Aggregate claims model, Panjer recursion model, (a,b,0), (a,b,1) and mixed Poisson models; Models for future claim amounts for claims that have occurred but are not settled. Estimation of premiums using both claims experience and general information, credibility theory, limited fluctuation, greatest accuracy credibility theory and empirical Bayes method.

**MATH 473: Mathematical Economics I (3,1, 3)**

Theory of Consumer Behavior: Constrained Optimizing Behaviour. The Slutsky Equation, Construction of Utility Number. Theory of the Firm: Constrained Optimizing Behaviour, Constant Elasticity of Substitution (CES), and Production Function. Market Equilibrium with Lagged Adjustment and Continuous Adjustment. Multi Market Equilibrium. Pareto Optimality. Linear Models. Input-Output (I-O) models, Concepts of Linear Programming and Applications.

**MGT 471: Principles of Management I (3,0, 3)**

It covers nature and scope of management, managerial functions, organizational theories, and goals of business organizations–economic and social responsibilities of management, decision making techniques and influence, the nature and types of organization and their implications for organizational administration.

**Year 4 Semester 2**

**STAT 462: Project Report (0,2, 2)**

Students will continue to work on their project works assigned to them in the first semester and submit their final research reports for assessment in a defense.

**STAT 464: Introduction to Bayesian Statistics (3,1, 3)**

Topics include: Problems associated and connections the with classical approach; Prior and posterior distributions; Specification of prior distribution; Bayesian point and interval estimation, properties of Bayes' estimators; Bayesian testing procedures; Examples of situations where Bayesian and classical approaches give equivalent or nearly equivalent results; Bayesian computation and Markov Chain Monte Carl Gibbs Sampling; Modern Bayesian methods.

**STAT 466: Multivariate Analysis (3,1, 3)**

Introduction to analysis of multivariate data with examples from various fields such as economics, education, social and physical sciences, and health care; Topics include examples of multivariate data; Mean vectors and covariance matrices, correlation matrix; Multivariate normal distribution; Sampling from a multivariate normal distribution: Wishart and Hotelling’s T^{2} distribution and their properties; Inference about the mean vector; Multivariate regression, multivariate analysis of variance (MANOVA); Principal components analysis; Factor analysis; Discriminant analysis and classification; Canonical correlation analysis; Cluster analysis; Use statistical computer packages for multivariate data.

**STAT 468: Design and Analysis of Experiments II (3,1, 3)**

Factorial experiments and designs: basic definitions and principles, 2^{2} and 2^{3} designs, calculation and interpretation of effects and interactions, Yate’s algorithm for the 2^{k} design; Latin square design: situations of its use, model and its specification, randomization, analysis of variance test and its test of treatment effect, treatment of missing observations; Incomplete block design, optimality criteria; Crossed and nested block structures; Confounding: reasons for confounding, complete confounding test of treatment effects, rules of confounding in 2^{p }blocks; Analysis of Covariance: concomitant variables, the covariance model and its underlying assumptions, estimation and comparison of treatment effects, adjusted treatment means, analysis of covariance table hypothesis testing: Use of statistical computer packages for data analysis and interpretation.

**STAT 470: Operations Research II (3,1, 3)**

Network Analysis: Basic definitions, minimal spanning tree, travelling salesman, maximal flow problems, project management control techniques (CPM and PERT); Inventory Control: basic definitions, inventory costs, inventory models; Queuing Theory: definitions and classes of queues, simple queue model and its characteristics, applications to various situations; Markov Process: definition, transition matrix and its formation, equilibrium or long run situations to markov process; Simulation as an operation research tool; Non-linear optimisation techniques; Methods of forecasting.

**STAT 472: Statistical Quality Control (3,1, 3)**

Topics covered are: Historical background of statistical quality control; Concepts of quality management including quality improvement philosophies, total quality management (TQM), and quality tools; Statistical process control: control charts for variables and attributes; Process characterization and capability analysis, CUSUM and EWMA, short production runs; Acceptance sampling by attributes and variables: definition of terminologies, sampling plans, operating characteristic and average outgoing curves, effects of lot size, tolerance interval; Role of design of experiments in quality improvement; Iinternational quality standards.

**STAT 474: Topics in Biostatistics (3,1, 3)**

Topics covered are Measures of disease frequency and risk, and alternative sources of epidemiological data; Cross-section, cohort, case-control and intervention studies; Experimental versus observational data; Issues of causation, randomization, placebos Interpretation of epidemiological studies; Preventive strategies, measures of public health impact and screening; Validity, measurement of response, sample size determination, matching and random allocation methods; Design and analysis of randomized clinical trials, group sequential designs and crossover trials; Survival studies; Diagnosis testing; statistical analysis of the medical process; Image analysis of PET and MRI scans; A computing tutorial will be used to introduce a statistical package like Stata, R or SAS.

**STAT 476: Actuarial Statistics II (3, 1, 3)**

Topics include: Brief of theory of interest; Force of mortality and life tables; Life annuities, assurances and premiums, reserves; Insurance policies with expenses and bonuses introduced, Gross Premiums and Gross Premium Reserves of insurance policies; Joint life and last survivor statuses, multiple decrement tables, expenses, individual and collective risk theory; Population projections;

**STAT 478: Financial Accounting (3,1, 3)**

Topics to be covered include: Profit and loss account or income statement, balance sheet and cash flow statement; Journal, ledger and book keeping principles; Preparation of financial statement for sole trader and partnership businesses and that for limited liability companies, basic cash flow statement for limited liability companies; Application of accounting standards and case studies.

**MATH 474: Mathematical Economics II (3,1, 3)**

Macro-economic theory is treated with a Mathematical approach in the following areas: Simple model of Income Determination, Consumption and Investment, the Investment Savings (IS) Curve. Monetary Equilibrium, the Liquidity Preference/ Money Profit (LM) Curve. Labour Wages and Price (Inflation) models. Full employment equilibrium models of Income Determination. Aggregate demand and Supply analysis. Balance of Trade (Payments), Model of Income Determination. Dynamic Models of Income Determination. Stabilisation Policy, Comparative Statics Analysis of Monetary Fiscal Policy, the Harod Domar Growth model, the Neo-classical growth model. Interest Theory.

**MGT 472: Principles of Management II (3,0, 3)**

Organizational behaviour/human relations – interpersonal and group processes, the application of concepts, like leadership, motivation, communication, morale, to the management of people and organizations, time management, analysis of causes, of change, managing change, innovation, management control.