Name of Programme:                   Bachelor of Science Honours Degree in Applied

Statistics

Duration:                                       4 Years

Actual Credit load:                          492

Minimum Credit load:                    480

Maximum Credit load:                    540

Maximum MBKs Credit Load:       408

ZNQF Level:                                   8

1.0   PURPOSE OF THE PROGRAMME

The purpose of this programme is to provide a solid foundation and skills in the basic subjects of mathematical knowledge and its applications in the big data world. In addition to the enhanced career prospects that can be gained by taking this programme, it also allows complementary scientific training in mathematics with further studies in other scientific fields, extending the range of knowledge and skills of the students and, consequently, increasing the possibility to enter the labor market.

ENTRY REQUIREMENTS

For all entry pathways candidates must have at least five Ordinary Level subjects/ National Foundation Certificates including English Language, Mathematics and a Science subject at grade C or better.

 

Normal Entry:	At least two Advanced Level passes including Mathematics or its recognized equivalence (Mechanics, Statistics, Pure Mathematics) plus at least five Ordinary Level passes/ National Foundation Certificates including Mathematics and English Language OR National Certificate.
Special Entry:	National Diploma and Higher National Diploma.
Mature Entry:	At least 25 years plus relevant work experience.

 

3.0  PROGRAMME CHARACTERISTICS

3.1.          Areas of Study: Calculus; Linear mathematics Applied Statistics; Statistical Computing ; Regression Analysis; Multivariate Analysis; Research methods; Probability theory; Statistical Inference; Hypothesis testing theory Estimation Theory; Linear Models and Survival modelling.

3.2.          Specialist Focus: Understanding fundamentals of Statistics and its application in big data and analytics for making informed decision making.

 

3.3.          Orientation: Teaching and learning are professionally oriented and focused on application of Statistics to solve real world problems.

3.4.          Distinctive Features: The programme focuses on knowledge development and application using a student-centred approach.

4.1.          Employability: After students graduate, they are employable in the following areas: Actuarial sciences; Financial Institutions: (banks, building societies, insurance companies and pension funds) as market or financial analysts; Meteorology (forecasting); Manufacturing industry (production/operation management); Industrial Research; Research and Project Management in NGOs, research stations, and many other areas of applications; Mining Sector; Schools and Universities and many other relevant areas of the economy.

4.2.          Further Studies: Master’s and doctoral studies in Applied Statistics or in interdisciplinary programmes related to applied mathematics.

5.0  PROGRAMME DELIVERY

5.1.Teaching and Learning Methods

Lectures, tutorials, practicals, group work, work related learning report, mini WRL/Industrial Attachment Research Project, individual independent study.

5.2.Assessment Methods

Written examinations, tests, practical, presentations, work related learning report, mini Industrial Attachment Research Project, final year research project report, continuous assessments.

6.0  LEARNING OUTCOMES

Upon successful completion of the programme a graduate will be able to:

 

§  Understand statistics and how its various disciplines are integrated.

§  Work effectively in a broad range of scientific, government, financial, analytic, health, technical and other related fields.

§  Understand the relationship between theory and applications of statistics.

§  Use statistical thinking, training, and approach to problem solving in a diverse variety of disciplines.

 

§  Read and interpret statistical literature of various types, including online sources, survey articles and books.

§  Modify and improve existing statistical models to solve real world problems.

§  Use software and quantitative models to analyse statistical data. §  Communicate statistical information orally and in writing to a wide variety of audiences.

 

7.0  GENERAL PROVISIONS

Refer to Section 4 of the Faculty of Science and Technology Regulations.

8.0  PROGRAMME ASSESSMENT

 

Continuous Assessment:	25%: Test (15%), Assignments (10%)
Written Examinations:	75%
Other:	a)        Research Project is assessed on the basis of a research project (90%), Oral presentation (10%). b)       Work related learning is assessed based on Work related learning report (30%), assessment by work supervisor (50%), and assessment by Academic supervisor (20%).

 

9.0            PROVISION FOR PROGRESSION

Refer to Section 7 of the Faculty of Science and Technology regulations.

10.0         FAILURE TO SATISFY THE EXAMINERS

Refer to Section 10 of the General Regulations for Undergraduate Degrees.

11.0     GRADING AND DEGREE CLASSIFICATION

Refer to Section 5 of the General Regulations for Undergraduate Degrees.

12.0         DEGREE WEIGHTING

Refer to Section 11 of the Faculty of Science and Technology regulations.

13.0         PROGRAMME STRUCTURE

N.B Modules marked * are MBK modules.

Level 1

Semester 1

Code           Module Description                                                     Credits

HMAT101  *Calculus 1                                                                         12

HMAT102  *Linear Mathematics 1                                                       12

HSTA102    *Applied Statistics                                                              12

HSTA103    *Probability Theory I                                                         12

CS111         Communication Skills                                                        12

HCSCI 132 Principles of Programming Languages                               12

Semester 2

HSTA104    *Statistical Computing I                                                     12

HMAT111  Ordinary Differential Equations                                         12

HSTA105    *Regression and Anova I                                                    12

HMAT105   Mathematical Discourse and Structures                             12

HSTA106    *Probability Theory 2                                                         12

HSTA107    *Statistical Inference 1                                                       12

Annual credits                                                                                              144

 

Level II Semester 1

 

HSTA201    *Design and Design Issues I                                               12

HSTA204    *Statistical Computing II                                                    12

HSTA205    *Hypothesis Testing Techniques                                        12

HSTA206    *Survey Techniques                                                            12

HSTA212    Research Methods &Statistics                                            12

GS201         Gender Studies                                                                    12

Semester 2

HSTA207    *Time Series Analysis                                                        12

HSTA208    Statistical Inference II                                                         12

HSTA209    *Estimation Techniques                                                     12

HSTA210    *Operations Research I                                                       12

HSTA211    *Official, Social & Economic Statistics                             12

TCNP201    Technoprenuership                                                              12

Annual credits                                                                                           144

 

Level III
HMAT301	*Work-Related Learning Report	36
HMAT302	*Academic Supervisor’s Report	24
HMAT303	* Employer’s Assessment Report	60
Annual Credits		120
Level IV
Semester 1
HSTA401    *Linear Models		12
HSTA402    *Multivariate Analysis		12
HSTA408    *Econometrics		12
HSTA409    *Demography		12
HSTA412    *Survival Models		12
Semester 2 HSTA410    *Stochastic Processes		12
HSTA471    *Research Project		36
Elective Modules for Level IV
HSTA406	Design & Design Issues II	12
HSTA411	Regression & Anova II	12
HMAT444	Mathematical Modelling	12
HSTA405	Operations Research and Quality Control Techniques	12
HMAT436	Mathematical Programming	12

Annual credits                                                                                           132

NB: Students must choose at least two elective modules from the given list

14.0         MODULE SYNOPSES

HMAT101: Calculus I Number systems: The principle of mathematical induction. The real number system: Functions: Limits of functions. Continuity. Sequences: Differentiation: Derivatives of functions of a single variable. Integration: Method of substitution, integration by parts and reduction formulae, fundamental theorem of calculus.

HMAT102: Linearmathematics I Complex numbers: De Moivre’s theorem polynomials and roots of polynomial equations. Matrices and determinants: solutions of simultaneous linear equations, applications to geometry and vectors. Differential equations: separable, homogeneous, exact, integrating factors, linear equation with constant coefficients.

 

HSTA102: Applied statistics Measures of central tendency. Measures of variability. Empirical distributions. Moments. Skewness and Kurtosis. Indicators. Contingency Tables. Introduction to Time Series and trends. Sampling. Introduction to estimation procedures: Judgemental method and Method of moments. Introduction to Hypothesis testing. Non-parametric statistics. Chi-square contingency methods, Goodness of fit tests, Q-Q plots, Z-test and t-test.   HSTA103: Probability theory I Axiomatic probability, sets and events, sample space, conditional probability, Independence, laws discrete and continuous random variables, probability density functions, mean, variance, expectation. Independence, Chebyshev’s inequality, moments and moment generating functions. Common Discrete and continuous Distributions. Joint Probability Distributions. Approximations, Law of large numbers, Central limit Theorem.

HSTA104: Statistical computing 1 Introduction to use of statistical software. Training on database software including Microsoft Excel, Microsoft Access, SPSS, Epi-Data and Epi-Info. Use of these softwares for data entry, data management and analysis. Interpretation of analysis results and statistical report writing.

HSTA105: Regression and analysis of variance I Method of least squares. General linear model assumptions. Checking validity of assumptions. Outliers. Pearson’s and Spearman’s correlation coefficients, predictions. Regression in terms of sums of squares and sums of products. Estimation of parameters. Multiple linear regression. Testing and inference in multiple linear regression using matrices. Partial correlation. Analysis of variance (ANOVA). Assumptions underlying ANOVA. One- way, balanced design ANOVA

HSTA106: Probability theory II Bivariate probability distributions. Moment generating functions. Characteristic functions. Multinomial and multivariate normal distributions. Distributions of functions of random variables. Cumulative distribution function technique. Expectations of functions of random variables. The transformations of discrete, continuous functions and random vectors. Probability integral transform. Sampling distributions. Law of large numbers.   HSTA107: *Statistical inference 1 Deductive inference, population and sample concepts as the basis of statistical inference, parameters and statistics, review of probability theory. Central Limit Theorem, Chi-square, student-t and F distributions, distribution of min and max. Estimation: methods of estimation, properties of estimators and their sampling distributions. Interval estimation. and Hypothesis testing.

 

HMAT111: Ordinary Differential Equations Modelling with first order ODEs in population dynamics, and second order ODEs (mass- spring systems, RLC circuits). Methods of undetermined coefficients, reduction of order and method of variation of parameters. Existence and uniqueness of solutions, revision of continuous functions and Lipschitz conditions. Series solutions of ODEs, solutions near ordinary and singular points. Systems of linear first order ODEs, solution and stability. Differential equations of special functions. Laplace transforms and inverse Laplace transforms, applications to solving IVPs, Heaviside and Dirac functions.

HSTA201: Design and design issues 1 Principles of experimentation. Completely randomized designs, randomized block designs, latin square design. Ecological Studies, Cross Sectional Studies, Correlational studies, Case control studies, Cohort and randomized control trials. Epidemiology Methods, Framingham Heart Study, Measurement in Epidemiology, Binary Outcomes, Definition of Prevalence, Determinants of Prevalence, Incidence, Measures of Association, Odds Ratio, Attributable Proportions.

HSTA206: Survey techniques Uses, scope and advantage of sample surveys. Types of surveys. The phases of a survey. Survey organisation. Questionnaire design, dummy tables, pre-tests, training of field workers. Report writing. Errors in surveys, monitoring reviews, quality control. Sampling techniques, sample design. Further sampling theory. Estimation of means, totals, proportions. Ratio estimation. Variance calculations. Practical work.

HSTA207: Time series analysis Time series models. Box-Jenkins model building technique, white noise, and random walk. Autocovarince functions. Autocorrelation functions, Yule-Walker equations. General linear process. Autocovariance generating function. Stationarity and Inevitability. Autoregressive processes and Moving average process. Yule-Walker equation. ARIMA models for non- stationary processes. Parameter estimation. Goodness of fit tests. Forecasting. Application to SARIMA processes. Time series in frequency domain.     HSTA208 : Statistical inference II Types of statistical data. Order statistics. Exact and asymptotic distribution of order statistics. Wilcoxon one-sample and two sample tests. Tests of location a tests of variability. Non- parametric tests. Test for extreme reactions. Hollander. Tests for dichotomised or cardinal data. Kendal’s measures. Fisher’s exact test. Chi-square based tests. Kolmogorov’-Smirnov, generation of random numbers. Bootstrap and Jackknife estimation. Resampling. M-, L- and R-estimator.

HSTA209: Estimation techniques

 

General Minimum Variance Unbiased Estimation, Cramer-Rao Lower Bound, Linear Models & Unbiased Estimators, Maximum Likelihood Estimation, Least squares estimation, Bayesian Estimation, Statistical Detection Theory, Deterministic Signals, Random Signals, Non-parametric and robust detection. Case studies and mini project.

HSTA210: Operations research I M-technique, Dual linear programming methods. Dynamic programming. Project scheduling: network construction, PERT-CPM methods, project control. Queuing theory: single and multi-queuing models, finite queue variation and P. K. formula. Inventory Control Models. Probability models. Decision Analysis: Bayesian methods, mini-max, maxi-maxi criteria, maximum likelihood, maximal opportunity criteria, introduction to Utility Theory.

HSTA401: Linear models Regression: Linear regression model, point and interval estimation of parameters. Pure error and lack of fit. Residual analysis. Multiple regression: estimation and confidence intervals. General linear hypothesis. Stepwise methods. Experimental design models: one factor models. Fixed and random effects. Two factor models, with and without interaction. Qualitative and quantitative contrasts.   HSTA402: Multivariate analysis Multivariate data, descriptive statistics, graphical techniques. Random vectors and matrices. Multivariate normal distribution. Wishart distribution. Transformation to near normality. Inferences about mean vector. Comparison of several multivariate means: one-way MANOVA. Simultaneous confidence intervals for treatment effects, profile analysis, ideas of two-way MANOVA. Principal component analysis. Factor analysis, Canonical correlation and Discriminant analyses.   HST405: OPERATIONS RESEARCH AND QUALITY CONTROL TECHNIQUES OR techniques with a strong orientation towards computer based solution techniques and case studies. LP problem formulation as an illustration of alternatives and objectives. Transportation problems and algorithms, Assignment problems, Hungarian method with emphasis on formulation, structure and computer solution. Multi-objective programming making emphasis on goal programming and integer linear programming. Dynamic programming, Napsack problem, Advanced linear programming, non-linear programming algorithms, classical optimization theory, unconstrained and constrained problems with practical problems. Control charts, 𝑋̅ charts, R charts, S charts, P chart. Average run length capability analysis or indices. Reliability of system, structures of the system, parallel and series system, system life as a function, expected system life and failure rate   HSTA406: Design and design issues 2 Issues in the design of Balanced incomplete designs, crossover designs, nested designs, split plot designs, repeated measures, factorial designs, fractional factorial designs. Open and Closed Cohort, Prospective and Retrospective Cohort Studies. Threats to validity of results;

 

Bias, Confounding. Controlling for confounding at both design and analysis stage. Missing observations. Prospective Cohort Studies. Retrospective Cohort Studies.

HSTA408: Econometrics Role of Econometrics in Zimbabwe. Review of general linear model. Linear restrictions, Generalised least squares, GLS estimator, heteroscedasticity, pure and mixed estimation, group observations and grouping of equations. Autocorrelation. Heteroscedasticity. Multicollinearity. Stochastic regressors. Simultaneous equations systems. Restrictions on structural parameters. Two stage and three stage least squares.   HSTA409: Demography Basic techniques of demographic analysis. Sources of data available for demographic research. Population composition and change measures will be presented. Measures of mortality, fertility, marriage and migration levels and patterns will be defined. Life table, standardization and population projection techniques. Case studies.   HSTA410: Stochastic processes Integer-valued variables: probability generating functions, convolutions. Markov chains: transition probabilities, classifications of states, stationary distributions, transient states. Gambler ruin, random walk. Markov processes: Chapman-Kolmogorov equations, transition rate matrix, forward and backward systems. Poisson process, normal equations, machine operation machinery breakdown, queuing model.   HSTA411: Regression and analysis of variance 2 Review of simple linear and multiple linear regression techniques. Linear regression model in matrix notation. Least squares estimation techniques. Goodness of fit and lack of fit tests. Estimation, testing hypotheses and confidence regions for parameters in full rank linear regression model. Regression diagnostics. A practical in R or STATA on regression modelling and regression diagnostics   HSTA412: Survival models Survival time, survival function, hazard function, types of censoring and truncation. Methods (including life table, Kaplan Meier and Nelson Aalen) for estimating survival function, hazard function. Semi parametric (e.g., Cox-Proportional hazards model) survival models and parametric survival models. Evaluation of the proportional hazards assumption. Practical work on fitting semi parametric and parametric survival models in Stata or R software.     HMAT436 MATHEMATICAL PROGRAMMING Introduction to mathematical programming problems: Linear programming problem formulation; simplex method; Chmens and two phase techniques; sensitivity analysis;

 

duality in LP; Dual simplex method; transportation and assignment methods; integer programming; dynamic programming; quadratics and separable programming; K T conditions for optimality.

HMAT444 MATHEMATICAL MODELING

Aims and Philosophy of Mathematical Modeling. Modeling methodology, role and limitations. Mathematical modeling with sequences and series. Differential calculus, first order differential equations. Population and ecological models: application of linear autonomous systems to the physical and biological sciences. Optimal Policy Decisions: Models based on optimization techniques. Case studies.

HSTA471: Research project

The dissertation helps students to plan, design and carry out their research project, provides guidelines on how to choose a suitable topic, undertake literature review, apply appropriate research methods, collect and analyse data and manage the write up process.

GS201: Gender studies

The module empowers the students with knowledge and skills that enable them to be gender sensitive in the university, workplace and in all their social interactions. Students will be exposed to Understanding Gender, Theories of Gender Inequalities, Historical Development of Gender, Gender Analysis, Gender Issues in (their African country/region, redressing Gender Imbalances, Empowerment and Strategies for creating a gender responsive environment.

HMAT443: Numerical Solutions of PDEs

The module is centered on finite difference technique and finite element method (FEM). Th are relevant to linear PDEs and cover applications in the areas of heat flow, elasticity, aco The lecturer and students are encouraged to solve practical problems using software Overview of PDEs, the situations they model. Boundary value problems (BVPs). Grid m PDEs. Applications to steady-state heat flow. Parabolic PDEs. Unsteady-state heat flow and Convergence, stability and consistency. The explicit and implicit methods. Crank-Nicolson, Theta methods. Hyperbolic PDEs. The wave equation. Comparisons of difference and d solutions. Propagation of solutions along characteristics. Discretisation. Global and local c and variables. Combining the equations and global stiffness matrix. BCs. Calculus of var FEM. Shape functions. Two-dimensional finite elements and heat flow. Flux on the boundar heat source. Variational methods for FEM in general case. Euler’s equation.

HMAT444; Mathematical Modelling

Aims and Philosophy of Mathematical Modeling. Modeling methodology, role and l Mathematical modeling with sequences and series. Differential calculus, first order equations. Population and ecological models: application of linear autonomous systems and biological sciences. Optimal Policy Decisions: Models based on optimization techniques. Case studies.

HMAT445: Mechanics

Kinematics, projectiles, Newton’s Laws, forces, momentum, work, energy, power, conservative and dissipative forces. Orbits. Oscillations, elastic forces and resonance. Equivalent systems of forces plane statistics, system of particles, elementary theory of rigid bodies.

HMAT426: Mathematical Finance II

Introduction to the mathematical models used in finance and economics with emphasis on pricing derivative instruments. Financial markets and instruments; elements from basic probability theory; interest rates and present value analysis; normal distribution of stock returns; option pricing; arbitrage pricing theory; the multiperiod binomial model; the Black-Scholes option pricing formula; proof of the Black-Scholes option pricing formula and applications; trading and hedging of options; Delta hedging; utility functions and portfolio theory; elementary stochastic calculus; Ito’s Lemma; the Black-Scholes equation and its conversion to the heat equation.

TNCP201: Technopreneurship

The aim of this general education course is to Introduce students to marketing, financial decision- making, global marketing and management of human resources. Technical innovations (from bench to bank); To build creative thinking skills; Develop and communicate a new product concept; chemical industry; basic business rules; visit to chemical industry; corporate finance, strategic management, supply chain management; Introduction of the concept of Intellectual Property and how it can be protected; understand patents, design rights and copyright and how to extract key information from Chemistry patents; Trade Secrets, Confidentiality Agreements and Ownership of IP and how IPR can be valued and traded including licensing and assignment.

CS111: Communication Skills

Module is aimed at assisting students to achieve their full potential through equipping them with the necessary communication skills essential for their degree studies as well as post university work experience.Components include study habits and time management, academic writing skills, reading skills, listening skills and oral communication.

 

HCSCI 132: Principles of Programming Languages Refer to Computer Science and Computer Engineering CS111: Communications Skills

Refer to Department of Communication Skills

GS201: Gender Studies

Refer to the Gender Institute