**YEAR I**

**SMA1101 Calculus 10 Credits**

The module looks at the limits of functions; one-sided and infinite limits; continuity; differentiation: definition, basic properties, Rolle’s theorem, mean value theorem, Cauchy’s mean value theorem, Leibniz’s rule, applications, Taylor series as well as integration: definite integrals, antiderivatives, fundamental theorem of calculus, improper integrals, Gamma and Beta functions, definition of natural logarithm as integral of 1/x and exponential as inverse. It also covers area, volume of revolution, arc length, surface area; parametric equations: arc length, surface area; polar coordinates; graph sketching; area in polar coordinates; complex numbers; algebra of complex numbers; DeMoivre’s theorem and exponential form.

**SMA1102 Linear Algebra 10 Credits**

The module explores vector Algebra: scalar and vector product. Collinear, coplanar vectors; applications; equations of lines and planes; matrices: products, sums, echelon form, rank, inverse; determinants: definition, properties, evaluation; systems of Linear equations, Gauss’s method, Cramer’s rule, homogeneous systems as well as vector Spaces: definition, linear independence, bases, subspaces.

**SCS 1101 Introduction To Computer Science And Programming**

**10 Credits**

The module examines information and Knowledge Societies, Evolution of Computers, Computer Organisation and Architecture: CPU; Memory; I/O, Number Systems and Conversions ( Bin; Dec; Hex; Oct), Concepts of Computer Languages: high\low level languages; compiler; interpreter, Programming Techniques: grammar; recursion; Variables; Data types; Initialization; Comments; Keywords; Constants; Assignment, Programming constructs: branching; looping; recursion; Programming using data structures: arrays; lists; trees; hash tables; queues; stacks; files, Programming Algorithms for Problem Solving: Sorting; compression; numerical and encryption, Fundamentals Operating System, Fundamentals Data Bases as well as the Fundamentals of Networks.

**SMA1103 Discrete Mathematics 10 Credits**

This module looks at sets; union, Intersection, Compliment, Empty and Universal sets; number systems; natural Numbers, Integers, Rationals; induction; field axioms; order axioms; completeness; real numbers; decimal representation; irrationals; interval notation; inequalities; functions; definition; domain, range, inverse functions; logic; predicate calculus; truth tables; proportional calculus; methods of proof; contrapositive; converse; contradiction and combinatorics.

**SPH1101 Mechanics (10 Credits)**

The module is on kinematics and Kinetics: Inertial frames of reference; motion in two and three dimensions; dynamics of system of particles; interactions between bodies, relative motion; conservation of momentum and energy; motion of systems of particles with variable mass; collisions of particles. Rotational Dynamics: Rotation of rigid bodies; moment of inertia and its calculations for bodies of various shapes and about different axes; work and energy in rotational motion; angular momentum; principles of conservation of angular momentum; gravitation: Kepler's laws of planetary motion; gravitational potential; gravitation and gravity; effect of earth's rotation on "g"; gyroscope; motion of a satellite; coriolis force; the fundamental forces and their unification; inertial forces in linearly accelerating frame; oscillatory motion; simple harmonic motion; mechanical oscillators; superposition of S.H.M's. damped and forced S.H.M., Lissajous Resonance. It also looks at properties of Matter:Hooke's law; modulli of elasticity and their inter –relationship; applications of elasticity; fluid mechanics: Fluid at rest; surface tension and capillarity; the continuity equation; various types of flows; boundary layers and turbulence; steady state flow of fluids; Bernoulli's equation; viscous flow and viscosity. Friction: Nature of frictional forces; motion in frictional medium and rolling and sliding friction. It also covers relativity: Space-time frames of reference; Galileo's principle of relativity; simultaneity of events; Einstein's Special theory of relativity; Lorentz transformations; momentum and energy systems.

**SMA1108 Introduction To Computer Packages In Mathematics 10 Credits**

This module shall be a practical module, dealing with the use of computers in a variety of fields through the use of software tools. This is an introductory module in scientific writing, computer algebra and data analysis. It is an introduction to scientific writing; mathematical package; spreadsheet and a statistical package.

**SMA1201 Calculus Of Several Variables 10 Credits**

The module explores cartesian coordinates in three dimensions; functions of several variables; quadric surfaces; curves; partial derivatives; tangent planes; derivatives and differentials; directional derivatives; Chain rule. Div, grad and curl; Maxima and minima; lagrange multipliers; double and triple integrals; change of order; change of variable; polar and spherical coordinates; line and surface integrals; green’ theorem in the plane; divergence theorem; stokes theorem and applications.

**SMA1204 Ordinary Differential Equations 10 Credits**

The module looks at first order differential equations; separable, linear, exact; integrating factors; existence, uniqueness and applications; second Order Equations; linear equations and linear differential operators; linear equations and linear differential operators; linear independence, Wronskian; ordinary Linear Differential Equation with constant coefficients; undetermined coefficients; variation of parameters; applications; systems of equations; phase plane portraits for Linear systems; introduction to Non-linear systems; predator-prey and Lotka - Volterra equations; series solution of ordinary differential equations; method of Frobenius; legendre polynomials and Bessel functions.

**SMA1202 Real Analysis 10 Credits**

This module explore real numbers; completeness, Supremum and Infimum; maximum and Minimum; sequences; definition of convergence; uniqueness of limits; continuity of algebraic operations; bounded sequences; subsequences; bolzano-Weierstrass Theorem, cauchy sequences; series; definitions, elementary properties; series of positive terms; comparison test, ratio test, root test.; integral test; alternating series; absolute and conditional convergence; power series; limits of functions; continuity; taylor’s theorem (with remainder); riemann integration.

**SCS1206 Visual Programming Concepts And Development 10 Credits**

The module examines the structure and Nature Of Visual Applications, user interface Contexts (webpage; business applications; mobile applications; games), Canonical uses (GUIs; mobile devices; robots; servers) , Events and event handlers, Separation of model, view, and controller, Visual Design Elements :Object; Controls; Windows; Forms; Dialogues; Templates; Panels; Panes; etc., user-centred development, interaction design: Physical capabilities; Cognitive models, Social models, Principles of good design and good designers, Accessibility, Principles of graphical user interfaces (GUIs), Elements of visual design, User interface standards, Functionality and usability requirements, Techniques for gathering requirements, Internationalisation, interaction styles and techniques, Representing information to users, Design, implementation and evaluation of non-mouse interaction.

**SORS1201 Applied Statistics 10 Credits**

The module is an introduction to Applied Statistics; Statistics: its definition and scope; Descriptive Statistics/Initial Data Exploration: summary statistics, measures of central tendency, mean, mode, median, measures of dispersion, range, variance, standard deviation, Graphical presentation of data, stem and leaf plots, histograms, box plots. Point Estimation/Tests of Hypothesis, interval estimation,; Design and Analysis of Experiments, completely randomised designs, randomised complete block designs, Latin squares, factorial designs; Simple linear regression and Statistical computing.

**CTL1101 Conflict Transformation And Leadership 10 Credits**

The thrust of the module is understanding peace and conflict; theories of conflict; conflict analysis and tools; economic roots of conflict; gender and conflict; leadership; leadership and conflict handling mechanisms; leadership and conflict handling mechanisms; women in leadership; leadership ethics; interplay: leadership, conflict and development.

**YEAR II**

**SMA2102 Advanced Linear Algebra 10 Credits**

This module highlights linear Mappings; Matrix representation; Change of basis; Kernel and image of linear mapping; Vector spaces, basis, dimensions; Eigenvectors and eigenvalues; Diagonalization. Basis of eigenvectors; Orthogonal bases; Method of Gramm-Schimdt; Inner product spaces; Cayley-Hamilton theorem; Jordan form and Quadratic forms.

**SMA2103 Theoretical Mechanics 10 Credits**

The module looks at frames of reference; Motion of particle in two or three dimensions; Work, power energy for variable forces; Conservative forces; Motion of a system of particles; Rigid body motion; Generalized coordinates; Lagrange's and Hamilton's equations.

**SMA2108 Computer Packages In Mathematics 10 Credits**

This module shall be a practical module, dealing with the use of computers in a variety of fields through the use of software tools. It is designed to complement the understanding of some Statistical and Mathematical concepts through practical use. Statistical packages, including data handling, descriptive statistics, distribution fitting, graphs and Mathematical packages including: Solution of equations, Limits, Differentiation and Integration; the Solution of first and second order differential equation and the Solution of systems of linear equations shall be covered.

**Sors2103probability Theory 10 Credits**

This module examines probability: random/statistical experiments, sample spaces, events, set theory; Axioms of probability; Laws of probability; Finite sample spaces; Conditional probability, independent events; Random variables and probability distributions; Discrete probability distributions; Continuous probability distributions; Discrete bivariate distributions; Continuous bivariate distributions; Marginal probability distributions; Independent random variables; Conditional probability distributions; Distributions of functions of a single random variable; Conditional probability distributions of mathematical expectations; expectations of discrete and continuous random variables; Expectation of a function of a single random variable; Expectation of a function of several random variables; Properties of expectations; Variance and covariance; Markov and Chebyshev inequalities; Moment generating functions; Properties of moment generating functions; Special Distributions: Bernoulli, Binomial, Geometric, Negative Binomial, Hypergeometric, Poisson, Normal, Gamma, Weibull, Exponential and Beta.

**SORS2105 Linear Programming 10 Credits**

The module looks at model formulation Solution methods: graphical, simplex, two phase, computer solutions; Duality and sensitivity analysis; Transportation: initial feasible solution methods—north-west corner, least cost, Vogel’s methods; Balanced and unbalanced problems, unacceptable routes, degeneracy, Transhipment problems, Assignment problems; Integer Programming: model formulation; Solution methods: graphical, branch and bound method, cutting plane algorithm, implicit enumeration method; Goal programming: model formulation as well as Goal programming algorithms—the weighting and pre-emptive methods.

**SORS2104 Operations Research Techniques 10 Credits**

This module explores project management: Critical path analysis. Deterministic activity times. Probabilistic activity times. Gantt charts. Resource scheduling. Cost crashing. Inventory Models: Deterministic demand models: Economic order quantity, Economic production lot size, Economic order quantity with backorders, Quantity discounts. Probabilistic demand models: Single period models, safety stock, Multiple period models. Inventory control: Material requirements planning, materials resource planning, product structure, gross requirements, net requirements. Network Analysis: Terms and definitions; Minimum Spanning Tree problem (Kruskal’s Algorithm); Shortest Route problem (Dijkstra’s Algorithm); Network Flow problems: Maximum network flow problem (Ford-Fulkerson Labelling Algorithm), Max-flow Min-cut Theorem, Integral flows; Heuristic Problem Solving: Ill structured problems, Heuristics- the human approach to problem solving, Satisfying, heuristic procedures and programs. A case study (e.g. solving a facility location problem) will be looked at.

**SMA2201 Complex Analysis 10 Credits**

The module will look at the analytic functions; Cauchy-Riemann Equations; Conformal Mappings; Line Integrals; Cauchy’s Integral Theorem and Formula; Power series; Taylor series, Laurent series; Zeros and singularities; The Residue Theorem; Evaluation of real integrals and series.

**SORS2203 Optimisation 10 Credits**

The module looks at the deterministic and stochastic dynamic programming; Markov programming: value and policy iteration procedure; Advanced Linear Programming: The revised simplex algorithm, validity proofs of the simplex method, use of column generation to solve large-scale linear programming problems, bounded variables algorithm, parametric linear programming, Dantzig-Wolfe decomposition algorithm as well as the Karmarkar interior point algorithm.

**SORS2206 Survey Methods 10 Credits**

This module explores simple random sampling, sample size estimation; Systematic sampling; Sample survey and questionnaire design, postal and telephone questionnaires, interviewer-administered questionnaires; Errors in sample surveys; Ratio and regression estimators, separate and combined ratio estimators; Stratified populations and stratified simple random sampling, optimum allocation and Neyman allocation; Cluster multi-stage sampling and the survey method project.

**SMA2206 Numerical Analysis 10 Credits**

The module looks at errors in numerical analysis; Taylor Series; Solutions of equations in one variable: Bisection and Newton-Raphson methods; Fixed point iteration; Order to convergence; Direct and iterative methods of solving linear systems; Gaussian elimination with scaled partial pivoting; Jacobi and Gauss-Seidel iterations; Convergence criteria; Interpolation and extrapolation; Lagrange interpolating polynomial; Newton interpolating polynomial; Richardson extrapolation; Integration;Trapezoidal rule, Simpson’s rule. Gaussian quadrature and Numerical Solutions of Ordinary Differential Equations.

**SMA2204 Partial Differential Equations 10 Credits**

The module looks at Fourier Analysis; Fourier Series and Fourier Transforms. Laplace Transformations: Definition. Heaviside function; Convolution. Applications to the solution of Ordinary Differential Equations; Sturm-Liouville problems; Orthogonality; Partial Differential Equations; Classification of second order partial differential equations; The partial differential equations of mathematical physics; Derivation of the wave equation and heat equation in one dimension; Separation of variables; Fourier sine and cosine transforms and Fourier transform methods.

**SMA2209 Mathematical Modelling 10 Credits**

This module shall be a practical module, dealing primarily with the application of mathematical techniques encountered elsewhere in the degree programme. Whenever necessary, new mathematics shall be introduced. Topics covered may include: Introduction to Mathematical Modelling - Modelling methodology, modelling skills, dimensional analysis. Simple examples. Data Modelling: fitting curves and distribution to data; Simulation Modelling: use of random numbers in investigating simple stochastic situations. Use of Algebra, Statistical and Operational Research Computer Packages.

**YEAR III**

**SMA3010 Industrial Attachment 120 Credits**

**YEAR IV**

**SMA4103 Fluid Mechanics 10 Credits**

The module explores fundamental concepts; Fluids in equilibrium; The principle of fluid motion; Continuity equations; Bernoulli’s equation; Momentum equation; Introduction to viscous flow; Laminar flow problem; Dimensional analysis; Potential flow and vorticity.

**SMA4135 Dynamical Systems 10 Credits**

The module looks at second order differential equations in the phase plane; First order systems in two variables; Linear systems; Nonlinear systems and linearization; Index of a point; Limit cycles; Poincare-Bendixon theory; Stability; Poincare stability; Liapunov stability; Liapunov’s direct method and Liapunov functionals.

**SMA4162 Numerical Methods For Differential Equations 10 Credits**

The module looks at systems of Ordinary Differential Equations. Initial Value Problems. Numerical Integration using Runge - Kutta methods. Multistep formulas; Predictor corrector methods; Convergence and stability; Boundary value problems; Shooting methods; Finite difference methods; Partial differential equations; Finite differences; Parabolic equations;Crank-Nicolson methods; Elliptic equations – Dirichlet and Neumann problems; Hyperbolic equations; Methods of characteristics and Finite element methods.

**SMA4010 Project 20 Credits**

Projects may be carried out on an individual basis. Where possible the project shall be done in an industrial setting. The projects test students’ ability to organise, complete and report on a significant piece of Applied Mathematics.

**SMA4112 Modern Algebra 10 Credits**

The module groups definitions and examples; Permutation and symmetric groups; Congruence; Lagrange theorem; Isormophisms and homomorphisms; Quotient groups; Fundamental homomorphism theorem; Rings; Integral domains; Characteristic; Ordered rings; Ring of integers; Fields; Rational numbers; Real numbers; Complex numbers.

**SORS4102 Statistical Inference 10 Credits**

The module looks at indicator function, exponential family of densities; Parametric Point Estimation: parameter space and point estimators; Methods of finding estimators, method of moments, maximum likelihood method, least squares method; Properties of point estimators; unbiased estimators, minimum variance unbiased estimators (most efficient estimators), consistent estimators, sufficient estimators, asymptotic normality of estimators; Confidence Intervals: One-sided confidence intervals; Methods for finding confidence intervals, pivotal quantity, statistical and Bayesian; Hypothesis Testing: definitions. Simple and composite hypotheses, test statistic, critical regions, type I and II errors, level of significance, power of a test; Neyman-Pearson lemma; Uniformly most powerful tests and Likelihood-ratio tests.

**SMA4172 Mathematical Programming 10 Credits**

The module explores dynamical programming; Elements; Recursive equations; Computational procedure and dimensionality; Deterministic and stochastic applications; Markov programming;

Value and policy iteration procedure; Non-linear programming; Unconstrained optimisation; Equality and inequality constraints; Search methods; Separable, quadratic and stochastic programming; Geometric programming; Basic concepts; Necessary and sufficient conditions for optimality and Solution procedures.

**SORS4106 Experimental Design And Multiple Regression 10 Credits**

The module looks at the theory and applications of Statistics which include: Experimental Design and Analysis, 2k Factorial Experiments; Confounding, complete and partial confounding; Orthogonal contrasts; Fractional Factorial Experiments, Aliasing; Multiple Linear Regression: Variable selection and model building; Multiple coefficient of determination, r2; Mullow’s Cp and Sp statistics; Covariance analysis; Stepwise regression methods; Forward selection, backward elimination, and stepwise regression.

**SMA4107 Time Series Analysis And Simulation 10 Credits**

The module looks at time series: Smoothing techniques; Moving averages, simple exponential smoothing, decomposition, identification of trend, seasonal, cyclic and irregular components; Additive and multiplicative models, autocorrelation functions; Autoregressive moving average models; Statistical Process Control: x charts, range charts, statistical control, capable processes; Simulation: Simulation by hand, pseudo random numbers, data collection, distribution fitting, activity cycle diagrams, model development; Verification, validation, experimentation; Analysis of results; Method of common random numbers and the use of simulation package.

**SMA4211 Functional Analysis 10 Credits**

The module explores metric spaces; Definitions and examples; Open and closed sets, neighbourhoods; Convergence, completeness; Contraction mapping theorem; Application to linear systems, integral equations, differential equations; Normed spaces; Banach space; Finite dimensional spaces; Compactness and Reisz lemma; Lemma; Linear operators and functionals; Dual space; Hilbert spaces; Cauchy-Schwarz inequality, Pythagoras" theorem; Orthogonal complements and direct sums; Orthonormal sets; Fourier series and orthogonal polynomials; Self adjoint operators; Eigenvalues and eigenfunctions.

**SMA4236 Control Theory 10 Credits**

The module highlights the types of control; Feedback control and open loop systems; Principle of superposition; Transfer functions; Block diagrams; State space formulation; Direct solution; Solution using Laplace transforms; Stability; Asymptotic stability; Routh stability criterion; Liapunov’s method; Nyquist stability criterion; Controlability and observability criteria; Optimal control; Variational calculus; Free end conditions; Constraints; Optimal control with unbounded continuous controls; Bang-bang control; Pontryagin’s principles; Switching curves as well as Transversality conditions.

**SMA4241 Financial Mathematics 10 Credits**

The module is an introduction to financial derivatives, the Cox-Ross-Rubinstein model, finite security markets, the Black-Scholes model, foreign market derivatives, American options and exotic options.

**SMA4213 Graph Theory 10 Credits**

The module is an introduction to the abstract known as a graph; Definitions and characterisation of classes of special graphs; Distance and connectedness measures; Various algorithms applied to graphs and some of their proofs, classical and contemporary.

**SORS4207 Multivariate Analysis 10 Credits**

The module is about methodology and applications of multivariate analysis; Hotelling’s T2, multivariate regression and analysis of variance; Classification and discrimination; Principal components, clustering, multidimensional scaling as well as the use of computer packages, MANOVA.

**SMA4273 Queuing Theory And Stochastic Processes 10 Credits**

The module explores the Queuing Theory; Elements of queuing models, Queues as birth and death process, Poisson queuing models, non-Poisson queues, P;K; formula, Some simple generalizations such as series queues and applications of queuing theory; Stochastic Processes; Theory and applications of random processes, including Markov chains, Poisson processes, birth-and-death processes, random walks and recurrent events.

**SORS4210 Official Statistics 10 Credits**

The module looks at the functions of statistical services; National and International statistical agencies as well as methods of data collection. The module shall put more emphases on; Environmental statistics, Health statistics, Agricultural statistics, Industrial statistics, Economic statistics, Postal censuses and fieldworker surveys.

**SERVICE MODULES**

**SMA1111 Mathematics For Science I 10 Credits**

This module is recommended for students in Applied Sciences who have passed Mathematics at A-level. It looks at Linear Algebra: Matrices, Operations, Inverses, Determinants, Solution of Linear Equations; Calculus: Limits, continuity, derivatives; Techniques of differentiation; MacLaurin and Taylor series; Applications to extremal problems; Definite and indefinite integrals; Methods of integration; Numerical integration; Simpson's rule; Newton- Raphson method; Complex Numbers: Algebra of complex numbers; De Moivre's Theorem and Complex exponentials.

**SMA1112 Preparatory Mathematics 10 Credits**

The module is recommended for students in Applied Sciences who have not passed Mathematics at A-level it looks at Algebra: Quadratic equations; Laws of indices and logarithms; Partial fractions; Factor and remainder theorems; Binomial expansion; Complex numbers; Trigonometry: Definition of six trigonometric functions for any angle; Trigonometric identities; Compound angles; Matrices: Operations, Inverses; Determinants; Solution of Linear Systems; Functions: Exponential, Logarithmic, Circular functions and their inverses; Calculus: Idea of limit, continuity and derivative; Techniques of differentiation, maxima and minima; Definite and indefinite integrals; Methods of integration as well as application to areas and volume.

**SMA1211 Mathematics For Science II 10 Credits**

This module explores vectors; Equations of lines and planes; Vector and scalar products; Partial differentiation and Applications; Total derivative; Small changes; Maxima and minima; Double Integrals: Evaluation; Change of order; Change of variables; Differential Equations; First order ordinary differential equations; Linear and separable equations; Applications to radioactive decay, mixing problems, reaction rates; Second order linear equations with constant coefficients; Systems of first order equations; Numerical solution of ordinary differential equations: Euler, modified Euler and Runge -Kutta methods.

**SMA1116 Engineering Mathematics IA 10 Credits**

This module examines calculus in one Variable: Limits and continuity of functions; Differentiation; Leibniz's Rule; L'Hopital's Rule; Elementary functions including hyperbolic functions and their inverses; Integration - techniques including reduction formulae; Applications - arc-length, area, volumes, moments of inertia, centroids; Plane polar coordinates; Complex Numbers: Basic algebra; De Moivre's theorem; Complex exponentials; Linear Algebra: Vector algebra in 2 and 3 dimensions; Scalar and vector products and equations of lines and planes.

**SMA1216 Engineering Mathematics IB 10 Credits**

This module looks at the functions of Several Variables: Partial derivatives, chain rules; Applications - maxima and minima problems, Lagrange multipliers; Linear Algebra: Matrices - basic operations, rank, inverses; Systems of linear equations – Gauss elimination; Determinants and their properties; Eigenvalues and eigenvectors; Linear independence; Ordinary Differential Equations; First Order differential equations - separable, linear; Integrating factors; Linear second order equations with constant coefficients; Variation of Parameters; Systems of equations as well as Applications of differential equations to mechanics, physics and engineering.

**SMA2116 Engineering Mathematics II 10 Credits**

This module looks at multiple Integrals; Iterated integrals, change of order; Change of variable; Polar, cylindrical and spherical coordinates; Applications in three dimensions; Vector Calculus; Scalar and vector fields; Directional derivatives; Gradient, divergence and curl; Line and surface integrals; Theorems of Green, Gauss and Stokes; Fourier Analysis; Fourier Series; Half range series; Fourier integrals and transformations.

**SMA2217 Engineering Mathematics III 10 Credits**

This module outlines Laplace Transforms; Definitions; Basic ideas; Applications to ordinary differential equations; Statistics; An Introduction to Applied Statistics; Introduction to probability and distribution theory; Descriptive statistics/initial data exploration; Summary statistics, graphical presentation of data; Point estimation/test of hypothesis; Interval Estimation; Analysis of Variance and regression analysis.

**SMA3116 Engineering Mathematics IV 10 Credits**

This module highlights differential Equations; Power series solutions; Singular points; Frobenius method; Special functions and their properties; Legendre polynomials, Bessel functions; Partial Differential Equations; Solution of the partial differential equations (the wave equation, the one dimensional heat flow problem); Method of separation of variables; Numerical Methods; Errors, absolute and relative; The solution of nonlinear equations; The solution of linear systems; Interpolation and polynomial approximation; Curve fitting; Numerical differentiation and integration as well as the approximate solution of differential equations.

**Employability**

Careers in the retail and manufacturing industry; banking, finance and insurance industry; research institutions; non-governmental organisations; positions in academia, data mining.

**Further Studies:**

Master’s and Doctoral studies in Applied Mathematics