**ALPHA SEMETER 300 LEVEL**

**MAT310: Dynamics of a Rigid Body (3 Units)**

General motion of a rigid body as a translation plus a rotation. Moment and products of inertia in 3-dimensions. Parallel, and perpendicular axes theorems. Principals axes. Angular momentum, kinetic energy of a rigid body. Impulsive motion, examples involving one and two dimensional motion of simple systems. Moving frames of reference rotating and translating frames of references. Coriolis force. Motion near the earth’s surface. The Foucault’s pendulum. Euler’s dynamical equations for motion of a rigid body with one point fixed. The symmetrical tops procession.

**MAT312: Numerical Analysis I (3 Units) **Numerical solution of ordinary differential equations. Existence of solution. One-step schemes and theory of convergence and stability. Linear multistep methods: Development, theory of convergence and stability. Extrapolation processes. Integral equation and boundary value problem.

**MAT313: Complex Analysis I (2 Units)**

Functions of a complex variable: polynomials, rational, trigonometric, logarithmic functions and their inverses. Branch point. Convergence of sequences and series; absolute and uniform convergence. Limit and continuity of a complex-valued function of a complex variable. Differentiation: complex derivative. Cauchy-Riemann equations. Analytic functions.

**MAT314: Introduction to Operations Research (2 Units)**

Phases of operations research study. Classification of operations research models. Linear, dynamic and integer programming. Decision theory, inventory models, critical path analysis and project control.

**MAT315: Probability Distributions (2 Units)**

Discrete and continuous probability distributions. Mathematical expectation and moments of random variables. Moment generating functions. The binomial, Poisson, geometric, hypergeometric and negative binomial distributions. The normal, uniform, gramma and beta distributions. The central limit theorem (proof by moment generating function) Functions of a univariate random variables. Bivariate distributions. Independence; sums of independent random variables.

**MAT316: Vector & Tensor Analysis (3 Units) **

Vector algebra. Vector, dot and cross Products. Equating of curves and surfaces. Vector differentiation and applications. Gradient, divergence and curl. Vector integrate, line surface and volume integrals Greens Stoke's and divergence theorems. Tensor products of vector spaces. Tensor algebra. Symmetry. Gartesian tensers.

**MAT317: Mathematical Methods III (3 Units)**

Linear Dependence and the Wronskian, Analytic Regular and Similar points, Series representation of solution of an Ordinary Differential Equation in the neighbourhood of an ordinary point. Series Solution near a regular singular point. The classical orthogonal polynomials (Legendre, Hermite and Laguerre polynomials). Rodrigue’s formula. Special functions: gamma and beta functions. Bessel functions. Euler Equation. Elementary properties of the hypergeometric functions.

**MAT318: Statistical Inference (2 Units)**

Analysis of variance: two way analyses. Use of unbiasedness and minimum variance in selecting good estimators. Interval estimation. Derivation of point and interval estimators of means, proportions and standard deviations. Methods of estimation; maximum likelihood, least squares and method of moments. Principles of hypothesis testing: type I and II errors. Likelihood ratio test.

**MAT319: Mathematical Modelling I (3 Units)**

Methodology of model building: identification, formulation and solution of problems, cause-effect diagrams. Equation types: algebraic, ordinary differential equations, partial differential equations, difference, integral and functional equations, Applications of mathematical models to physical, Biological, Social and Behavioural Science.

**Regression Analysis II (2 Units)**

Linear estimation: Multiple linear regression equations. Partial correlation coefficients. Gauss-Markoff linear model. Least square estimators; Estimable functions. Tests of independence of regression coefficients. Testing of hypotheses relating to linear models. Logistic regression.Cochran’s theorem. Model selection procedures. Use of dummy variables. Non-linearity in parameters requiring simple transformation.

**MAT332: Non-Parametric Methods (2 Units)**

Other statistics and their distributions. Test based on runs. Tests of Goodness of fit. Sign, Median, Run, Wilcoxon, Kolmogrov-Smirnov rank tests.One sample and two sample linear ranks for location and scale. Tests for independent samples. Measure of association for bivariate samples and multiple classifications.

**MAT333: Introduction to Industrial Mathematics (2 Units)**

This course introduces the students to industrial mathematics and covers various problems that can be found in industry. A problem-based learning approach is recommended. Each problem studied motivates the need for learning the mathematical techniques necessary to solve the problem. Part of the course involves writing a report on a project and giving a presentation of the results. It is suggested that students learn to use appropriate computer packages. Previous problems include Monte-Carlo methods for a financial application, circadian rhythm analysis, atmospheric refraction correction and the Fourier synthesis of ocean scenes.

**MAT335: Mathematical Computing (2 Units)**

An introduction to R: Data and text implementation in R, including regular expressions and database operations; R programming: data structures and types, object orientation, flow control, functions, efficient programming, parsing/expressions/formulas; Numerical methods; numerical linear algebra; simulation studies and Monte-Carlo; ** **object-oriented programming; graphics programming. Numerical integration and numerical differentiation, symbolic integration and differentiation optimization.

**MAT337: Financial Mathematics (3 Units)**

Various topics in mathematics of finance are covered, including annuities, actuarial, statistics and mortality analysis; principles and methods of actuarial treatment of statistical data, including the compilation and other rates, exposed to risk formula selection. Multiple decrements, history and distinctive features of the principles actuarial tables in common use. Vital statistics, including censuses of births, deaths, marriages, and migration statistics. Forecasting rates of Mortality. General Theory of Projection. A short account of the population of Nigeria. Construction of National Life table, Sickness and other rates. Construction of Tables. Valuation of liabilities under life policies and Special topics. Multiple decrement (service) and associated single decrement tables; values of and contribution for sickness benefits; pension benefits, disability benefits and widows and orphans benefits.

**CSC 313: Object-Oriented Programming (2 Units)**

Basic OOP Concepts: Classes, Objects, inheritance, polymorphism, Data Abstraction, Tools for developing, Compiling, interpreting and debugging, Java Programs, Java Syntax and data objects, operators. Central flow constructs, objects and classes programming, Arrays, methods. Exceptions, Applets and the Abstract, OLE, Persistence, Window Toolkit, Laboratory exercises in an OOP Language.

**CSC 314: Theory of Computing (2 Units)**

Chomsky Hierarchy**: **Type 0, type 1, type 2 and type 3 grammar. Finite Automata:

Deterministic and non-deterministic finite automata; Conversion of non-deterministic finite automata to deterministic finite automata; Regular expressions and their relationships to finite automata. Pushdown Automata and Context-Free Grammars: Deterministic and non-deterministic pushdown automata; Context-free grammars; Useless productions and emptiness test; Ambiguity; Context-free grammars for pushdown automata and vice-versa. Properties of Context-Free Languages: Pumping lemma; Closure properties; Existence of non-context-free languages. Turing Machines, Decidability and Undecidability.

**EDS311: Entrepreneurship Development Studies V (1 Unit)**

Practical Side of Entrepreneurship (Part1). Objective: To expose the students to a greater depth in the practical aspects of entrepreneurship, particularly the development of skills. The aim is to distinguish Covenant University graduates from graduates of other institutions of higher learning.

Practicum: All students are sent to the entrepreneurial village in-groups for skill acquisition in different specialization fields. Mini trade fairs will be organized where the students will display all their products. This program includes both theoretical and practical aspects of entrepreneurship. Production and Quality control of entrepreneurship material Management will be taught. These specialized fields include: tailoring, carpentry, millinery (hat making), mechanical, catering, shoe making, interior decoration, software development, candle and soap making, fishery, farming, snail rearing, poultry farming, piggery, textile development (tie & dye), cooking, paint manufacturing, photography, ice-cream making, saloon and barbing etc.

**TMC311: Total Man Concept V (1 Unit)**

Man in Society (Part 1). This course examines Man in different environmental contexts – the biblical, biological, cultural and ecological. The emphasis here is the civic and social responsibilities of man in society and the expectations of community living. The place of social relationships, diversity, issues of difference, conflict, family issues are explored looking at God’s mandate and current trends and challenges.

**TMC312: Total Man Concept - Sports (0 Unit)**

Aerobics (Cardio respiratory) Aerobics exercise: This is said to be any activity that can get the heart rate going and keeps it at a sustained rate over a period of time. E. g twenty minutes. An aerobic activity helps to increase cardiorespiratory fitness which is one of the fine essential components of physical fitness. Being aerobically fit you can feel it as you go about. Games (modified sports): Modified level of sports prepares student for the real activity itself and beyond. The philosophy of modified is to maximize participation and playing time for students. The level focuses on growth of basic skills and sportsmanship. During these events we make every attempt to include as many students on possible teams. Athletics (Field Events): Institutional athletics programme represent a multi financial industry and are generally linked to school branding and reputation. Athletic programme drive enrolment and heightens institutional profile, and often resulting in financial windfall for those whom their students engaged in.

**GST311: History and Philosophy of Science (2 Units)**

The focus of this course shall be in the discipline of science, which at present, is held in high esteem as the greatest agent of development in the 21st century. This course is a survey of the philosophical foundation of science. Major topical issues in Philosophy of science will be treated. It will begin with a brief account of the the role of metaphysics in scientific explanation, and determinism in the sciences. The student shall therefore be expected to, among other things, examine the main areas of philosophy; the meaning and characteristics of science, explanations in science, its objectives, methods, laws and theories with the view to justifying or debunking the superiority that has been accorded to the discipline of science over other discipline, that is where this becomes necessary. The course will also treat the philosophical thoughts of thinkers like Karl Popper, Copernicus, Newton and Fereyarband.

**OMEGA SEMESTER 300 LEVEL **

**MAT329: Industrial Training (6 Units)**

Students will be attached to various industries and establishments for 20-24 weeks (6 Months) during the 300 level Omega Semester and the long vacation in order to expose them to the practical applications of mathematics. All students enrolled in this course would be required to submit a report and give presentation at the end of the attachment. The grading will normally be based on the reports, seminars and assessment of the industry based supervisor.