MATHEMATICS OPTION

PHILOSOPHY AND OBJECTIVES

PHILOSOPHY

The undergraduate degree programme in Mathematics covers a wide spectrum of both pure and applied Mathematics to produce highly skilled graduates.

OBJECTIVES:

(i)    to provide students a broad and balanced foundation in Mathematics;

(iii)    to develop in students the ability to apply their mathematical knowledge and  
skills to the solution of theoretical and practical problems;

(iii)    to generate in students an appreciation of the importance of Mathematics in an 
industrial, economic, environmental and social context;

(iv)    to produce excellent and trainable graduates for further academic works;

(v)    to develop in students a range of transferable skills of value in mathematical related and non-mathematical related employment;

A.    LIST OF COURSES BY LEVELS
100 LEVEL
Course Code    Course Title                                        Credit(s)
MAT 111        Calculus and Trigonometry                3
MAT 112        Elementary Mathematics I                 3
MAT 115        Algebra                                           3
MAT 120        Sets and Logic                                 2
MAT 122        Elementary Mathematics II                3
MAT 125        Vectors and Analytical Geometry         3
STA 111        Probability I                                      3
CIT 115        Introduction to Computer Programming I 2
CIT 126        Introduction to Computer Programming II wit Lab 3   
GST 110        Use of English                                   2
GST 113        Christian Education                             2
GST 122        Introduction to Information and Communication     
                    Technology                                        2
GST 123        Library and information Literacy Skills   2

200 LEVEL
MAT 210        Abstract Algebra I                              3
MAT 213        Numerical Methods                             2
MAT 217        Ordinary Differential Equations             3
MAT 218        Introduction to Mechanics                    3
MAT 219        Introduction to Analysis                       3
MAT 225        Analysis                                            3
MAT 226        Mechanics                                         3
MAT 227        History of Mathematics                        2
MAT 228        Linear Algebra                                    3
GST 201        Studies in Entrepreneurship and New Ventures 2
GST 216        History and Philosophy of Science          1
GST 228        Peace Studies and Conflict Resolution    2

300 LEVEL
MAT 310        Abstract Algebra II                               3
MAT 311        Metric Space Topology                           3
MAT 312        Mathematical Methods I                        3
MAT 313        Numerical Analysis I                              3
MAT 314        Vector and Tensor Analysis                     3
MAT 315        Complex Analysis I                               2
MAT 317        Hydromechanics                                    3
MAT 318        Wave Theory                                        2
MAT 320        Number Theory                                     2
MAT 321        Dynamics I                                           3
MAT 322        Mathematical Methods II                        3
MAT 323        Optimization                                         3
MAT 325        Differential Geometry                             3
MAT 326        Introduction to Mathematical Modelling     3
MAT 327        Real Analysis                                        3
MAT 390        Industrial Training                                 2
GST 301        Culture and Civilization in Africa              1
GST 302        Studies in Philosophy and Logic              1

400 LEVEL
MAT 411        General Topology                                    3
MAT 412        Ordinary Differential and Integral Equations 3
MAT 413        Numerical Analysis II                              3
MAT 414        Entrepreneurship in Mathematical Sciences 2
MAT 415        Complex Analysis II                               3
MAT 416        Viscous Flow Theory                                3
MAT 417        Commutative Algebra                             3
MAT 418        Measure Theory and Integration              3
MAT 420        Functional Analysis                                 3
MAT 421        Dynamics II                                          3
MAT 422        Partial Differential Equations                    3
MAT 423        Operations Research                              3
MAT 424        Mathematical Modelling                           3
MAT 425        Continuum Mechanics                             3
MAT 426        Quantum Mechanics                                3
MAT 427        Compressible Flow Theory                        3
MAT 490        Seminar                                                 2
MAT 499        Research Project                                      5

B.    SUMMARY OF DEPARTMENTAL GRADUATION REQUIREMENTS
          (No. of credits in brackets)

100 LEVEL
CORE:
MAT 111(3), MAT 115(3), MAT 120(2), MAT 125 (3), STA 111(3), CIT 115 (2), CIT 126(3), GST 110(2), GST 113(2), GST 122(2), GST 123(2).
Total                                            27 Credits

ELECTIVES:
Students are advised to register for not less than 3 credits from the following courses: CHM 110(3), CHM 117(1), PHY 110(2), PHY119 (1), BLY 113(2), CIT 114(2), STA 110(3), STA 122(3) and any other relevant ones with the permission of the Head of Department.

200 LEVEL
CORE:
MAT 210(3), MAT 213(2), MAT 217(3), MAT 218(3), MAT 219(3), MAT 225(3), MAT 226(3), MAT 228(3), GST 201(1), GST 216(1), GST 228(2).
Total                                            27 Credits

ELECTIVES:
Students are advised to register for not less than 3 credits from the following courses: MAT 227(2), CIT 211(2), CIT 221(2), PHY 211(2), PHY 251(2), STA 210(3), STA211(3), STA 220(3) and any other relevant ones with the permission of the Head of Department.

300 LEVEL
CORE:
MAT 310(3), MAT 311(3), MAT 312(3), MAT 314(3), MAT 315(2), MAT 317(3), MAT 321(3), MAT 322(3), MAT 390(2), GST 301(1), GST 302(1).
Total                                            27 Credits

ELECTIVES:
Students are advised to register for not less than 3 credits from the   following courses: MAT 313(3), MAT 318(3), MAT 320(2),  MAT 323(3), MAT 325(3), MAT 326(3), MAT 327(3), STA 311(3), STA 320(3), CIT 310(3), CIT 312(3), PHY 341(3), PHY 351(2) and any other relevant ones with the permission of the Head of Department.

400 LEVEL
CORE:
MAT 411(3), MAT 412(3), MAT 414(2), MAT 416(3), MAT 418(3), MAT 420(3), MAT 422(3), MAT 490(2), MAT 499(5).
Total                                            27 Credits

ELECTIVES:
Students are advised to register for not less than 3 credits from the following courses: MAT 413(3), MAT 415(3), MAT 417(3), MAT 421(3), MAT 423(3), MAT 424(3), MAT 425(3), MAT 426(3), MAT 427(3), STA 410(3), STA 411(3), STA 413(2), STA 414(2) and any other relevant ones with the permission of the Head  of  Department.

C.     COURSE DESCRIPTIONS
100 LEVEL

MAT 111    CALCULUS AND TRIGONOMETRY    3 Credits
Trigonometric ratios, sum and products formulae. Multiple and sub multiple angles. Graphs of trigonometric functions. Inverse circular functions. Solution of triangles and trigonometric equations.  Functions: concepts and notation, polynomial, rational and trigonometric, exponential and logarithmic; limits and techniques of finding limits. Differentiation and its applications, Integration: Definite integrals, reduction formulae, application to area and volumes.
45h(T);C.

MAT 112    ELEMENTARY MATHEMATICS I    3 Credits
Indices, logarithms and surds, set theory; linear quadratic and simultaneous equations (one linear, one quadratic). Sequences and series with applications from social sciences. Applications of differential calculus to problems in the social sciences.
45h(T). (For Non-Mathematics Majors).

MAT 115    ALGEBRA    3 Credits
Polynomials: Remainder and factor theorems, equation and inequalities, domains and zeros of rational functions. Partial fractions; mathematical induction; binomial theorem; sequences and series. Permutations and combinations. Complex numbers. Fundamental theorem of algebra (statement only).
45h(T);C.

MAT 120    SETS AND LOGIC    2 Credits
SETS: Definition of terms; set, elements of a set, subsets, etc, union and intersection; Venn diagram, Binary Operations, Mappings and equivalent relations.  LOGIC: statements, symbols for the three simplest connectives truth tables, tautology and equivalence. Laws of the algebra of statements, viz commutative, associative, distributive, idempotent, identity, the complement and De-morgan’s Laws.
30h(T);C.

MAT 122    ELEMENTARY MATHEMATICS II    3 Credits
Further differential and integral calculus, matrix algebra and applications to solutions of linear equations, inequalities; linear and quadratic. Rational and partial fraction, permutation and combination. Polynomials.
45h(T). (For Non-Mathematics Majors).

MAT 125    VECTORS AND ANALYTICAL GEOMETRY    3 Credits
Coordinate geometry: distance, gradient, equations of straight line in different forms. Conic sections: parabola, ellipse and hyperbola.                                                                                                        
Vectors: Definition and representation of a vector, vectors addition. Components of a vector, unit vectors i,  j , k, Magnitude of a vector. Vector multiplication (scalar, vector, scalar triple and vector triple products.)
45h(T);C.

200 LEVEL

MAT 210    ABSTRACT ALGEBRA I    3 Credits
Sets, Cartesian product of sets, relation, equivalence relation. Mappings, permutations on finite sets. Fundamental theorem of Arithmetic congruences. Euler’s function, Φ (n). Definition and examples of groups. Subgroups. Cyclic subgroups. Lagrange’s theorem and its consequences. Homomorphism and isomorphism of groups. Definition and examples of rings. Commutative rings and integral domains. Fields.
45h(T);C.

MAT 213    NUMERICAL METHODS    2 Credits
Numerical differentiation and integration, solutions of O.D.E’s. Direct and iterative methods for solutions of linear systems, least square polynomial approximations, introduction to numerical solutions of partial differential equations.
30h(T);C.

MAT 217    ORDINARY DIFFERENTIAL EQUATIONS    3 Credits
Introduction, order and degree of differential equations. Equations of first order and first degree, separable equations, homogeneous equations, exact equations, linear equations, Bernoullis and Riccati equations. Applications to Mechanics and electricity. Second order equations with constant coefficients.
45h(T);C.

MAT 218    INTRODUCTION TO MECHANICS    3 Credits
Statics: Moments and couples. Equilibrium of a particle and a rigid body under the action of a system of coplanar forces centre of mass of simple bodies. Moments of inertia of simple bodies.  Dynamics: Newton’s laws of motion. Force, work, power, energy and momentum.
Rectilinear Motion: Motion with constant acceleration, force as a function of time, distance and velocity.  Impulsive Motion: Elastic and inelastic collisions.
45h(T);C.

MAT 219    INTRODUCTION TO ANALYSIS    3 Credits
Logic: Review of Logic.  Sets and Function: Cartesian products of sets; Relations, functions, family of sets. A function as a triple (F,X,Y). Direct and inverse images, subjective and injective functions and one-to-one correspondence. Finite sets, infinite sets countable sets; Existence of uncountable sets.  True Real Number System:  ,  as an ordered field. Axioms of addition and multiplication, the distributive laws.  Mathematical induction. Definition of the natural rational numbers, irrational numbers, upper and lower bounds supremum and infininimum. The completeness axiom. Open intervals, Open sets of real numbers.
45h(T);C.

MAT 225    ANALYSIS    3 Credits
Sequences: Sequence of real numbers. Elementary properties of Units, Convergence of sequences, county convergence principle.  Series: Convergence of series, Tests for convergences absolute convergence, conditional and uniform convergence power series.
Real valued functions: Limits and continuity of functions, bounded functions. Elementary properties of continuous functions.  Differentiability of functions: Partial differentiation, total derivatives, implicit functions, change of variables. Rolle’s Theorem, Mean value Theorem, Taylor’s theorem, fundamental theorem of calculus.
45h(T);C; CR: MAT 219.

MAT 226    MECHANICS    3 Credits
Statics: System of line vectors. Couples and wrenches. Principle of virtual work. Stability of equilibrium.  Dynamics: Elastic strings. Hooke’s law. Motion in resisting media, changing mass. Motion along a curve, frenets formulae.
45h(T);C; CR: MAT 218.

MAT 227    HISTORY OF MATHEMATICS    2 Credits
The origin of Mathematics: Egyptian and Babylonian Mathematics, Greek Mathematics, Pythagoras school, the golden age, the decline of Greek Mathematics.. Mathematics in other cultures: Hindu and Arabian Mathematics. The European renaissance:  Solutions of quadratic and cubic equations.  Modern Mathematics: The origin and development of number theory, calculus, projectile and analytical geometry.
30h(T).

MAT 228    LINEAR ALGEBRA    3 Credits
Vector spaces over fields. Subspaces. Linear dependence of vectors. Spanning and Linearly independent vectors. Basis and dimension. Linear transformation of vector spaces. Matrices. Addition and multiplication of matrices. Elementary row operations on matrices. The echelon form. Rank (row) of a matrix via elementary row operations. Determinants. Adjoint of a square matrix. Inverses. Solutions of systems of Linear equations. Cramer’s rule. Eigenvalues and eigenvectors.
45h(T);C.
300 LEVEL

MAT 310    ABSTRACT ALGEBRA II    3 Credits
Normal subgroups and quotient groups. The isomorphism theorems. Automorphism of groups. Conjugate classes and normalisers. The Sylow theorem and some applications. Direct products. Rings, ideals and quotient rings. The isomorphism theorems for rings. Commutative rings. Integral domains and prime ideals. Fields and maximal ideals.
45h(T);C; PR: MAT 216.

MAT 311    METRIC SPACE TOPOLOGY    3 Credits
Metric space Definitions and examples of metric spaces. Usual metric, Euclidean and Cauchy Schwartz inequality, Minkowski’s inequality. The space C(X, ) as a metric space.
Open sets. Definitions of open balls, closed balls, sphere, sequences in metric spaces: Convergence, Completeness, Continuity of function on metric spaces: Definition and examples, pasting lamina, contraction mapping principle. Compactness and connectedness: Open covening, Lébesque covering lemma, total boundness., Ascoli’s Theorem Topological spaces.
Definition of topological spaces. Metrizable topologies. Homeomorplism. Topological invariant properties.
45h(T);C; PR: MAT 225.

MAT 312    MATHEMATICAL METHODS I    3 Credits
Linear dependence; Wronskian, reduction of order, variation of parameters, series solutions about ordinary Legendre, hypergeometric e.t.c. Laplace transformation and applications to initial value problems.
45h(T);C; PR: MAT 217.

MAT 313    NUMERICAL ANALYSIS I    3 Credits
Polynomial and splines approximations: orthogonal polynomials and Chebyshev approximations. Numerical integration. Boundary value problems. Introduction to numerical solutions of partial differential equations.
45h(T); PR: MAT 213.

MAT 314    VECTOR AND TENSOR ANALYSIS    3 Credits
Vector algebra. Vector, dot and cross products. Equation of curves and surfaces. Differentiation, applications, gradient, divergence, curl, integration, line, surface and volume  integrals. Green’s, Stroke’s and divergence theorem. Tensor products and vector spaces. Tensor algebra. Symmetry, Cartesian tensors.
45h(T);C; PR: MAT 125.

MAT 315    COMPLEX ANALYSIS I    2 Credits
Functions of a complex variable, limits, continuity,  convergence of sequences and series. Deriving the Cauchy-Riemann equations, conformal mapping, contour Integrals, Cauchy’s theorem and the main consequences. Functions of complex variables. Power and Taylor series.
30h(T);C.

MAT 317    HYDROMECHANICS    3 Credits
Historical introduction. Physical properties. Differentiation following the motion. Equation of continuity. Stream lines and path lines. Momentum equations. Eulers and Bernoullis equations.  Inviscid fluids: Kelvins circulation theorem. Irrotattional motion and velocity potential. Stream functions, 2 dimensional flows, complex potentials sources and sinks, Doublets. Method of images. 3 dimensional flows with axial symmetry, flow past a circular cylinder. Circle and Blasius Theorems. Conformal mapping, Schwartz Christoffel transformation. Joukowski theory and aerofoils. D’Alemberts paradox.
45h(T);C; PR: MAT 226.

MAT 318    WAVE THEORY    2 Credits
Nature of waves. Equation of wave motion. Waves in strings, finite and infinite strings. Waves in membranes. Longitudinal waves. Sound waves. Water waves, tidal waves, surface waves.
45h(T); PR: MAT 226.

MAT 320    NUMBER THEORY    2 Credits
Algebraic number theory: Numbers, quadratic and cyclotomic fields. Factorization intoirreducible ideals.Minkowski’s theorem, class group and class number. Fermat’s last theorem, Dirichlet’s unit theorem.
30h(T).

MAT 321    DYNAMICS I    3 Credits
Generalized motion of a rigid body as a translation plus rotation. Moment and products of inertial in three dimensions. Parallel and perpendicular axes theorems. Principal axes, Angular momentum, Kinetic energy of a rigid body. Impulsive motion. Examples involving one and two dimensional motion of simple systems, moving frames of references: rotating and translating frames of reference. Foucault’s pendulum. Euler’s dynamical equations for motion of a rigid body with one point fixed. True symmetrical top precession.
45h(T);C; CR: MAT 312.

MAT 322    MATHEMATICAL METHODS II    3 Credits
Sturm-Liouville problem, orthogonal, polynomials and Functions. Fourier series and integrals. Partial differential  equations. First and second order equations: Classification of second order linear equations, solution of heat, wave and Laplace equations by the method of separation of variables; eigenfunction expansions and Fourier transforms.
45h(T);C; CR: MAT 312.

MAT 323    OPTIMIZATION    3 Credits
Linear programming models. The simplex method, formulation and theory. Duality integer programming. Transportation problem, two-person zero-sum games. Non-linear programming, quadratic programming and Kuhn tucker methods. Optimality criteria, simple variable optimization, multivariate techniques. Gradient methods.
45h(T).

MAT 325    DIFFERENTIAL GEOMETRY    3 Credits
Vector functions of a real variable. Boundedness, limits, continuity, differentiability, functions of class Cm. Taylor’s formulae. Analytic function curves, regular, differentiable and smooth. Curvature and torsion, tangent line and normal plane vector. Linear continuity and limits. Directional  functions of class Cm. Taylor’s theorem and inverse function theorem. Concept of a surface, parametric representation, tangent plane and normal line. Topological properties of simple surfaces.
45h(T).

MAT 326    INTRODUCTION TO MATHEMATICAL MODELLING    3 Credits
Methodology of model building; Identification, formulation and solution of problems, cause - effect diagrams. Equation types - Algebraic, ordinary and partial differential, difference, integral and functional equations. Applications of Mathematical models to physical, biological, social and behavioural sciences.
45(T); CR: MAT 312.

MAT 327    REAL ANALYSIS    3 Credits
Integration: The integral as the area of the ordinate set of a function. Definition of the Riemann integral. Properties of the integral.
Riemann-Stietjes integral: Functions of bounded variations. Integration with respect to functions of bounded variation. Partial Integration formula. Sequences and series of functions. Convergence of sequences and series of functions, Uniform Convergence. Tests for convergence of series. Term  by term integration and differentiation of a series of continuous functions. Implicit function, inverse mapping theorem.
45(T); PR: MAT 225.

MAT 390    INDUSTRIAL TRAINING    2 Credits
Students are required to undertake three months of Industrial Training. He/She would be required to present a seminar of his/her industrial training experience and submit a report to the department for evaluation purposes.
90h(P);C.

400 LEVEL

MAT 411    GENERAL TOPOLOGY    3 Credits
Topological spaces; Definition and examples. Open bases, open sub-bases. Topologizing of sets, G,F, sets. Continuous maps, open maps and closed maps. Homeomorphisms, Weak topologies, function algebras ( (X, ) C(X,C) Compact spaces, Product of spaces. Relative topology, Quotient topology; Tychonoff’s theorem. Locally compact spaces. The separation axioms. Connectedness. T1 space, T2 (Hausdorff) space, T3 space and T4 space. The Weirstrass approximation theorem.
45h(T);C; PR: MAT 311.

MAT 412    ORDINARY DIFFERENTIAL AND INTEGRAL EQUATIONS    3 Credits
Existence and uniqueness theorems. Dependence of solution on initial data and parameter. Properties of solutions, strum comparison and Sonin- Polya theorems. Linear systems, Flouquet’s theory. Non-linear systems, stability theory. Integral equations, classification. Fredholm’s equations, Neumann’s series, Resolvent Kernel. Voltera equations. Applications to ordinary differential equations.
45h(T);C; PR: MAT322.

MAT 413    NUMERICAL ANALYSIS  II    3 Credits
Numerical quadrature: Romberg, Gauss integrable singular integrands, infinite range, multiple integrands. Discrete and continuous Tau method for solving O.D.E’s error analysis. Partial differential equations: finite difference methods, stability, convergence and errors, orthogonal expansions.
45h(T); PR: MAT 313.

MAT 414    ENTREPRENEURSHIP IN MATHEMATICAL SCIENCES    2 Credits
Use of statistical packages (SPSS, Excel, Matlab etc) imputing of business/industrial, demographic and research data. ANALYSIS of data and interpretation of results from software packages. Determination of position of shock waves, subsonic, transonic, supersonic and hypersonic flows. 
15h(T);45h(P);C.

MAT 415    COMPLEX ANALYSIS II    3 Credits
Laurent expansions, isolated singularities and residues theorem, Calculus of residue and application to evaluation of integrals and to summation of series. Maximum modulus principle. Argument principle. Rouche’s theorem. The fundamental theorem of algebra. Principle of analytical continuation, multiple valued functions and Riemann surfaces. 
45h(T); PR: MAT 315.

MAT 416    VISCOUS FLOW THEORY    3 Credits
Stress and Strain. Navier Stokes equation. Energy equation, simple exact solutions. Dynamical similarity, slow flows(flows at small Reynolds numbers). Stokes and Oseens flows. Lubrication theory, laminar boundary flow (flow at large Reynold numbers). Thickness, skin friction and heat transfer. Blasius solution for the flat plate and similar solutions.
45h(T);C; PR: MAT 317.

MAT 417    COMMUTATIVE ALGEBRA    3 Credits
Rings and ideals. Prime ideals and maximal ideals. The nilradical and the Jacobson radical. Modules and their properties. Exact sequences and additive functions. Multiplicatively closed subset and rings of fractions. Local rings and localization. Primary decomposition. Noetherian and Artinian rings.
45h(T); PR: MAT 310.

MAT 418    MEASURE THEORY AND INTEGRATION    3 Credits
Measure theory: Measure of open and closed sets, outer and inner measure. Measurable sets Properties of measure. Non-measurable sets.  Measurable Functions. Simple Function Algebra. The hebesgue integral: lebesgue measure. Lebesgue integral integral of non-negative functions. Integral as a measure of ordinate set, as a limit of approximate sums. Integral of an unbounded function. Integral over an infinite range. Simple properties of the integral. Sequences of integral (positive functions, functions with positive and negative values) Lebesgue non-monotone convergence theorem. Fatuou’s Lemma. Domented connergence. Bepo’s Lemma. Bounded convergence. Sets of measure zero. Integration by parts. Funini’s Theorem and applications to multiple integrals.
45h(T),C; PR: MAT 327.

MAT 420    FUNCTIONAL ANALYSIS    3 Credits
Definition and examples of normed linear spaces. Convex sets Holders inequality Micowski’s inequality. Riez-Fisher theorem Linear operators on finite dimensional spaces. Linear functionals. Banach spaces, examples Quotient space. Inner product spaces. Linear Topological spaces. Hilbert spaces, examples. Linear operators on Hilbert spaces. Adjoint operators. Hermitian operators. Orthogonality. Orthogonal complement and projections in Hilbert spaces.
45h(T);C; CR: MAT 418.

MAT 421    DYNAMICS II    3 Credits
Degree of freedom. Holonomic and non-holonomic constraints. Generalized co-ordinates, LaGrange’s equations for holonomic systems, force dependent on co-ordinates only, force obtainable from a potential impulsive force, and variational principles. Canonical transformation, normal modes of variation, Hamilton-Jacobi equations
45h(T);PR: MAT 321.

MAT 422    PARTIAL DIFFERENTIAL EQUATIONS    3 Credits
Theory and solutions of first order equations, second order linear equations, classifications, characteristics, canonical forms Cauchy problem. Elliptic equations: Laplace’s and Poisson formulae, properties of harmonic functions. Hyperbolic equations, retarded potential transmission line equation; Riemann method parabolic equation, diffusion equation, singularity function, boundary and initial value problems.
45h(T);C; CR: MAT 412.

MAT 423    OPERATIONS RESEARCH    3 Credits
Dynamic programming: continuous state dynamic programming, multiple state variables, applications. Non-linear programming. Basic concepts: unconstrained optimization; constrained optimization (equality and inequality constraints). The general non-linear programming. Applications. Decision analysis. Forecasting and time series analysis. Applications.
45h(T); PR: MAT 323.

MAT 424    MATHEMATICAL MODELING    3 Credits
Simulation modeling. Examples from life, physical and social sciences. Examples of the consequences of crude approximations of models. Criticism of some known models in Genetics, Species interaction and disease control. Case studies.
45h(T); PR: MAT 326.

MAT 425    CONTINUUM  MECHANICS    3 Credits
Bodies, configurations and motions, the referential and spatial description’s of motions, mass, momentum, force and torque. The theory of stress. Equations of motion. The kinetic equation, first and second laws of thermodynamics.
45h(T).

MAT 426    QUANTUM MECHANICS    3 Credits
Particle-wave duality. Quantum postulates. Schrödinger equation of motion. Potential steps and wells in 1-dim, Heisenberg formulation. Classical limit of quantum mechanics. Computer brackets. Linear harmonic oscillator. Angular momentum. 3-dim square well potential. The hydrogen atom. Collision in 3-dim. Approximation method for stationary problems. Systems of many particles(Pauli principle).
45h(T).

MAT 427    COMPRESSIBLE FLOW THEORY    3 Credits
Thermodynamics. Compressibility effects. Equations of continuity and motion. Energy equation. One dimensional unsteady flow. Small disturbance theory. Speed of sound and mach number. Normal and oblique shocks. Shocks tubes. Small perturbation theory for subsonic and supersonic flows.
45h(T); CR: MAT 419.

MAT 490    SEMINAR    2 Credits
Each student would be required to give a seminar topic in consultation with a staff supervisor and approved by the head of department.  On the approved topic, the student would be required to consult latest literature and present the same in the seminar. He/She would deposit a written copy of the seminar in the department for record purposes.
90h(P);C.

MAT 499    RESEARCH PROJECT    5 Credits
The project shall involve analysis of mathematical problems in various fields of pure and applied mathematics selected in consultation with a staff supervisor and approved by the Head of Department. The student would be required to submit a critical report on his/her work in triplicate to the Department for evaluation purposes.
225h(P);C.

B.Sc. Degree Programme in Statistics

PHILOSOPHY AND OBJECTIVES

PHILOSOPHY
Statistics deals with the collection, analysis, presentation and interpretation of numerical data. Therefore the philosophy of the degree programme requires a highly professional and academic training that would enable its graduates to function as statisticians, teachers, researchers and policy makers.

OBJECTIVES
(i)    to provide students with a broad and balanced foundation in Statistics;
(ii)    to instill in students a sense of enthusiasm for Statistics, an appreciation of its application in different areas and to involve them in an intellectually stimulating, and satisfying experience of learning and studying;
   
(iii)    to develop in students the ability to apply their statistical knowledge and skills to the solution of theoretical and practical problems in mathematics;

(iv)    to provide students with a knowledge and skills base from which they can proceed to further studies in specialized areas of Statistics or multidisciplinary areas involving Statistics;

(v)    to generate in students an appreciation of the importance of Statistics in an industrial, economic, environmental and social context.

A.    LIST OF COURSES BY LEVELS
100 LEVEL
Course Code   Course Title                                   Credit(s)
STA 110        Descriptive Statistics                    3
STA 111        Probability I                               3
STA 112        Introductory Statistics for Non-Majors 2
STA 121        Laboratory for Statistics               2
STA 122        Basic Statistical Methods              3
MAT 111       Calculus and Trigonometry           3
MAT 115       Algebra                                      3
CIT 114        Introduction to Computer Science  2
CIT 115        Introduction to Computer Programming I 2
CIT 126        Introduction to Computer Programming II 3
GST 110        Use of English                            2
GST 113        Christian Education                     2
GST 122        Introduction to Information and Communication
                   Technology                                 2
GST 123        Library and Information Literacy Skills 2

200 LEVEL
STA 210        Distribution Theory I                    3
STA 211        Probability II                              3
STA 212        Statistics for Physical Sciences      2
STA 220        Inference I                                3
STA 221        Introduction to Socio-Economic Statistics 2
STA 222        Laboratory for Inference              2
STA 223        Statistics for Life Sciences            2
STA 224        Statistics for Social Sciences         2
MAT 217        Ordinary Differential Equations      3
MAT 219        Introduction to Analysis                3
MAT 228        Linear Algebra                             3
CIT 211        Structured Programming                2
CIT 222        Low Level Languages                    2
GST 201        Studies in Entrepreneurship and New Ventures 2
GST 216        History and Philosophy of Science   1
GST 228        Peace Studies and Conflict Resolution 2

300 LEVEL
STA 310        Distribution Theory II                    3
STA 311        Probability III                               3
STA 312        Design and Analysis of Experiments I 3
STA 313        Regression Analysis                      2
STA 314        Laboratory/Field Work on Experimental Design 2
STA 315        Laboratory/Field Work on Regression 2
STA 316        Survey Methods and Sampling Theory3
STA 320        Inference II                                    3
STA 321        Analysis of Variance                         2
STA 322        Operations Research I                     2
STA 323        Demography I                                2
STA 324        Statistical Quality Control I               2
STA 325        Biometric Methods I                        2
STA 326        Statistical Computing                      3
STA 327        Field Work on Survey    Methods      2
STA 390        Industrial Training                          2
GST 301        Culture and Civilization in Africa       1
GST 302        Studies in Philosophy and Logic        1

400 LEVEL
STA 410        Distribution Theory III                     3
STA 411        Inference III                                  3
STA 412        Design and Analysis of Experiments II 3
STA 413        Econometric methods                      2
STA 414        Stochastic Processes                       2
STA 415        Statistical Quality Control II             2
STA 416        Biometric Methods II                      2
STA 417        Sampling Techniques                      3
STA 418        Operations Research II                   2
STA 420        Demography II                              2
STA 421        Bayesian Inference and Decision Theory 2
STA 423        Non-Parametric Methods                 3
STA 424        Actuarial Statistics                          2
STA 425        Educational Statistics                      2
STA 426        Medical Statistics                           2
STA 427        Psychometrics                               2
STA 428        Environmental Statistics                 2
STA 430        Health Statistics                            2
STA 431        Energy Statistics                            2
STA 432        Multivariate Analysis                      3
STA 433        Stationary Time Series                   3
STA 490        Seminar                                       2
STA 499        Research Project                            5       

B.    SUMMARY OF DEPARTMENTAL GRADUATION REQUIREMENTS
          (No. of credits in brackets)

100 LEVEL
CORE:
STA 110(3), STA 111(3), STA 121(2), STA 122(3), MAT 111(3), MAT 115(3), CIT 115(2),  GST 110 (2), GST 113(2), GST 122(2), GST 123(2).
Total                                            27 Credits

ELECTIVES:
Students are advised to register for not less than 3 credits from the following courses: MAT 120(2), MAT 125(3), CIT 114 (2), CIT 126(3), PHY 110(2), BLY 113(2), ECN 110(3) with the permission of the Head of Department.
 
200 LEVEL
CORE:
STA 210(3), STA 211(3), STA 220(3), STA 221(2), STA 222(2), MAT 228(3), MAT 219(3), CIT 211(2), GST 201(2), GST 216(1), GST 228(2).
Total                                            26 Credits

ELECTIVES:
Students are advised to register for not less than 4 credits from the following courses: MAT 213(2), MAT 217(3), CIT 212(3), CIT 220(3), CIT 222(2) with the permission of the Head of Department.

300 LEVEL
CORE:
STA 310(3), STA 311(3), STA 312(3), STA 313(2), STA 314(2), STA 315(2), STA 320(3), STA 321(2), STA 326(3), STA 327(2), STA 390(2), GST 301(1), GST 302(1).
Total                                            29 Credits

ELECTIVES:
Students are advised to register for not less than 1 credit from the following courses: STA 316(3), STA 322(2), STA 323(2), STA 324(2), STA 325(2), MAT 323(3) with the permission of the Head of Department.

400 LEVEL
CORE:
STA 410(3), STA 411(3), STA 412(3), STA 417(3), STA 423(3), STA 432(3), STA 433(3), STA 490(2), STA 499(5).
Total                                            28 Credits

ELECTIVES:
Students are advised to register for not less than 2 credits from the following courses: STA 413(2), STA 414(2), STA 415(2),  STA 416(2), STA 418(2), STA 420(2), STA 421(2), STA 424(2), STA 425(2), STA 426(2), STA 427(2), STA 428(2) STA 430(2), STA 431(2) with the permission of the Head of Department.

C.    COURSE DESCRIPTIONS
100 LEVEL

STA 110    DESCRIPTIVE STATISTICS    3 Credits
Basic Statistical concepts. Methods of collection, presentation, and interpretation of Statistical data: tables, charts, and graphs. Errors and approximation. Frequency and cumulative distributions. Measures of location, partition, dispersion, skewness, and kurtosis.
45h(T);C.

STA 111    PROBABILITY I    3 Credits
Generation of Statistical events from set theory. Concepts and principles of Probability. Permutation and Combination. Introduction to Probability distribution functions. Basic distributions: Bernoulli, Binomial, Hyper geometric, Poisson, and Normal.
45h(T);C.

STA 112    INTRODUCTORY STATISTICS FOR NON-MAJORS    2 Credits
Definition of statistics: uses and limitation of statistics, data collection and presentation: use of tables, diagrams, and charts. Measures of location and dispersion.
30h(T). (Exclusively for Non-Statistics Majors).

STA 121    LABORATORY FOR STATISTICS    2 Credits
The student is introduce to the use of calculators. Computation and interpretation of statistical data (using calculators) involving topics in STA 110, STA 111, and STA 120. Introduction to the use of computer in Statistics.
90h(P);C.

STA 122    BASIC STATISTICAL METHODS    3 Credits
Time series. Index numbers. Demographic measures, population and samples. Random sampling. Estimation and test of hypothesis. Regression and correlation.
45h(T);C.

200 LEVEL

STA 210    DISTRIBUTION THEORY I    3 Credits
Random variables and their distributions; p.d.f and c.d.f. Expectation and variance. Discrete and continuous probability distributions: Binomial, Poisson, Hypergeometric, Negative Binomial, Geometric, Uniform. Normal approximation to binomial distribution.
45h(T);C.

STA 211    PROBABILITY II    3 Credits
Combinatorial analysis. Probability models for the study of random phenomena in finite sample generating functions and its properties. Chebychev’s inequality and limit theorems in probability. Central limit theorem. Bivariate, marginal and conditional distributions. Variance and covariance.
45h(T);C.

STA 212    STATISTICS FOR PHYSICAL SCIENCES    2 Credits
Measures of location and dispersion in simple and grouped data. Elementary probability and probability distributions; Normal, Binomial, Poisson, Geometric and negative binomial distribution. Estimation and test of hypothesis concerning the parameters of these distributions. Regression, correlation, and analysis of variance. Contingency tables. Non-parametric inference.
30h(T). (For Non-Statistics Majors).

STA 220    INFERENCE I    3 Credits
Estimation: Point and interval estimation. Elementary properties of point estimation (no proofs). Simple tests of hypotheses. Test using large samples and some standard small sample situations. Contingency tables. Goodness-of fit-test.
45h(T);C.

STA 221    INTRODUCTION TO SOCIO-ECONOMIC STATISTICS    2 Credits
Index numbers: theory, construction and problems. Errors in index numbers. Socio-economic indicators-nature, types, uses, and computation. Statistics relating to Nigerian banking and accounting system. Nature, sources, contents, and limitations of official statistics in industrial, agriculture, financial, and commercial sectors.
30h(T);C.

STA 222    LABORATORY FOR INFERENCE    2 Credits
Presentation and Analysis of data. Curve fitting, goodness-of-fit-test, estimation, test of hypotheses and analysis of contingency tables. Construction of questionnaires.
90h(P);C.

STA 223    STATISTICS FOR LIFE SCIENCES    3 Credits
Use of statistical methods in biology and agriculture. Frequency distribution. Laws of probability. The binomial, Poisson, and Normal probability distributions. Estimation and tests of hypotheses. Design of simple agriculture and biological experiment. Analysis of variances and covariances, simple regression and correlation. contingency tables and non-parametric tests.
30h(T). (For Non-Statistics Majors).

STA 224    STATISTICS FOR SOCIAL SCIENCES    2 Credits
Nature of statistics, statistical inquiries, forma and design. The role of statistics, basic concepts in statistics. Discrete and continuous variables, sources of data, methods of collecting primary data. Data presentation. Measures of central tendency and dispersion. Moments, skewness, and kurtosis. Elementary probability distribution: Binomial, Poisson, Hypergeometric and Normal.
30h(T). (For Non-Statistics Majors).

300 LEVEL

STA 310    DISTRIBUTION THEORY II    3 Credits
Distribution associated with the normal distribution; Student-t, Gamma, Chi-square, Exponential, Multinomial and F-distributions. Sampling distribution, central limit theorem for independently and identically distributed random variables. Tests of significance concerning means, proportion and variance. Contingency tables and Chi-square test; goodness-of-fit-test.
45h(T);C; PR: STA 210.

STA 311    PROBABILITY III    3 Credits
Probability generating functions. Probability spaces measures and distribution.   Distribution of random variables as measurable functions. Product spaces; product of measurable spaces. Product probabilities. Univariate and bivariate moment generating functions. Convergence of random variables. Law of large numbers and the central limit theorem using characteristic functions. Inversion formula.
45h(T);C; PR: STA 211.

STA 312    DESIGN AND ANALYSIS OF EXPERIMENTS I    3 Credits
Basic concepts: randomization, replication and error control. Basic designs: completely randomized designs. Randomized complete block designs, Latin square designs. Orthogonality, transformation, analysis and efficiency of the above designs. Missing plots techniques. Analysis of nested designs.
45h(T);C.

STA 313    REGRESSION ANALYSIS    2 Credits
Simple linear regression: Linear estimation selection of the best regression equation. Least squares estimators. Multiple linear regression equations. Multicollinearity and other problems associated with “best regression models”. Tests of independence of regression co-efficient. Partial, total and multiple correlations. Simple non-linear regression. Use of dummy variables. Non-linearity in parameter requiring simple transformation.
30h(T);C.

STA 314    LABORATORY/FIELD WORK ON EXPERIMENTAL DESIGN    2 Credits
Computations based on field work and laboratory of some of the techniques and problems on experimental design: Completely randomized design, Randomized complete block design, Orthogonality, Missing plot, Factorial experiment
90h(P);C; CR: STA 312.

STA 315    LABORATORY ON REGRESSION ANALYSIS    2 Credits
Computations involving linear, quadratic and multiple regression analysis. Partial correlation coefficient, Analysis of covariance model. Testing of hypothesis relating to linear model.
90h(P);C; CR: STA 313.

STA 316    SURVEY METHODS AND SAMPLING THEORY    3 Credits
Survey design: planning, programming and methods of data collection. Design of forms and questionnaires. Data processing, analysis and interpretation. Sampling strategy. Sampling and non-sampling errors, probability and non-probability sampling; standard sampling procedure. Sample random sampling, stratified sampling, systematic sampling, cluster and two-edge sampling. Nigeria’s experience in sample surveys. Various problems arising in sample surveys.
45h(T).

STA 320    INFERENCE II    3 Credits
Criteria for estimation: unbiasedness, minimum variance, consistency, efficiency and sufficiency. Methods of estimation; maximum likelihood, least squares and methods of moments. Confidence intervals. Simple and composite hypotheses. Likelihood  ratio test. Inferences about means and variances.
45h(T);C;PR: STA 220.

STA 321    ANALYSIS OF VARIANCE    2 Credits
Analysis of simple, double and multiple classification of balanced data in crossed and nested arrangements. Analysis of two-way contingency tables for test of homogeneity, independence and interactions. Analysis of variance involving unbalanced data such as with missing observations. Multivariate analysis of variance. Analysis of multifactor, multiresponse data. Non-normality, heterogeneity of variance.
30h(T);C;CR: STA 313.

STA 322    OPERATIONS RESEARCH I    2 Credits
Nature and scope of operations research. Linear programming, graphical and simplex methods. Sensitivity analysis. Duality theory. Transportation and assignment problems. Network analysis: CPM and PERT. Inventory scheduling and applications. Sequencing and scheduling.
30h(T).

STA 323    DEMOGRAPHY I    2 Credits
Data types and sources of demographic data. Methods of collection: population census, vital registration and demographic sample surveys. International classification of diseases, injuries, and causes of fertility, mortality, nuptiality and migration. Introduction to life tables: construction and applications. Standardization, vital statistics in Nigeria.
30h(T).

STA 324    STATISTICAL QUALITY CONTROL I    2 Credits
Quality assurance in modern business. Control charts for attributes: p and np chart, C-chart, s-chart. Acceptance sampling by attributes: single, double and multiple sampling plans. Sequential sampling plan. Sampling by variables.
30h(T).

STA 325    BIOMETRIC METHODS I    2 Credits
Introduction to population genetics. Statistical methods sin biology. Sampling and estimating biological population. Design and analysis of clinical trials. Bioassays: type and nature. Direct and indirect assays. Parallel line assays. Slope ratio assays.
30h(T).

STA 326    STATISTICAL COMPUTING    3 Credits
Programming in FORTRAN and PASCAL computer language. Computation of mean, variance and correlation. Sorting and ranking of data. Basic statistical computing in regression analysis and the analysis of designed experiments. Introduction to Monte Carlo methods. Use of statistical packages like SPSS, SAS, GENSTAT, EPI-INFO, SYSTAT
135h(P);C.

STA 327    LABORATORY/FIELD WORK ON SURVEY METHODS    2 Credits
Computation based on data obtained from survey designs. Probability and Non- probability Sampling. Simple Random Sampling, Stratified sampling, systematic sampling, cluster sampling, two- edge sampling
90h(P);C; CR: STA 316.

STA 390    INDUSTRIAL TRAINING    2 Credits
Students are required to undertake three months of Industrial Training. He/She would be required to present a seminar of his/her industrial training experience and submit a report to the department for evaluation purposes.
90h(P);C.

400 LEVEL
STA 410    DISTRIBUTION THEORY III    3 Credits
Distribution of quadratic forms. Fisher-Cochran theorem. Multivariate normal distributions. Distribution of order statistics from continuous population. Characteristic and moment generating functions. Uniqueness and inversion theorems. Limit theorems.
45h(T);C; PR: STA 310.

STA 411    INFERENCE III    3 Credits
General linear hypothesis and analysis of linear models. Further treatment of estimation and tests of hypothesis-extension of uniparameter to multiparameter situation. Basic ideas of distribution-free tests. Bayesian Inference.
45h(T);C; PR: STA 320.

STA 412    DESIGN AND ANALYSIS OF EXPERIMENTS II    3 Credits
Factorial experiments: analysis of 2n and 3n factorial experiments. Yates algorithm, confounding and fractional factorial replication. Split plot. Unbalanced designs, incomplete block and lattice designs. Introduction to response surface designs.
45h(T);C; PR: STA 312.

STA 413    ECONOMETRIC METHODS    2 Credits
Nature of econometrics. Econometric models: nature, types and characteristics. Econometric Problems related to single equation models involving lagged variables. Simultaneous equation systems; estimation and tests. Applications econometric models: demand analysis, production functions, consumption and investment function.
30h(T).

STA 415    STATISTICAL QUALITY CONTROL II    2 Credits
MIL–STD–IOSD – Description and procedures. Dodge-Roming sample plans. MIL–STD–414. Description and use of tables. Cusum charts, control chart for individual units. Process capability analysis. Evolutionary operations. Chain sampling. Continuous sampling. Other sampling methods.
30h(T); PR: STA 324.

STA 416    BIOMETRIC METHODS II    2 Credits
Stability models, simultaneous selections models. Path analysis. Discriminant analysis. Parallel line and slope ratio assays in completely randomized, randomized blocks and incomplete block designs. Logistic curve and logic transformations in relation to bio-assays. Quantal response assays. Angular transformation in relation to bio-assays.
30h(T); PR: STA 325.

STA 417    SAMPLING TECHNIQUES    3 Credits
Ratio, regression and difference estimation procedures. Double sampling. Interpenetrating scheme. Multiphase and multistage sampling, cluster sampling with unequal sizes, problem of optimal allocation with more than one item. Further stratified sampling.
45h(T);C; PR: STA 316.

STA 418    OPERATIONS RESEARCH II    2 Credits
Integer programming: problem formulations and solutions. Non-linear programming: search methods, Newton-Raphson method, Frit-John optimality conditions and Langrangian multipliers. Network analysis. Path methods (including Bellman’s equations, cyclic and network with positive paths). Dynamic programming: routine of problems, resource allocation and equipment replacement.
30h(T); PR: STA 322.

STA 420    DEMOGRAPHY II    2 Credits
Estimating fertility, mortality and nuptiality from limited and defective data. Stationary. Stable and quasis-stable population models: theory and applications. Multiple decrement life tables. Population projections: mathematical models, component methods and matrix analysis. Path analysis and multiple classification analysis.
30h(T); PR: STA 323.

STA 421    BAYESIAN INFERENCE AND DECISION THEORY    2 Credits
Decision theory: Elements of the theory of games and decision theory. Criteria of preference of decision procedures. Estimation theory: Minimax, Bayes theorem, prior and posterior distributions for proportions, mean and variances. Tests of hypothesis including testing of equality of K means, multinomial probabilities and contingency tables.
30h(T).

STA 423    NON-PARAMETRIC METHODS    3 Credits
Order statistics and their distributions. Tests based on runs. Tests of goodness of fit. One sample and two samples linear rank tests for location and scale. Tests for independent samples. Measure of association for bivariate samples and multiple classifications.
45h(T);C.

STA 424    ACTUARIAL STATISTICS    2 Credits
The time value of money: compound interest and discounting; present values and accumulated values of streams of payments. Decremental rates and other indices, annuities and sinking funds; solving equations of value, investment and appraisal techniques, analysis of experiments data and derivation of exposure to risk formulae. Graduation Methods  and their application to curve fitting, construction of mortality, sickness, multiple decrements and similar tables with applications to life insurance. National social security and pension schemes.
30h(T).

STA 425    EDUCATIONAL STATISTICS    2 Credits
Scope, nature and uses of educational statistics. Sources and methods of collection of educational statistics. Educational indicators, design of education information systems. Education flow models and performance evaluation. Multivariate methods in educational analysis, operations research in educational management.
30h(T).

STA 426    MEDICAL STATISTICS    2 Credits
Scope and nature of medical statistics. Epidemiology methods: relative risks and odd ratios, adjustment of data with and without the use of multivariate models, cohort studies (life tables). Competing risks, survival analysis. Sequential methods in clinical trials. Stochastic models epidemiology.
30h(T).

STA 427    PSYCHOMETRICS    2 Credits
Introduction: scaling procedures: scaling individual test items. Percentile scaling, sigma scaling, T-scaling, scaling of rating or ranking. Test theory, item analysis. Parallel test, methods of estimating reliability and validity. Intelligent tests and IQ. Element of factor analysis.  
30h(T).

STA 428    ENVIRONMENTAL STATISTICS    2 Credits
Scope, nature and sources of environmental statistics, assessment of environmental quality and measurement of air and water pollution. Sampling methods in natural and applied sciences. Environmental impact assessment. Requirement for environmental reporting system. Characteristics and uses of the United Nations framework for the development of environmental statistics. Capacity development for environmental reporting system.
30h(T).

STA 430    HEALTH STATISTICS    2 Credits
Scope and types of health statistics. Classification of disease; injuries and causes of death. Sources and methods of collecting health statistics; census, sample surveys, vital registration and administrative statistics. Health indicators: types, uses and problems. Health systems. Health planning and financing. Health information systems. Operations research in the health services.
30h(T).

STA 431    ENERGY STATISTICS    2 Credits
Energy sources: renewable and non-renewable, Nature, scope and uses of energy statistics. Concepts, definitions, and units of measurements in use in energy statistics.
Energy production and consumption surveys. Data requirements and the procedure for developing an energy database. Constructing an energy balance sheet with Nigeria as a case study. Modelling energy supply and demand.
30h(T).   

STA 432    MULTIVARIATE ANALYSIS    3 Credits
Multivariate distributions and associated marginal and conditional distributions. Estimation of mean vector and variance matrix. Hottelings T2 and Mahalonobis D2 Statistics. Multivariate analysis of variance. Canonical Correlation Analysis. Discrimination and classification. Principal components and factor analysis. Cluster Analysis
45h(T);C; CR: STA 410.

STA 433    STATIONARY TIME SERIES     3 Credits
Objectives, types of variations. Estimation and isolation of compounds of tome series, stationary and non-stationary time series. Theoretical moments, autocorrelations and partial auto-correlations, univariate time series model: identification and estimation. Auto-regressive (AR), Moving average (MA) and Auto-regressive moving average (ARMA) models. Linear prediction and forecasting. Spectral (Harmonic) analysis.
45h(T);C.

STA 490    SEMINAR    2 Credits
Each student would be required to give a seminar topic in consultation with a staff supervisor and approved by the head of department.  On the approved topic, the student would be required to consult latest literature and present the same in the seminar. He/She would deposit a written copy of the seminar in the department for record purposes.
90h(P);C.

STA 499    RESEARCH PROJECT    5 Credits
The project shall involve collection, analysis and interpretation of primary and/or secondary data in consultation with a staff supervisor approved by the Head of Department. The Student would be required to submit a critical report on his/her work in triplicate to the Department for evaluation purposes.
225h(P);C.