[B.Sc] 100 MATHEMATICS

B.SC. 200L MATHEMATICS

400 Level B.SC MATHEMATICS

COURSE DESCRIPTION FOR 100 LEVEL

MTH 112: CALCULUS

Elementary function of single real variable and their graphs, limits and the idea of continuity. Graphs of simple functions polynomial, rational, trigonometric, etc. rate of change, tangent and normal to a curve. Differentiation as limit of rate of change of elementary functions, product, quotient, function of function rules. Implicit differentiation, differentiation of trigonometric, inverse trigonometric functions and of exponential functions. Logarithmic and parametric differentiation. Use of binomial expansion for any index.

Stationary values of simple functions: maxima, minima and points of inflexion, area of surface revolution.

Integration as an inverse of differentiation. Integration of harder functions. Integration by substitution and by parts. Definite integrals: volume of revolution, area of surface of revolution.

MTH 112 – ALGEBRA AND TRIGONOMETRY

Real number system. Simple definitions of integers, rational and irrational numbers. The principle of mathematical induction. Real sequences and series. Elementary ratios of convergence of geometric, arithmetic and other simple series. Theory of quadratic equations.

Simple inequalities: absolute value and the triangle inequality.

Identities: partial fractions- sets and subsets: union, intersection, complements. Properties of some binary operations of sets distributive, closure, associative, commutative laws with examples. Relatives in a set equivalence relation. Properties of set functions and inverse set functions. Permutations and angles of any magnitude. Addition and factor formulae. Complex numbers. Algebra of complex numbers, the Argand diagram, De Moivre’s theorem, nth root of unity.

MTH 123 – VECTOR AND COORDINATE GEOMETRY

Types of vectors: points, line and relative vectors, geometrical representation of vectors in 1-3 dimension. Addition of vectors and multiplication by a scalar. Components of vectors in 1-3 dimensions; direction cosines. Linear independence of vectors. Point of division of a line.

Scalar and vector products of two vectors. Simple applications. Two dimensional coordinate geometry; straight lines, angle between two lines, distance between points. Equation of circle, tangent and normal to a circle.

Properties of parabola ellipse, hyperbola straight lines and planes in space; direction cosines; angle between lines and between lines and planes, distance of a point from a plane.

MTH 125- STATISTICS

Statistical data: types, sources and methods of collection.  Presentation of data: tables, charts and graphs. Errors and approximations. Frequency and cumulative distributions. Measures of location, partitions, dispersion, skewness and kurtosis. Permutation and Combination. Concepts and principles of probability.

Random Variables. Probability distributions: Binomial, Poisson, Geometric, Hypergeometric, negative binomial and Normal.     Population and samples. Random sampling distributions, estimation (point and interval) and Tests of hypotheses concerning population mean and proportion (one and two large sample cases). Regression and Correlation.      

MTH 124 – DIFFERENTIAL EQUATIONS AND DYNAMICS 

Differential equations:

Formation of differential equations. Differential equation of 1^st degree and 1^st order of the type; variables separable, exact, homogeneous and linear differential equations of the 2^nd order with constant coefficients of the form

Dynamics:

Resume of simple kinematics of a particle. Differentiation and integration of vectors. W.r.t scalar variables. Application to radial and transverse, normal and tangential components of velocity and acceleration of a particle moving in a plane force momentum and laws of motion; law of conservation of linear momentum. Motion under gravity, projectiles. Angular momentum. Motion in a circle (horizontal and vertical). Law of conservation of angular momentum. Application of the law of conservation of energy. Work, power and energy. Description of simple harmonic motion (SHM). SHM of a particle attached to an elastic string or spring. The simple pendulum. Impulse and charge in momentum. Direct rigid body motion; moments of inertia, parallel and perpendicular axes theorem. Motion of a rigid body in a plane with one point fixed on the compound pendulum. Reactions at the pivot. Pure rolling motion of a rigid body along a straight line.Triangle and parallelogram of forces, resultant forces, Lami’s theorem, polygon of forces, condition for equilibrium of coplanar, friction, smooth bodies laws of friction, particles on rough planes, inclined or otherwise,parallel forces moments, couples, centre of gravity, lamina of elementary shapes, jointed rods, curved surfaces of cone sphere and solids of elementary shapes, thrust on plane surface, centre of pressure intensity, transmission of fluid, pascal’s principle, balancing column of liquids.

MTH 211- LINEAR ALGEBRA I

Vector space over the real field. Subspaces, linear independence, basis and dimension. Linear transformations and their representation by matrices - range, null space, rank. Singular and non-singular transformation and matrices. Algebra of matrices.

MTH 212- REAL ANALYSIS  1

Bounds of real numbers, convergence of sequence of numbers. Monotone sequences, the theorem of nested Intervals. Cauchy sequences, tests for convergence of series. Absolute and conditional convergence of series and rearrangements. Completeness of reals and incompleteness of rationals. Continuity/and differentiability of functions R….) R. Rolles's and mean value theorems for differentiable functions Taylor series

MTH 214- VECTOR ANALYSIS

Elementary Vector Algebra, Vector and Triple vector Products (more application solution of vector equation, plain curves and space curves. Geometrical equation of lines and planes. Linear independence of vectors; components of vectors, direction cosines; position vector and scaler products; senentfrenent formulae; differential definition of gradients, divergent and simple multiplication)

MTH 229- NUMERICAL ANALYSIS 1

Solution of algebraic and transcendental equations. Curve fitting. Error analysis. Interpolation and approximation. Zeros or non-linear equations ‘to one variable’. Systems of linear equations. Numerical differentiation and integration.

 MTH 213- MATHEMATICAL METHODS 1

Some techniques of integration; by substitution , by parts and partial fraction.

Differentiation; reduction formula, partial differentiations, applications and classification of critical points of functions of two variables. Lagrangian multipliers, Coordinate systems: change from Cartesian to polar, spherical and cylindrical coordinate systems. Taylor’s and Maclaurin’s series. Differential coefficients of the nth order. Liebnitz’s rule; application to the solution of differential equations.  Complex numbers; Hyperbolic functions, De Moivre’s theorem. Roots of complex numbers. Roots of polynomials, Exponential form. Functions of complex variables.

MTH 214- VECTOR ANALYSIS

Elementary Vector Algebra, Vector and Tripple vector products (more application of solution of vector equation, plain curves and space curves. Geometrical equation of lines and planes. Linear independence of vectors; components of vectors, direction cosines; position vector and scalar products; senentfrenent formulae; differential definition of gradients, divergent and simple multiplication)

MTH 215-  MATHEMATICAL STATISTICS

Regression and correlation: least squares estimation of simple linear regression, interpretation of regression coefficient ; use of regression. The product-moment and rank correlation, their interpretation and use. Elementary time series analysis.

Probability: finite  sample space, axioms of probability, simple theorems, concepts of probability addition and multiplication rules, conditional probability and independence, tree diagrams, Bayes’s theorem. Combinatorial analysis. Probability distributions: random variables, means and variances, binomial, hypergeometric, poisson, normal distributions.

MTH 224- MATHEMATICAL METHODS 2

Differential equations; Exact differential equations, in homogenous second order differential equations, Rigorous treatment of D-operator and application to integrations by parts, Series development of differential equations. Fourier series and application. Partial differential equations.Separation of variables. Fourier method of solution

MTH 221-  LINEAR ALGEBRA II

Systems of linear equation change of basis, equivalence and similarity. Eigenvalues and eigenvectors. Minimum and characteristic polynomials of a linear transformation (Matrix). Caley -Hamilton theorem. Bilinear and quadratic forms, orthogonal diagonalisation. Canonical forms.

MTH 222- REAL ANALYSIS 2

Uniform Continuity, Monotone functions, Riemann integration, Fundamental theorem of calculus. improper and infinite integrals. Special functions of analysis. Exponential, logarithmic and trigonometric functions.

MTH 216- INTRODUCTION TO OPERATIONS RESEARCH

Concept of operations research(OR). History of OR. Roles of OR in industries. Types of models. Introduction to OR Techniques. LP(problem formulation and graphical methods of solving LP). Feasible and infeasible region. Integer programming(graphical methods only). Concept of queuing system, use of M/M/1 and M/M/2 formulae (excluding derivation).Elements of Network Analysis. Use of forward and backward pass. Application of expected value criterion and decision tree analysis in Decision making.

Pre requisite Algebra and Trigonometry.

MTH 223- APPLIED STATISTICAL METHODS

Revision of descriptive statistics: measures of location and dispersion, graphical representation of data.

  Inference about means, proportions and standard deviations; large and small samples. The chi-square test of independence and goodness -of -fit. One way analysis of variance. Correlation and regression; tests of simple regression and correlation coefficients. Estimation and prediction in multiple regressions. Use of calculators, tables and statistical packages. Introductory inference: meaning and existence of sampling distribution, sampling distributions of the mean and proportion in samples, point and interval estimation of means and proportions, simple hypothesis testing.

MTH 225-GRAPH THEORY

Graphs : Undirected graphs. Directed graphs. Basic properties. Walk. Path.Cycles. Connected graphs. Components of a graph. Complete graph.Complement of a graph. Bipartite graphs. Necessary and sufficient conditionfor a Bipartite graph.Eulergraphs : Necessary and Sufficient condition for a Euler graph.Königsberg Bridge Problem.Planar graphs : Face-size equation, Euler’s formula for a planar graph. Toshow : the graphs K5 and K3, 3 are non-planar.Tree : Basic properties, Spanning tree, Minimal Spanning tree, Kruskal’salgorithm, Prim’s algorithm, Rooted tree, Binary tree.

MTH 227-DYNAMICS OF A PARTICLE

Motion of a particle  in a resisting medium, harder problems. Forced oscillations. Plane motion of a particle in  coordinates. Harder examples on cases on projectiles. Gravitating Particles. Changing mass.

MTH 228-  NUMBER THEORY

Prime numbers. Theory of convergence. Quadratic residues. Reciprocity  theorem. Arithmetic functions. partitions.

ENT 211: INTRODUCTION TO ENTREPRENURIAL STUDIES I

The course introduces students to the definitions, functions, types and characteristics ofentrepreneurship. This course further examines entrepreneurship and ethics, entrepreneurship theories and practice; new venture creation; forms of business, business opportunities, starting a new business, innovation, legal issues in business, insurance and environmental considerations, possible business opportunities in Nigeria and introduction to biographies of successful entrepreneurs etc.

MTH 317- INTRODUCTION TO MATHEMATICAL MODELLING

Methodology of model building; Identification, formulation and solution of problems, cause-effect diagrams Equation types. Algebraic, ordinary differential, partial differential, difference, integral and functional equations. Application of mathematical models to pluprical, biological, social and behavioural sciences.

MTH 324- OPERATION RESEARCH

Phases of operation Research Study. Classification of operation Research models, linear Programming, Simplex methods, integer linear programming, Pure and Mixed cases by Gomory Algorithm and Branch and Bound method,  Dynamic programming. Decision Theory. Inventory Models, Critical Path Analysis and project Controls.

MTH 313- COMPLEX ANALYSIS 1

Functions of a complex variable. Limits and continuity of functions of a complex variable. Derivating the Cauchy-Riemann equations. Analytic functions. Bilinear transformations, conformal mappling. Contour integrals. Cauchy's theorems and its main consequences, Convergence of sequences and series of functions of a complex variable. Power series. Taylor series.

MTH 321- COMPLEX ANALYSIS II

Laurent expansions. Isolated singularities and residues. Residue theorem Calculus of residue, and application to evaluation of integrals and to summato of series. Maximum Modulus principle. Argument principle. Rouche's theorem. The 141 fundamental theorem of algebra. Principle of analytic continuation. Multiple valued functions and Riemann surfaces.

MTH 325- NUMERICAL ANALYSIS 2

Floating – point arithmetic, use of mathematical subroutine packages; interpolation; approximation,numerical integration and differentiation; numerical solutions of ODEs. Initial valued problems(IVP)

MTH 326- COMPUTER DATA ANALYSIS TECHNIQUES

Multiple regression and the general linear models. Discrimination and classification, contingency table and non –parameter methods, computer-aided design and analysis of experiments, factorial, taguchi and other designs. Analysis of survival, reliability and quality control data. Simulation techniques in reliability analysis, uses of S-PLUS, SPSS, MATLAB, STATISTICA, GENSTAT for data analysis.

MTH 312- REAL ANALYSIS 3

Double limits. Double sequences and series. Limits and continuous functions of several variables. Derivatives of functions of several variables. Taylor’s theorem. Inverse functions and implicit function theorems.

MTH 328- STATISTICAL INFERENCE

Principles and methods of estimation, methods and maximum likelihood. Use of unbiasedness and minimum variance in selecting good estimator. Interval estimation. Derivation of point and interval estimators of means, proportions and standard deviations.

  Principle of hypothesis testing; type I and type II errors. Power curve-values. The s.t. chi-square and f-tests. Use of non-parametric tests: the sign and median tests. Wilcoxon two sample rank test. Analysis of variance: two analysis. Quality control; acceptance sampling, control chart, cumulative-sum techniques.

MTH 311- ABSTRACT ALGEBRA

Vectors  functions of a real variable. Boundedness. limits, continuity and differentiability. functions of class C’. Taylor’s formulae. Analytical functions. Curves; regular differentiable and smooth. curvature and torsion. Tangent line and normal plane.

  Vector functions of a vector variable; linear continuity and limits. Directional derivatives. Differentiable functions and functions of class C’. Taylor’s theorem and inverse function theorem. Concept of a surface parametric representation, tangent plane and normal lines.Topological properties of simple surfaces. 

MTH 316- VECTOR AND TENSOR ANALYSIS

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 tensors.

MTH 313- COMPLEX ANALYSI 1

Functions of a complex variable. Limits and continuity of functions of a complex variable. Derivating the Cauchy-Riemann equations. Analytic functions. Bilinear transformations, conformal mappling Contour integrals. Cauchy's theorems and its main consequences, Convergence of sequences and series of functions of a complex variable. Power series. Taylor series.

MTH 321-COMPLEX ANALYSIS II

Laurent expansions. Isolated singularities and residues. Residue theorem Calculus of residue, and application to evaluation of integrals and to summato of series. Maximum Modulus principle. Argument principle. Rouche's theorem. The 141

fundamental theorem of algebra. Principle of analytic continuation. Multiple valued functions and Riemann surfaces.

MTH 314- DYNAMICS OF A RIGID BODY

General motions of a rigid body as a translation plus a rotation. Moment, and products of inertia 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 reference; rotating and translating frames of reference. 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 top. Procession.

MTH 318- LEBESGUE MEASURE AND INTEGRALS

Lebesgue measure; measurable and non-measurable sets. Measurable functions. Lebesgue integral: Integration of non-negative functions, the general integral convergence theorems

MTH 315 FLUID DYNAMICS

Real and ideal fluids. Differentiation following motion of fluid particles. Equations of motion and continuity for incompressible inviscid fluids. Velocity potentials and Stoke’s stream functions. Bernoulli’s equation  with application to flow along curved paths. kinetic energy. Sources, sinks, doublets in 2- and 3- dimensions, limiting stream lines. Images in rigid infinite plane.

MTH 327- PROBABILITY THEORY

Combinatorial analysis. Probability models for study of random phenomena in finite sample spaces. probability distributions of discrete and continuous random variables. Expectations and moments generating functions, Chebyshev’s inequality. Bivariate, marginal and conditional distributions and moments. Convolution of two distributions, the central limits theorem, and its uses. probability generating functions. Univariate characteristics functions. Various models of convergence/ Laws of large numbers and central limits theorem using characteristics functions. Random walks and markov chains Intoduction to poisson processes.  

MTH 322- ANALYTICAL DYNAMICS

Degrees of freedom. Holonomic and holonomic constraints. Generalised co-ordinates lagrange's equations for holonomic systems; face dependent on co-ordinates only, force obtainable from a potential. Impulsive force.

MTH 323 -MATHEMATICAL METHODS 3

specialoperators:Hermitan,projection and unitary operators.eigenvalues and eigenvectors:use of net and bra-notation.Infinite dimensional vector space; the classical orthogonal polynomial  (Legendre, Hermite and Laguerre polynomials). Rodrigue’s formula. Special functions; gama and beta functions. Bessel functions.

Elementary properties of the hypergeometric function, Detailed treatment of multiple integrals. General theory of operators. Finite dimensional representations of operators, diagonalization of opeartors. Special theory functions of operators, integral and differential operators

MTH 319 GENERAL RELATIVITY

Particles in a gravitational field: Curvilinear coordinates, intervals. Covariant differentiation;Chris-tofell symbol and metric tensor. The constant gravitational field. Rotation. The Curvature tensor. The action function for the gravitational field. The energy momentum tensor. Newton's law. Motion in a centrally symmetric gravitational field. The energy moment pseudo-tensor. Gravitational waves. Gravitational fields at large distances from bodies. Isotropic space. Space-time metric in the closed and in the open isotropic models.

MTH 329- REAL ANALYSIS 4

Riemann-satieties integration, functions of bounded variation. Uniform convergence sufficient condition for uniform convergence. sums. term by term differentiation and integration of a series of functions. Power series. Uniform continuity. Weierstrass approximation theorem.

MTH 302: SIWES

The students are required to undergo compulsory industrial attachment with the aim of acquiring industrial experience in the use, management and applications of computers. Log books are to be provided for each students in order to enable the management of the companies to assess and keep records of performance of the students, at the end of the attachment, the students will submit the log books with a written report to the department for assessment by presenting the work in a seminar to be organized by the department

ENT 311: ENTREPRENUERIAL SKILLS I

The course focuses the attention of the students to the practical aspects of entrepreneurship by venturing into the following categories: Agriculture/Agro Allied (fish farming, crop production, animal husbandry such as poultry, piggery, goat etc,  groundnut oil making, horticulture (vegetable garden, flower garden), poultry), Services (bakery, radio/TV repairs, barbing/ hair dressing salon, car wash, catering, courier, event planning, fashion design, vehicle maintenance, film production, interior decoration, laundry, music production, phone call centre, rental, restaurant, tailoring/ knitting, viewing centre), Manufacturing (carving, weaving, sanitary wares, furniture making, shoe making, plastic making, table making, bead making, bag making, sachet water production, cosmetics, detergents), Commerce (buying and selling, purchasing and supply, bookkeeping, import and export etc), Information & Communication Technology (ICT) (business centre, computer maintenance, handsets repairs, internet cafe etc), Mining/Extraction (kaolin, coal mining, metal craft such as blacksmith, tinsmith etc, vegetable oil/and salt extractions etc), Environment (fumigation, household cleaning waste disposal etc), Tourism (car hire, craft work, hotel/catering, recreation centre), Power (generator mechanic, refrigeration/air conditioning, electricity wiring etc), Production/Processing (glassware production/ceramic, metal working/fabrication, steel and aluminium door and windows, paper production water treatment/conditioning/packaging, brick laying, bakery, iron welding, building drawing, tailoring, carpentry, leather tanning, printing, food processing/packaging/preservation). Students are to select two of the following areas of interest for practical. Topics should also include Products/Service Exhibition and Quality Control, Business Ownership Structures, Mentorship.

ENT 321: ENTREPRENEURIAL SKILLS II

The course is a continuation of ENT 311. It focuses the attention of the students on creativity, feasibility study, legal framework, governmental policies, business negotiation, etc.  Students should select two areas of interest for practical and exhibition. At the end of the semester students will undertake excursion and internship and produce report.

multiple integrals. Existence and evaluation by repeated integration. Change of variables.

MTH 414- OPTIMIZATION THEORY

Linear programming models. The simplex Method: formulation and theory. Quality integer programming; Transportation problem. Two-person zero-sum games. Nonlinear programming: quadratic programming Kuhn-tucker methods. Optimality criteria. Simple variable optimization. Multivariable techniques. Gradient methods.

MTH 415- STOCHASTIC PROCESSES

Random walk, simple and general random walk with absorbing and reflecting barriers. Markovian processes with finite chains. Limit theorem. Poisson, branching, birth and death processes. Queueing processes; M/M1, M/M/S, M/G/1 queues and their waiting time distributions. Relevant applications.Pre-requisite -probability distribution, statistical inference.

MTH 421-SURVEY METHODOLOGY AND QUALITY CONROL

Survey methodology,planning of surveys, simple random, stratified, cluster and systematic scenes. sampling for means, totals and proportions. sample size allocation in stratification. comparison of precisions. ratio and regression estimation. two stage sampling.Process control: use of control charts to achieve process stability. Tolerance limits as a function of component variability. Product control: design of simple, double multiple, sequential sampling plans. Cumulative sum charts, feedback theory for controlling continuous process.

MTH 422-  NUMERICAL ANALYSIS III

Finite difference equation and operations; Discrete variable methods for solution of IUPS – ODES. Discrete and continuous Tan methods for solving IUP – ODES, error analysis. Partial differential equation. Finite difference and finite elements methods. Stability convergence and error analyses.

MTH 425- FUNCTIONAL ANALYSIS

Hilbert Spaces, bounded linear functionals, operators an Banach spaces, topological vector spaces, Banach algebra

MTH 427- GENERAL TOPOLOGY:

Topological spaces, definition, open and closed sets neighbourhoods. Coarser, and finer topologies. Basis and sub- bases. Separatic axioms, compactness, local compactness, connectedness. Construction of new topological spaces from given ones; Sub-spaces, quotient spaces. Continuous functions, homeomorphons, topological invariants, spaces of continuous functions: Pointivise and uniform convergence.

ENT 411: ENTREPRENUERSHIP DEVELOPMENT I

This course further exposes the students to the entrepreneurial process of writing feasibility studies and business plans.  The students are required to form cooperative societies in order to collaboratively generate business ideas and funds. Topics should include models of wealth creation, sustainability strategies, financial/ investment intelligence and international business.  Students are to select one area of interest for practical and exhibition. The programme involves Recognition, Reward and Awards (RRAs) and Mentorship.

ENT 421: ENTREPRENEUSHIP DEVELOPMENT II

This course, which is a continuation of ENT 411, further exposes the students to the entrepreneurial process of strategic management.  Topics include business financing, venture capital, managing business growth, negotiation, time and self-management, leadership, ICT and succession plan, defence of feasibility study and business plans.

ADMISSION REQUIREMENTS:

1. Four-Year Full Time Degree Programme(UTME)

Candidates seeking admission into this programme should posess any of the following qualifications:

• At least five Ordinary level credit passes in WAEC SSCE/ GCE/NECO SSCE at not more than two(2) sittings.

The subjects should include, English Language, Mathematics, and any three(3) of Physics, Chemistry, Biology, Agricultural Science.

The University Tertiary Matriculation Examination (UTME) subjects are;

• Use of English
• Mathematics
• Physics
• any of Biology, Chemistry, Agricultural Science.

1. Three- Year Full Time Degree Programme(Direct Entry)

In addition to the UTME requirements above, candidates who possess any of the following qualifications may be considered for admission:

• At least two Advanced level Passes ion the General Certificate of Education(GCE) or Higher School Certificate(HSC) or any of the recognized equivalent at not more than two sittings. The subjects should include Mathematics and any of Physics, Chemistry.
• Diploma from other recognized Universities with at least an Upper credit level pass in related discipline.
• Ordinary National Diploma(OND) with at least an Upper credit level passes in Mathematics/Statistics, Computer Science, or Science Laboratory Technology(SLT) from any recognized Polytechnic or College of Technology.
• Higher National Diploma(HND) with at least a Lower credit level passes in Mathematics/Statistics, Computer Science, or Science Laboratory Technology(SLT) from any recognized Polytechnic or College of Technology.
• Nigeria Certificate of Education(NCE) with at least a credit level in Mathematics and Physics/Chemistry/Computer Science/Geography from a recognized College of Education. In addition candidates should have at least overall credit level pass or at least a 9-point GPA.
• A Bachelor of Science(B.Sc) degree certificate in any of the Sciences(Physics, Chemistry, Geology/Mining, Biochemistry, Environmental Science, Microbiology, Biological Science,Plant Biology And Biotechnology, Animal and Enviromental Biology(Zoology), SLT, Statistics, Computer Science and Engineering) with at least 3^rd Class Honours.