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Department of Mathematics

INTRODUCTION

The Department of Mathematics was established in 2012 and started the first ever 4-year undergraduate programme in the year 2013. The main objective of the department is to pursue excellence in education and research by developing appropriate curricula and teaching practices, acquiring talented and highly skilled academics by providing a conducive environment for learning, teaching and research. The department tries to educate its students by providing them exposure to real-life problems, and inculcate in them a problem solving approach. They will also be encouraged to explore and solve problems, to break new grounds and to cultivate leadership qualities. The department is disposed to organizing national and international conferences, seminars, workshops, symposia and training.

ENTRY REQUIREMENTS

For a candidate to be admitted into the four years  undergraduate programme, he/she must have obtained  five credit O-LEVEL passes in Mathematics, Physics, English and any two of Chemistry, Biology, Geography, Economics. For the three years undergraduate programme, the candidate must have obtained three A-LEVEL credit passes in Mathematics, Physics and any one of Chemistry, Biology, Economics and Geography. A Holders of NCE and National Diploma with the overall grade of credit may also be considered for admission.

REQUIREMENTS FOR GRADUATION

Bachelor of Science Degree programme in Mathematics is a four year/ 8 semester programme. Students will be required to carry out course work comprising of subjects from Mathematics, Computer Science, Physics and General Studies division. The minimum number of credit units for graduation is 141 and must also have a CGPA of at least 1.5.

PROFESSIONAL SKILLS

As a graduate of this department, you would have been exposed to the elegance of Mathematics as an intellectual discipline and its enormous power as a tool for solving scientific problems, and encouraged from a very early stage to take pride in presentation of your work. This course will help you produce logical arguments and express yourself precisely and to actively enjoy solving problems. These qualities will make you attractive to potential employers of labour.

CAREER OPPORTUNITIES

Our graduates go on to rewarding careers in areas as diverse as finance; teaching; mathematical and scientific research; industry; management and information technology.

 

 

 

ADVICE ON COURSES

A student shall normally be required to register for and pass a prescribed minimum number of units in each academic session. In addition, a student must register for, and pass General studies spread over the first, second and third academics sessions. These Courses are made available in a particular session and detailed in the Head of Departments office and Department notice boards as well as the University website.

All students have to consult their Level Registration Officer and get their registration forms signed by them before handing over the same to the Dean’s office or academic office.

Changes to Registration (Addition, Deletion and Withdrawal from Courses)

After registration, a student may add or delete courses provided this is done with the approval of the Faculty and with the consent of the Department. All course changes add and drop must be made on the special course change form which is obtainable from the office of the Dean or Academic office.

Late Registration

For reasons beyond his/her control, if a student is not able to appear during registration or send an authorized representative with a medical certificate, he/she may apply to the Dean of the Faculty or the Academic Secretary for late registration.

PROGRAMMES OF STUDY

The Department of Mathematics offers programme of courses leading to the degree of B.Sc. (Hons) in Mathematics and provides service courses to other departments in the Faculty of Science, and Education SCHEDULE OF

100 LEVEL COURSES

Course Code

Title

Units

Semester

MTH 101

Elementary Mathematics I

3

1st

MTH 102

Elementary Mathematics II

3

2nd

MTH 103

Elementary Mathematics III

3

1st

STA 111

Probability I

4

1st

STA 112

Descriptive Statistics

3

2nd

 

 

 

CSC 101

Introduction to Computer Science

3

1st

PHY  101

General Physics I

3

1st

PHY  102

General Physics II

3

2nd

CHM 101

General Chemistry I

3

1st

CHM 102

General Chemistry II

3

2nd

GST 111

Communication in English I

2

1st

GST 112

Philosophy, Logic and Human Existence

2

2nd

GST 113

Use of Library, Study Skills and ICT

2

1st

GST 123

 

GST 124

Communication in French

      OR

Communication in Arabic

2

 

2

2nd

 

2nd

TOTAL  CREDIT UNITS                                                        39

Elective: A minimum of 0 unit

STA 121

Basic Statistical Methods

3

1st

 

200 LEVEL COURSES

Course No.

Course Title

Units

Semester

MTH 201

Mathematical Methods I

3

1st

MTH 202

Elementary Differential equations I  

3

2nd

MTH 203

Sets, Logic and Algebra I

3

1st

MTH 204

Linear Algebra I

2

1st

MTH 205

Linear Algebra II  

2

2nd

MTH 206

Real Analysis I

3

2nd

MTH 209

Introduction to Numerical Analysis

3

2nd

CSC   201

Computer Programming I

3

1st

CSC 202

Computer Programming II

3

2nd

STA 211

Probability II

4

1st

GST 211

History and Philosophy of Science

2

1st

GST 222

Peace Studies and Conflict Resolution

2

2nd

GST 223

Communication in English II

2

 

GST 224

Nigerian Peoples and Culture

2

 

TOTAL CREDIT UNITS 37

           Electives: A minimum of 0 unit and maximum of 4 units to be selected

 

Course No.

Course Title

Units

Semester

STA 201

Statistics For Agriculture And Biological Sciences

4

1st

STA 202

Statistics for Physical Science & Engineering

           

4

2nd

 

 

 

 

 

300 LEVEL COURSES

Course No.

Course Title

Units

Semester

MTH 301

Abstract Algebra I     

3

1st

MTH 302

Metric Space Topology

3

2nd

MTH 303

Ordinary Differential Equations II

3

1st

MTH 304

Vector and Tensor Analysis

3

2nd

MTH 305

Complex Analysis I

3

1st

MTH 306

Complex Analysis II

3

2nd

MTH 307

Abstract Algebra II

3

2nd

MTH 308

Real Analysis II

3

1st

MTH 309

Introduction to Mathematical Modeling

3

1st

MTH 310

Discrete Mathematics

4

2nd

GST 311

Introduction to Entrepreneurial Skills

2

1st

GST 312

Introduction to Entrepreneurship Studies

2

2nd

TOTAL CREDITS UNITS                                                     35 Units

 

 

 

Electives:        A minimum of 0 units from the list below-

MTH 311

Affine and Projective Geometry

3

1st

STA 311

Probability III

4

1st

STA 321

Distribution Theory

2

2nd

ST A 331

Statistical Inference II

4

1st

MTH 312

Optimization Theory  

4

2nd

MTH 313

Geometry

3

1st

MTH 314

Analytical Dynamics   I

3

2nd

MTH 315

Dynamics of a Ligid Body

3

1st

MTH 316

Introduction to operations Research

3

2nd

MTH 317

Differential Geometry

3

1st

MTH 318

Numerical Method I

2

1st

MTH 319

Numerical Method II

3

2nd

 

 

 

 

YEAR IV

400 LEVEL COURSES

Course No.

Course Title

Units

Semester

MTH 401

Theory of Ordinary Differential Equations

3

1st

MTH 402

Theory of Partial Differential Equations

3

2nd

MTH 403

Functional Analysis

3

1st

MTH 404

General Topology

3

2nd

MTH 405

Lebesgue Measure and Integration

3

1st

MTH 406

Project Report

6

1st& 2nd

MTH 407

Mathematical Method II

3

1st

MTH 412

Field Theory

3

2nd

MTH 415

System Theory

3

 

MTH 419

Graph Theory

3

2nd

 TOTAL CREDIT UNITS                                                                     30

Electives: A minimum of 0 units and a maximum of 18 units from:

 

 

MTH 408

Quantum Mechanics I

3

2nd

MTH 409

General Relativity

3

1st

MTH 410

Electromagnetism

3

2nd

MTH 411

Analytical Dynamics II

3

1st

MTH 413

Fluid Dynamics

3

1st

MTH 414

Elasticity

3

2nd

MTH 415

Systems Theory

3

1st

MTH 416

Measure Theory

3

2nd

MTH 417

Groups and their representatives

3

1st

MTH 418

Groups and their Characters

3

2nd

MTH 420

Combinatorial Geometries

3

2nd

MTH 421

Ring Theory

3

1st

MTH 422

Boolean Algebra

3

2nd

MTH 423

Lattice Theory

3

1st

MTH 424

Number Theory

3

2nd

MTH 425

Module Theory

3

1st

MTH 426

Catastrophe Theory

3

2nd

MTH 427

Set Theory

3

1st

MTH 428

Functional Analysis II

3

2nd

STA 411

Probability IV

4

1st

STA 412

Stochastic Processes

4

2nd

STA 424

Game Theory

4

2nd

 

COURSE DESCRIPTION

MTH 101 ELEMENTARY MATHEMATIC I: (3 Units)

Elementary set theory, subsets, union, intersection, complements, and Venn diagrams. Real numbers, integers, rational and irrational numbers, mathematical induction I, real sequences and series, theory of quadratic equations, binomial theorem. Complex numbers; algebra of complex numbers; the Argand Diagram, De Moivre's theorem, nth roots of unity; Circular measure, trigonometric functions of angles of any magnitude, addition and factor formalae.

 

MTH 102 ELEMENTARY MATHEMATICS II: (3 Units)

Geometric representation of vectors in 1-3 dimensions, components, direction cosines; Addition and Scalar multiplication of vectors, linear independence; Scalar and vector products of two vectors, differentiation and integration of vectors with respect to a scalar variable; Two-dimensional co-ordinate particles; Components of velocity and acceleration of a particle moving in a plane; Force, momentum; Impact of two smooth spheres, and of a sphere on a smooth sphere.

 

MTH 103 ELEMENTARY MATHEMATICS III: (3 Units)

Pre-requisite -MTH 101

Function of a real variable, graphs, limits and idea of continuity; The derivative, as limit of rate of change; Techniques of differentiation; Extreme curve sketching; Integration as an inverse of differentiation. Methods of integration;Definite integrals; Application to areas, volumes; Two-dimensional co-ordinate geometry. Straight lines, circles, parabola, ellipse, hyperbola Tangents and normal

STA 111: Probability I : 4 Units

Generation of statistical events from set-theory and combinatorial methods; Elementary principles of probability; Types and distributions of random variables; the binomial, Poison, hypergeometric, normal and exponential distributions; Expectations and moments of random variables; probability sampling from tables of random numbers; selected application/practical.

STA 112: Descriptive Statistics: 3 Units

Basic statistical concepts; Statistical data: Types, sources, methods of collection, classification, presentation and interpretation of statistical data. Frequency distribution, Measures of location, partition, dispersion, skewness and kurtosis; Moments and Sheppard’s correction. Error and Approximation, Rates, ratios and index numbers .Applications/Practical

STA 121: Basic Statistical Methods: 3 Units

Population and sample, sampling distribution, Estimation (point and interval) and tests of hypothesis concerning population mean and proportion; Elementary time series, demographic measures; Design of experiments; Analysis of variance and covariance; Simple regression and correlation; Contingency tables; Some non-Parametric tests; Applications/practical.

200 LEVEL COURSES

MTH 201MATHEMATICAL METHODS 1: (3 Units) (L30: P 0: T 1)

Pre-requisite –MTH 101, 103.

Real-valued functions of a real variable; Review of differentiation and integration and their applications; Mean value theorem; Taylor series; Real-valued functions of two or more variables; Partial derivatives; Chain rule, Extreme, langranges multipliers; Increments, differentials and linear approximations; Evaluation of line, integrals; Multiple integrals.

MTH 202: ELEMENTARY DIFFERENTIAL EQUATIONS I: (3 Units)

First order ordinary differential equations, existence and uniqueness, second order ordinary differential equations with constant coefficients, Laplace transforms, Solutions of initial-value problem by Laplace transform method, Simple treatment of partial differential equations in two independent variables with Applications,  Finite linear difference equations,  Application to geometry and physics. Pre-requisite-MTH 103

MTH 203: SETS, LOGIC AND ALGEBRA I: (3 Units)

Pre-requisite -MTH 101

Introduction to the language and concepts of modern Mathematics, Topics include; Basic set theory; mappings; relations; equivalence and other relations; Cartesian products, Binary logic, methods of proof, Binary operations, Algebraic structures, semi groups, rings, integral domains, fields.  Homeomaphics, Number systems, properties of integers rationals, real and complex numbers.

MTH 204: LINEAR ALGEBRA I: (2 Units)

Pre-requisite -MTH 101,102

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 205: LINEAR ALGEBRA II: (2 Units)

Pre-requisite MTH 101, 102. Co-requisite MTH 203, 204.

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 206: REAL ANALYSIS I: (3 Units)

Pre-requisite -MTH 101, 103

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 rearrangement, Completeness of reals and incompleteness of rationals, Continuity/and differentiability of functions from R to R. Rolles's and Mean value theorems for differentiable functions, Taylor series.

MTH 209: INTRODUCTION TO NUMERICAL ANALYSIS: (3 Units)

Pre-requisite -MTH 101, 103

Solution of algebraic and transcedental equations, Curve fitting, Error analysis, Interpolation and approximation, Eros of non- linear equations ‘to one variable’, Systems of linear equations, Numerical differentiation and integration, Initial value problems for ordinary differential equation.

STA 201: Statistics For Agriculture And Biological Sciences:  4 (Units)

Use of statistical methods in biology and agriculture, Frequency distributions, measure of location, partition and dispersion, Elements of probability, laws of probability; The binomial, Poisson, geometric, hypergometric, negative binomial and normal distributions, Estimation (point and interval) and tests of hypothesis, Design of simple agricultural and biological experiments; Analysis of variance; Simple regression and correlation; Contingency tables; Some non-parametric tests; Pre-requisite: O’ level pass in Mathematics.

STA 202: Statistics For Physical Sciences And Engineering:  (4 Units)

Use of statistical methods in physical sciences and engineering, Measure of location, partition and dispersion in ungrouped and grouped data, Elements of probability and probability distributions: Normal, binomial, Poisson, geometric, hypergeometric, negative binomial distributions. Estimations and tests of hypothesis concerning the parameters of distributions, Regression, correlation and analysis of variance, Contingency tables Non-parametric inference, Introduction to design of experiment. Analysis of variance, Pre-requisites: O’ level pass in Mathematics.

STA 211: Probability II: (4 Units)

Further combinatorial analysis, Probability laws, conditional probability, Independence, Baye’s theorem, Probability of discrete and continuous random variables: binomial, Poisson, geometric, hypergeometric, rectangular (uniform), normal, and exponential, Expectations and moments of random variables,Bayes’ Theorem.  Chebyshev’s inequality, Joint Bivariate, marginal and conditional distributions, The Chebyshev’s limit theorem, and its issues, Limiting distribution and moments. Pre-requisites: STA 111 and MAT 101 or equivalent.

MTH 301: ABSTRACT ALGEBRA I: (3 Units)

Pre-requisite -MTH 101, 203, 206

Group: definition, examples including permutation groups, Sub-groups, Cosets Langranges theorem and applications, Algebraic structures, semi groups, rings, integral domain, fields, Number systems: properties of integers, rational, real and complex numbers, Cyclic groups, Rings: definition examples including Z, Zn, rings of polynomials and matrices. Integral domains, fields, Polynomial rings, factorization, Euclidean algorithm for polynomials H.C.F. and L.C.M. of polynomials.

MTH 302: METRIC SPACE TOPOLOGY: (3 Units)

Review of Set theory, Metricspaces and examples, Open spheres (or balls), Open sets and neighbourhoods, Closed sets, Interior, exterior, frontier, limit points and closure of a set, Dense subsets and separable space, Convergence in metric space, Homeomorphisms, Continuity and compactness, connectedness. Pre-requisite -MTH 206.

 

MTH 303: ELEMENTARY DIFFERENTIAL EQUATIONS II: (3Units)

Pre-requisite.- MTH 202.

Series solutions of second order linear equations, Bessel, Legendre and hyper-geometric equations and functions. Gamma and Beta functions, Sturm-Liouvelle problem.Orthogonal polynomials and functions, Fourier, Fourier-Bessel and Fourier-Legendre Series, Fourier transformation, Solution of C.L Laplace, Wave and heat equations by Fourier method

MTH 304 VECTOR AND TENSOR ANALYSIS: (3 Units)

Pre-requisite -MTH 201, 204

Vector algebra, Vector, dot and cross Products, Equating of curves and surfaces, Vector differentiation and applications, Gradient, divergence and curl.Line,surface and volume integrals Green’s Stoke's and divergence theorems, Tensor products of vector spaces, Tensor algebra, Symmetry, Cartesiantensors.

MTH 305: COMPLEX ANALYSIS I: (3 Units)

Pre-requisite -MTH 203, 207

Functions of a complex variable; Limits and continuity of functions of a complex variable; Derivation of the Cauchy-Riemann equations; Analytic functions; Bilinear transformations, conformal mapping.

MTH 306: COMPLEX ANALYSIS II (3Units)

Pre-requisite -MTH 203, 207

Contour integrals-Cauchy’s theorems and its main consequences; Convergence of sequences and series of functions of a complex variable; Power series; Tailor series; Laurent expansions;  Isolated singularities and residues; Residue 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 analytic continuation; Multiple valued functions and Riemann surfaces.

MTH 307: ABSTRACT ALGEBRA II: (3 Units)

Pre-requisite -MTH 203, 206

Normal subgroups and quotient groups; Monomorphic isomorphism theorems; Cayley's theorems; Direct products; Groups of small order; Group acting on sets; Sylow theorems; Ideal and quotient rings. P.I.D. 8, U.F.D ’S euclides rings; Irreducibility; Field extensions, degree of an extension, minimum polynomial; Algebraic and transcendental extensions; Straight edged and compass constructions.

MTH 308: REAL ANALYSIS II: (3 Units)

Pre-requisite -MTH 206

Riemann integral of functions from R to R, continuous monopositive functions;  Functions of bounded variation; The Riemann Strielties integral; Point wise and uniform convergence of sequences and series of functions from R to R; Effects on limits (sums) when the functions are continuous differentiable or Riemann integrable; Power series.

MTH 309: INTRODUCTION TO MATHEMATICAL MODELLING: (3 Units)

Pre-requisite -MTH 201, 202, 204 (L 30: P 0: T 15)

Co-requisite -MTH 302, 303

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.

MTH 310: DISCRETE MATHEMATICS: (4 Units)

Groups and subgroups; Group Axioms, Permutation Group, Cosets, Graphs; Directed and un-directed graphs, subgraphs, cycles, connectivity, Application (flow Charts) and state transition graphs; lattices and Boolean Algebra, Finite fields: Mini polynomials. Irreducible polynomials, polynomial roots, Application (error-correcting codes, sequences generators). MTH -201, 202, 203

MTH 311: Affine and Projective Geometry (3 Units) 

Linear groups; affine transformations; symmetry; congruence; isometry. Convex hulls; Helly type theorems; separability; support lines, tangents, extreme points; properties of polyhedral; Projective spaces over a field. Desargues’ Theorem. Pre-requisite- MTH 204,205

MTH 312: OPTIMIZATION THEORY: (4 Units)

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 201, 202, 302, 303.

MTH 313: GEOMETRY: (4 Units)

Co-ordinate in R. Polar co-ordinates; Distances between points, surfaces and curve in space. The plane and the straight line. Basic projective Geometry, Affine and Eucidean Geometries.

Pre-requisite MTH 204

 

 

MTH 314: ANALYTICAL DYNAMICS: (3 Units)

Degrees of freedom. Holonomic and holonomic constraints. Generalized co-ordinates lagrange's equations for Holonomic systems; face dependent on co-ordinates only, force obtainable from a potential. Impulsive force. Pre-requisite MTH 204

MTH 315: DYNAMICS OF A RIGID BODY: (3 Units)

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 references; rotating and translating frames of reference;  Coriols 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.

Pre-requisite- MTH 201,202.

MTH 316: INTRODUCTION TO OPERATIONS RESEARCH: (3 Units)

Phases of operation Research Study; Classification of operation Research models, linear; Dynamic and integer programming; Decision Theory; Inventory Models, Critical Path Analysis and project Controls. Pre-requisite – MTH 204, STA 211

MTH 317: DIFFERENTIAL GEOMETRY: (3 Units)

Vector functions of a real variable; Soundedness; Limits; Continuity and differentiability; Functions of Class C; Taylor’s Formulae; Analytic functions; Curves: regular, differentiable and smooth; Curvature and torsion;Tangent line and normal plans Vector: Functions of Vector Variable: Linear continuity and limits. Directional 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 -313.

MTH 318: NUMERICAL ANALYSIS I :( 2 Units)

Floating – point arithmetic; Use of mathematical subroutine packages; Interpolation; Approximation; Numerical Integration and Differentiation; Solution of non-linear equations; Solution of Ordinary differential equations.

MTH 319: NUMERICAL METHODS II      (2 Units)

Floating point arithmetic; Use of mathematical subroutine packages; error analysis and norms; alternative methods, computation of eigenvalues and eigenvectors, related topics; numerical solution of boundary value problems for differential equations, solution of non-linear systems of algebraic equations; least-squares of over determined systems.

STA 311: Probability III : ( 4 Units)

Brief revision of basic concepts, Probability generating function for Bernnoulli, Binomial, poisson, Hypergeometric, negative binomial, and multinomial distributions, Univariate and bivariate moment generating functions, Urn models, Sampling with and without replacement, Inclusion-exclusion theorem, Allocation and matching problems, Univariate characteristic functions, Various modes of convergence, Law of large numbers and the central limit theorem using characteristic functions, Random walk and Markov chains, Introduction to Poisson Processes.

Pre-requisite: STA 211.

STA 321: Demography:  2(2L, 0p) Units

Demographic data: Types and Sources, Life table: Construction and applications, Definition of basic concepts, Estimation of Population parameters from defective data, Stable and quasi-stable population, population projections. Pre-requisite: STA 212.

STA 331: Statistical Inference III: ( 4 Units)

Criteria of estimation: consistency, unbiasedness, efficiency, minimum variance and sufficiency, Methods of estimation: maximum likehood, least squares and method of moments, Confidence intervals, Simple and composite hypotheses, Likehood ratio test.  Inferences about means and variance, Rao-Cramer inequality, consistency, efficiency, best asymptotic normality, Gauss-Markov and Fisher-Cochran theorems, Test of hypothesis, Neyman-Pearson theorem. Pre-requisite: STA 212.

400 LEVEL COURSES

MTH 401: THEORY OF ORDINARY DIFFERENTIAL EQUATIONS ( 3 Units)

Differential equations: existence and uniqueness theorems, Linear system of equations, Floquet’s theory, Stability theory, Classification of integral equations volterra and fredholmequations, Equations with Hermitian kernels, Hilbert-Schmidt theorem and consequences. Representation formulae for the solution of initial and boundary value problems, Green’s functions Applications. Pre-requisite- MTH 303

MTH 402: THEORY OF PARTIAL DIFFERENTIAL EQUATIONS ( 3 Units)

Theory and solutions of first-order and second order linear equations; Properties of partial differential equations and techniques for their solution; Fourier methods; Green’s functions; Integral transform methods; Variational techniques and complex variable methods; Perturbation theory; Applications. Pre-requisite- MTH 303

MTH 403:      FUNCTION ANALYSIS  3 Units

Introduction to the theory of normed spaces; Banach spaces; Hilbert Spaces; bounded linear functionals, operator on Banach spaces Spectral theory of operations on Hilbert spaces. Pre-requisite-MTH 302

MTH 404: GENERAL TOPOLOGY: (3 Units) Topological spaces, definition, open and closed sets neighbourhoods; Coarser, and finer topologies;  Basis and sub- bases; Separation axioms, compactness, local compactness, connectedness;  Construction of new topological spaces from given ones; Sub-spaces, quotient spaces. Continuous functions, homeomorphism, topological invariants, spaces of continuous functions: Point wise and uniform convergence. Pre-requisite MTH302

MTH 405: LEBESGUE MEASURE AND INTEGRALS (3 Units)

Lebesgue measure; measurable and non-measurable sets; Measurable functions. Lebesgue integral: Integration of non-negative functions, the general integral convergence theorems. Pre-requisite-MTH 308

MTH 406: PROJECT: (6 Units)

This research project is aimed at introducing and exposing the student to the methodology of conducting research in an area of mathematical interest, The student, with guidance of a staff member, select a topic of interest and thereafter seeks the approval of the Department; At least one seminar will be given by the student in connection with the project.

MTH 407: MATHEMATICAL METHODS II: (3 Units)

Calculus of variation: Lagrange's functional and associated density. Necessary condition for a weak relative extremum; Hamilton's principles; Lagrenge's equations and geodesic problems; The DU Bois-Raymond equation and corner conditions;Variable end-points and related theorems. Sufficient conditions for a minimum Isopherimetric problems. Variational integral transforms. Laplace, Fourier and Hankel transforms; Complex variable methods convolution theorems; Application to solution of differential equations. Pre-requisite-MTH - 303, 305.

MTH 408: QUANTUM MECHANICS: (3 Units)

Particle- wave duality.Quantum postulates.Schroedinger equation of motion. Potential steps and wells in 1-dim  Heisenlberg  formulation. Classical limit of Quantum mechanics. Computer brackets. Linear harmonic oscillators. Angular momentum. 3-dim square well potential. The hydrogen atom collision in 3- dim. Approximation methods for stationary problems.

Pre-requisite- MTH 303, 314

MTH 409: GENERAL RELATIVITY: (3 Units)

Particles in a gravitational field: Curvilinear coordinates, intervals; Covariant differentiations; Christofell symbol and metric tensor; the constant gravitational field; Rotation; The Curvature tensor. Theaction functions for the gravitational field. The energy momentum tensor; Newton's law; Motion in a centrally 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. The re shift.

Pre-requisite- MTH 302, 314.

 

MTH 410: ELECTROMAGNETISM: (3 Units)

Maxwell's field equations; Electromagnetic waves and Electromagnetic theory of lights. Plane electromagnetic waves in non -conducting media, reflection and refraction at place boundary. Waves guides and resonant cavities. Simple radiating systems. The Lorentz-Einstein transformation. Energy and momentum. Electromagnetic 4-vectors. Transformation of (E.H.) fields. The Lorentz force.

Pre-requisite- MTH 302. 303, 314

MTH 411: ANALYTICAL DYNAMICS II: (3 Units)

Lagrange's equations for non-holonomic systems. Lagrangian multipliers. Variational principles:  Calculus of variation, Hamilton's principle. Lagrange's equation from Hamilton's Principles. Canonical transformations. Normal equations. Pre-requisite-MTH 302. 303, 314

MTH 412: FIELD THEORY: (3 Units)

Gradient, divergence and curl: Further treatment and application of the differential definitions. The integral definition of gradient, divergence and curl: Line, surface and volume integrals: Green's Gauss' and Stoke's theorems. Curvilinear coordinates. Simple motion of tensors. The use tensor of notation.

Pre-requisite. MTH -304.

MTH 413: FLUID DYNAMICS; (3 Units)

Real and Ideal fluids. Differentiation following the motion of fluid particles. Equations of motion and continuity for incompressible solid fluids. Velocity potentials and Stoke's Stream functions. Bernoulli’s equation with application to flow along curved paths. Kinetic energy. Sources, sinks, doubles in 2-and-3-dimensions, limiting streamlines. Images and rigid planes.

Pre-requisite-MTH -314.

MTH 414:  ELASTICITY: (3 Units)

Particle gravitational field: Curvilinear coordinates, intervals. Covariant differentiation. Christffel symbol and metric tensor. The constant gravitational field. Rotation.

Pre-requisite- MTH 302, 303, 314

MTH 415: SYSTEM THEORY: (3 Units)

Lyapunov’s Theorems. Solution of Lyapunov stability equation ATP  PA - Q. Controllability and observability. Theorem on existence of solution of linear systems of differential operations with constant coefficients.

Pre-requisite- MTH 302

MTH 416: MEASURE THEORY: (4Units)

Abstract integration, Borel measures, LP-Spaces. Elementary Hilbert space theory.

Pre-requisite-MTH 403

MTH 417:  GROUP AND THEIR REPRESENTATIONS (3 Units)

Elements of group theory. Symmetric groups. Unitary vector spaces. Linear operators and their matrix representations. Invariance of functions and operators. Classification of eigen functions. Reducubility. Schur’s lemmas. General orthogonal relation. Kroneker product and adjoint representations.

Pre-requisite- MTH 301, 307

MTH 418: GROUP AND THEIR CHARACTERS (3 Units)

Group representation. Elementary properties of group characters. Induced characters. Permutation groups. Arithmetic properties of group characters. Real representations.

Pre-requisite- MTH 306

MTH 419: GRAPH THEORY   (3 Units)

Graphs and subgraphs. Trees. Conncetivity. Traversability. Matching. Edge colouring. Independent sets and cliques. Vertex colouring and chromatics polynomials. Planar graphs. Directory graphs. Hyper graphs.

Pre-requisite- MTH 312

MTH 420: COMBINATORIAL GEOMETRICS (3 Units)

Independent sets. Circuits. Bases. Flats and hyperplanes. Rank function. Closure operator. Graphic matroids. Transversal matroids. Duality. Representability of matroids. Excluded minor theorems. Union of matroids. Pre-requisite-MTH 309, 316

MTH 421: RING THEORY (3 Units)

Centre and normalizer of a ring. Nilpotent ideals. Maximal and minimal ideals. Sums and products of ideals. Rings of fractions. Noetherian and Arthinian rings. Pre-requisite-MTH 301, 307

MTH 422: BOOLEAN ALGEBRA (3 Units)

Definitions and properties of Boolean algebra. Boolean homomorphism. Filter and ideals. Types of Boolean algebra. Stone representation theorem. Axioms. Duality for ideals. Duality for homomorphism.

Pre-requisite- MTH 303, 306

 

MTH 423: LATTICE THEORY (3 Units)

Partial ordered sets. Ordinal numbers. Complete lattices. Definition and properties of lattices. Lattice-morphisms. Free lattices. Modilar lattices. Distributive lattices.

Pre-requisite- MTH 301, 306

MTH 424: NUMBER THEORY (3 Units)

Divisibility. Congruences. Quadratic reciprocity. Diophantine equations. Arithmetical functions.

Pre-requisite- MTH 301

MTH 425: MODULE THEORY (3 Units)

Modules and submodules. Modules homomorphism. Sums and products of modules of fractions and vector spaces. Quotient modules. Graded modules of fractions. Noetherian modules.

Pre-requisite- MTH 301, 306

MTH 426: CATASTROPHE’S THEORY (3 Units)

Smooth and sudden changes. Multi-dimensional geometry and calculus. Thorm’s theorem. Determinancy. Codimension. Classification. The preparation theorem. Unfieldings Catastrophe Germs.

Pre-requisite-MTH 303

MTH 427: SET THEORY (3 Units)

Axioms of set theory. Operations on sets. Ordinal and cardinal numbers, well-orderings, transfinites induction and recursion. Consequences of the axiom of choice. Boolean algebras. Cardinal arithmetics. Linear orderings and trees. Infinite combinatorics and partition calculus. Descriptive set theory. Stationary sets.

Pre-requisite- MTH 300

MTH 428: FUNCTIONAL ANALYSIS II (3 Units)

Convex sets and hyper planes in vector spaces. Linear and sub linear functionals. Separation theorems. Topological vector spaces. Locally convex topological spaces. Dual spaces. Weak topologies.

Pre-requisite- MTH 403

STA 411 Probability IV 4 Units

Probability spaces, measures and distribution. Distribution of random variables as measurable functions. Product spaces; product of measurable spaces, product probabilities. Independence and expectation of random variables. Convergence almost everywhere, convergence in path mean. Control limit theorem. Laws of large number. Characteristics function and Laplace transforms. Pre-requisite STA 311 Co-requisite MAT 405.

STA 412 Stochastic Processes 4 Units

Generating functions: tail probabilities and convolutions. Recurrent events. Simple and general random walk with absorbing and reflecting barriers. Gambler’s ruin problem.  Theory of Markov chains. Continuous time Markov  processes and finite chains. Limit theorem. Poisson, branching, birth and death processes. Introduction to Queuing NEWR, Queuing processes; M/M/1, M/M/S, M/G1 queues and their waiting time distributions. Relevant applications. Pre-requisites: STA 311 and STA 312.

STA 424 Game Theory:  4 Units

Extensive forms and pure strategies. Normal forms and saddle point. Mixed strategies and minimax theorem. Dominance of strategies. Matrix games. Non-co-operative games.Co-operative games. Linear programming and matrix games. Applications. Pre-requisites: STA 324, STA 326.

EXAMINATION REGULATION

i.A student shall be at the examination hall at least ten minutes before the time of the Examination. Each student is also required to supply his/her own pen, pencils, rulers etc.

ii A student may be admitted up to forty five minutes after the start of the examination but he shall not be allowed extra time.

iii. If a student arrives later than forty five minutes (45 minutes) after the start of the examination, an            invigilator        may at his/her discretion admit him if he is satisfied that the student had    good reason for his/her lateness. The invigilator shall report the circumstances to the faculty examination          officer who shall advise the board of examiners, which    shall decide whether to accept the      student’s paper.

iv. A student may be permitted by an invigilator to leave the examination room during the course of an examination provided that:-

  1. No student shall normally be allowed to leave during the first hour or last fifteen minutes of examinations.
  2.  A student must handover his/her script to the invigilator before leaving the examination hall.

v. A student who leaves the examination room shall not be re-admitted unless throughout the       period of his/her absence he has been continually under the supervision of an invigilator        or assistant invigilator.

vi A student shall bring his/her examination card and identity card to each examination and display them in prominent position on his/her desk.

vii. Each student shall complete an attendance form with his/her number, name and signature, which shall be collected by the invigilator of each examination.

Viii. During an examination, no student shall speak to any other student, or accept as essential, to the invigilator, or make any noise or disturbance.

ix. No book, printed paper, or written document or unauthorized aid may be taken in to the          examination room by any student, except as may be stated in the rubrics of any examination paper.

x.  A student must not doing an examination directly or indirectly give assistance to any other      student or permit any other student to copy from or otherwise use his/her papers.        Similarly, a student must not directly accept assistance from any other student or use any other student’s paper.

xi. If any student is suspected or found to be infringing any of the provisions by way of cheating or disturbing the conduct of the examination, the student shall be subjected to fill Examination Malpractice form and should be clearly stated the misconduct.

xii. A student shall write his/her examination number, not his/her name, directly at the top of the  cover of every answer booklet or separate sheet of paper.

xiii. The use of scrap paper is not permitted. All rough work must be done in answer booklet and  crossed neatly, or in supplementary answer books which must be submitted to the   invigilator. Except for the printed quest paper, a student may not remove from the        examination hall/room or mutilate any paper or other material supplied.

xiv. At the end of the time allowed, each student shall stop writing when instructed to do so and shall gather his/her script together in order for collection by the invigilator.

CATEGORIES OF PUNISHMENT FOR EXAMINATION MALPRACTICE

The following offences shall carry the punishment of rustification/expulsion:

1. Impersonation at examination. This may involve the exchange of examination numbers or          names on answer sheets or the intentional use of someone’s examination number.

2.  Introduction of relevant foreign materials and cheat notes into the examination hall. 

3. Exchange of relevant materials in examination hall which may involve 

    (a) The exchange of question paper containing relevant looting materials or

    (b) Collaborating/Copying from each other or

    (c) Exchange of answer script.

4. Theft/removal of examination script or materials.

5.  Mischief by fire to examination script or materials.

6. Copying from cheat notes.

7. Consulting cheat notes outside the examination hall.

8 . facilitating/abetting cheating.

RUSTICATION FOR ONE ACADEMIC YEAR

The following offences shall carry the punishment of rustication for one session.

After first warning, the student should be rusticassted for one year.

MODE OF EXAMINATION

The Department’s total score for examination is 100 marks. It is divided in to two. First is the Continuous Assessment (CA) which carries 30 marks and second is the examination which also carries 70 marks.

GRADING SYSTEM

The Department adopted the following as its grading system which is in line with National University Commission’s (NUC) BMAS.

Marks

Grade

70-100

A

60-69

B

50-59

C

45-49

D

0-44

F

 

assigned to that course, and then summing these up and dividing by the total number of Credit Units taken for the semester.

            GPA =                        [endif]-->

iii.        Cumulative Grade Point Average (CGPA)

This is the up-to-date mean of the Grade Points earned by the student in a programme of study. It is an indication of the student’s overall performance at any point in the training programme. Cumulative Grade Point Average is calculated by adding the weighed Grade Points obtained in all the courses offered up to the end of a given session (and/or up to a point in a student’s programme or end of the programme) and then divided the sum of the total number of Credit Units of all courses registered by the student at that point.

The session GPA is based on the courses taken in a single session while the Cumulative GPA takes into account all courses taken for degree credit in the University. Both the session and Cumulative GPA are used at the end of each session in assessing academic stand (performance) and in determining the rate of progress toward the degree.

CLASSIFICATION OF DEGREE

To qualify for a Bachelor’s degree, a student must obtain a minimum of credit units for each level of study (Core and elective courses) and the total units required for his/her programme as well as the credit Unit for General Studies Courses. The degree is awarded on the basis of the students CGPA at the end of his/her degree programme as follows:

CGPA Class of Degree

 

 

The Department has adopted the NUC BMAS for class of degree which is as follows:

4.50

5.00

First Class Honours

3.50

4.49

Second Class Honours (Upper Division)

2.40

3.49

Second Class Honours (Lower Division)

1.50

2.39

Third Class Honours

0.00

1.49

Fail

 

PROBATION AND WITHDRAWAL

1.         In order for a student to continue to pursue his/her degree programme in the University, the student must attain the minimum Cumulative Grade Point Average (CGPA) of 1.50 at the end of each session. Failure to do so will result in his/her being placed on Academic Probation (Warning period) during the subsequent session. If at the end of the session during which the student is on probation, his/her CGPA still falls below the stipulated minimum (i.e. CGPA falls below 1.50), then such a student shall incur Withdrawal from a Faculty.

However, in order to minimize waste of human resources, a student so withdrawn for poor academic performance in one programme may be considered for transfer to another programme on application if his CGPA is up to 1.0, if the University is convinced that he/she stands a chance in other programmes. Application forms for such transfer are available in the Academic Secretary’s office.

2.         A student who has spent the maximum number of years for his programme and has not graduated will be asked to withdraw from the University.

3.         A student who absents himself/herself for one semester without a valid reason shall be asked to withdraw from the University, irrespective of his/her CGPA.

SPILL OVER

Subject to the condition for withdrawal and probation, students who are unable to pass all their courses at the end of their approved period study are allowed to carry-over such courses “First spill-over”. All grades scored in that session shall be fully credited to the student and scored against the class of degree awarded. In other word, if such students are able to clear (pass) the course at the end of the first spill-over, they are credited with the class of degree obtained.

Failure in any course at the end of the first spill-over session, leads the student into a second academic session as “Second Spill-over”, until the student is able to pass all his registered courses

GRADUATING WITH AN “F” GRADE IN A COURSE

Generally, the University expects student to pass all registered courses as a prelude to graduation. However, in exceptional circumstances, they may apply to graduate with an “F” grade in a particular course. Such students are expected to meet the minimum requirements for graduation in terms of credit units at different levels.

The application is made through the students Head of Department and Faculty to the Registrar, provided the course is not a core course or prescribed elective.

COLLECTION OF EXAMINATION RESULTS SLIPS

Students are advised to always collect their MIS grade slip on-line or from the Head of Department at the beginning of every session. A student may also request in writing to the Dean of the faculty for his/her result slip or semester grade sheet if the need arises. Students shall report immediately to the Head of Departments or the Dean through examinations Officer for any discrepancies in the grade given to them.

DURATION OF DEGREE PROGRAMMES

The minimum number of years to be spent to be awarded a first degree in Mathematics Programme shall be Eight (8) semesters or four sessions (for student entering at 100 level) and shall not exceed Twelve semesters or Six Sessions.

PROJECT REPORT FORMAT/STRUCTURE

In order to provide uniformity for the presentation of undergraduate student projects in the department, the project report is likely to follow this broad structure, but your chapter’s subheadings will reflect the individuality of your own project. Your report needs to be presented in the following format:

1. Cover Title Page

2. Title Page

3. Certification

4. Dedication

5. Acknowledgements

6. Table of Contents

7. Abstract

 

8. Chapter One: Introduction

9. Chapter Two: Literature Review

10. Chapter Three: Methodology/System Analysis and Design

11. Chapter Four: Analysis and Discussion/System Implementation and Testing

 

12. References

13. Appendix (Appendices)

NB: other details include:

Paper size: A4

Type Setting: Times New Roman font should be used throughout the document in size 12 1.5 Line Spacing OR in size 14 Double Line Spacing. The left margin of your document must be at least one and one-half inches (11/2 ). When binding the document the spine will be on the left side so the extra space is needed. The right margin, top margin and bottom margin must all be one inch (1’’).

Binding: Hard Cover

Submission: 3 copies

PROJECT MARKING SCHEME

Aim and objectives

It is aimed at training the students to do independent work under the guidance of a Supervisor. It also to train them to formulate problems and propose solutions

Assessment

Marks (%)

Supervisor’s Assessment:

A supervisor is he/she who supervised the students’ project from beginning to the end. He/she takes into consideration the contacts and suggestions made to the student(s) in the course of the project.

15

Oral Examination

  • student is expected to present his/her research work before the members of the staff.
  • Response to Questions: At the end of the presentation, questions will be asked by the audience and the student be assessed on how he/she response to the questions.

10

 

20

Quality of the Project

The quality of the project will be assessed by taking into consideration the following:

  • Type setting
  •  
  • Correct Project format
  •  
  •  
  • Main body (9,10 &11 above)
  •  
  •  

 

 

5

5

5

5

5

20

5

5

Total

100

 

 

Note: There shall be a moderation of the projects by the external examiner

 

 

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