**100 LEVEL**

FIRST SEMESTER | SECOND SEMESTER | ||||||

Course Code | Course Title | Credits | Course Code | Course Title | Credits | ||

*MTH110 | Algebra Trigonometry | 03 | *MTH123 | Vectors, Geometry etc | 03 | ||

*MTH112 | Calculus | 03 | *MTH125 | Diff. equations and Dynamics | 03 | ||

*CSC110 | Introd to computing | 03 | *MTH129 | Statistics | 03 | ||

*CHM111 | General Chemistry I | 03 | *CSC120 | Introduction to use of Software Packages | 03 | ||

*CHM113 | Organic Chemistry I | 03 | *CHM122 | General Chemistry II | 03 | ||

GLY110 | Introduction to Geology | 03 | *CHM124 | Organic Chemistry II | 03 | ||

PHY109 | Practical Physics | 02 | PHY124 | Electromagnetism and Modern Physics | 04 | ||

PHY111 | Mechanics, Thermal Physics and Properties of Matter | 03 | +GST 121 | Peace Studies/ Conflict Resolution | 02 | ||

PHY113 | Vibrations, Waves and Optics | 03 | +GST 122 | Nigeria Peoples and History | 02 | ||

+GST111 | Use of English I | 02 | +GST 123 | History and Philosophy ofScience | 02 | ||

+GST112 | Philosophy and Logic | 02 | |||||

***Core +Mandatory**

**Students should not register more than 50 credits and not less than 40 credits including GST at this level. No other elective should be taken outside the ones in the table above.**

**200 LEVEL**

FIRST SEMESTER | SECOND SEMESTER | |||||

Course Code | Course Title | Credits | Course Code | Course Title | Credits | |

*MTH210 | Elementary Algebra and Analysis | +MTH220 | Algebra | 03 | ||

*MTH212 | Real Analysis I | 03 | *MTH222 | Real Analysis II | 03 | |

*MTH213 | Vector Analysis | +MTH223 | Dynamics of a particle | 03 | ||

*MTH218 | Mathematics Methods I | 03 | MTH227 | Introduction to Numerical Analysis | 03 | |

MTH219 | Statistics | 03 | +MTH228 | Mathematics Method II | 03 | |

*MTH230 | Linear Algebra | 03 | MTH229 | Applied Statistical Methods | 03 | |

+CSC213 | Symbolic Programming in Fortran | 03 | MTH240 | Number Theory | 03 | |

*CHM205 | Practical Chemistry I | 03 | +MTH242 | Further Analysis | 03 | |

*CHM211 | Organic Chemistry | 04 | *CHM221 | Inorganic Chemistry | 04 | |

*CHM213 | Physical Chemistry I | 03 | *CHM223 | Physical Chemistry II | 03 | |

*CHM214 | Introductory Environmental Chemistry | 02 |

***Core +Mandatory**

**Direct Entry students should register for 10 credits of General studies.**

**Students should not register more than 50 credits and not less than 30 at this level. **

**No other elective should be taken outside the ones in the table above.**

**300 LEVEL**

FIRST SEMESTER | SECOND SEMESTER | ||||

Course Code | Course Title | Credits | Course Code | Course Title | Credits |

*MTH310 | Abstract Algebra I | 03 | MTH320 | Abstract Algebra II | 03 |

*MTH312 | Real Analysis III | 03 | +MTH322 | Real Analysis IV | 03 |

*MTH313 | Complex Analysis I | 03 | *MTH323 | Complex Analysis II | 03 |

*MTH315 | Dynamic of a rigid body | 03 | +MTH325 | Analytical Dynamics | 03 |

*MTH316 | Fluid Dynamics | 03 | MTH326 | Electricity and Magnetism | 03 |

MTH317 | Numerical Linear Algebra | 03 | *MTH328 | Mathematics methods III | 03 |

MTH330 | Mathematical Logic | 03 | MTH340 | Differential Geometry | 03 |

+MTH332 | Topology I | 03 | MTH342 | Topology II | 03 |

*MTH336 | Vector Field Theory | 03 | *CHM312 | Inorganic Chemistry | 03 |

CSC313 | Data Structure | 03 | *CHM322 | Instructional Methods of Analysis | 04 |

+CED300 | Entrepreneurship Development | 02 | *CHM323 | Physical Chemistry | 03 |

*CHM310 | Practical Organic Chemistry | 02 | *CHM325 | Practical Analytical and Inorganic Chemistry | 02 |

*CHM311 | Aromatic and Alicyclic Chemistry | 03 | *CHM326 | Soil Chemistry | 02 |

*CHM312 | Inorganic Chemistry | 03 | CHM320 | Industrial Chemistry Practical | 02 |

*CHM314 | Separation Methods | 03 | CHM327 | Fibre Science and Technology | 03 |

***Core +Mandatory**

**Students should not register more than 50 credits and not less than 30 at this level. No other elective should be taken outside the ones in the table above.**

**400 LEVEL**

FIRST SEMESTER | SECOND SEMESTER | ||||||

Course Code | Course Title | Credits | Course Code | Course Title | Credits | ||

+MTH410 | Advanced Linear Algebra | 04 | MTH420 | Finite Group Theory | 04 | ||

+MTH412 | Lebesgue Measure and Integration | 04 | MTH421 | Measure Theory | 04 | ||

MTH414 | Functional Analysis I (NormedSpaces) | 04 | MTH423 | Elasticity | 04 | ||

+MTH415 | Quantum Mechanics | 04 | MTH424 | Systems Theory | 04 | ||

+MTH416 | Viscous Flow | 04 | MTH425 | General Relativity | 04 | ||

+MTH418 | Mathematical Methods IV | 04 | MTH426 | Wave Theory | 04 | ||

MTH430 | Electromagnetism | 04 | MTH428 | Mathematical Methods V | 04 | ||

*CHM411 | Selected topics in Industrial Chemistry | 03 | *MTH499 *CHM499 | Project Reading Course | 06 | ||

*CHM412 | Coordination Chemistry | 03 | *CHM421 | Chemical Technology | 03 | ||

*CHM413 | Advanced Chemical Kinetics | 03 | *CHM425 | Quantum Chemistry and Statistical Thermodynamics | 03 | ||

*CHM414 | Applied Spectroscopy | 03 | CHM428 | Radiochemistry and Nuclear Chemistry | 02 | ||

***Core +Mandatory**

**Students should not register more than 50 credits and not less than 30 at this level. **

**No other elective should be taken outside the ones in the table above.**

### DESCRIPTION OF COURSES

**MTH 110 (3 credits) Algebra and Trigonometry (1 ^{st} Semester)**

Real number system. Simple definition of integers, rational and irrational numbers. The principle of mathematical induction. Real sequences and series; elementary notions 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. Relations 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, n^{th} root of unity.

**Suitability A, B, C. D, E, F**

**MTH 112 (3 Credits) Calculus (1 ^{st }Semester)**

Elementary functions of a 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, are of surface of revolution.

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

**Suitability A, B, C. D, E, F**

**MTH 123 (3 credits) Vectors Coordeinate, Geometry and Statistics**

**(2 ^{nd} Semester**)

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 dimension; 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;

**Suitability A, B, C. D, E, F**

**MTH 125 (3 Credits) Differential Equations and Dynamics (2 ^{nd} Semester**)

**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 second order with constant coefficients of the form

**Dynamics**

Resume of simple kinematics of a particle. Differentiation and integration of vectors w.r.t scalar variable. 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. Simple cases of resisted vertical motion on the surface of rough inclined planes. Angular momentum. Motion in a circle (horizontal and vertical). Law of consecration 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 attaqched to an elastic string or spring. The simple pendulum. Impulse and change in momentum. Direct impact of two smooth spheres, and of a sphere on a smooth plane.

Rigid body motion; moments of inertia, parallel and perpendicular axes theorem. Motion of a rigid body in a plane with one point fixed the compound pendulum. Reactions at the pivot. Pure rolling motion of a rigid body along a straight line.

**Suitability A, B, C. D, E, F**

**MTH 129 (3 Credits) Elementary Algebra and Analysis [2 ^{nd} Semester]**

Introduction of statistics Diagrammatic representation of descriptive data. Measures of location and dispersion for ungrouped data. Grouped distribution measure of location and dispersion for grouped data. Problems of grouping. Associated graphs. Introduction to probability simple space and events, addition law, use of permutation and combination in evaluation probability. Binomial distribution. Linear correlation: scatter diagram, moment and rank correlation, Linear regression.

**Suitability A, B, C. D, E, F**

**MTH 210 (3 Credits) Elementary Algebra and Analysis [1 ^{st} Semester]**

Set theory. Cartesian products. Mappings, Piano’s axioms. Construction of integers and rational numbers. Dedekind cuts. Cardinal numbers. Bounds of real numbers. Division algorithm. Primes Fundamental theorem of arithmetric. G.C.D. and L.C.M.

**Suitability A, B, C. D, E, F**

**Pre-requisite: MTH 110, MTH 112**

**MTH 211 (3 Credits) Ancillary Mathematics I [1 ^{st} Semester]**

Elements of set theory. Quadratic equations. Graph of simple functions; polynomials, logarithmic and trigonometric. Matrices: addition, multiplications and inverses. Solution of equations in three unknowns. Trigonomerical ratios. Sums of angles, Small angles, Solution of triangles.

Differentiation and integration; Area and volume of revolution of solids. Descriptive statistics, means, median, mode and standard deviation, frequency distribution and related graphs,

**Suitability: Biochemistry, Pharmacy, Botany, Zoology and Microbiology.**

**MTH 212 (3 Credits) Real Analysis I [1 ^{st} Semester]**

Limits, Sum, products, quotient of limits. Convergence of sequences and series of real numbers. Tests for convergence of series of non-negative terms. Absolute and conditional convergence. Alternating series. Brackets, rearrangements, Cauchy multiplication. Continuity, Uniform continuity. Monotonic functions. Differentiability. Rolle’s and mean-value theorems for differentiable functions. Taylor series. Indeterminate forms.

**Pre-requisite: MTH 110, MTH 112**

**Suitability A, B, C. D, E, F**

**MTH 213 (3Credits) Vector Analysis [1 ^{st} Semester]**

Elementary vector algebra, vector and triple vector products. Solution of vector equations. Plane curves and space curves. Serret-trenet Differential definition of grad, div, and curl. Simple applications.

**Pre-requisite: MTH 110, MTH 125 Suitability: A, E, F**

**MTH 214: (3 Credits) Introduction to Operation Research [1 ^{st} Semester]**

Concept of 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/I 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 **Suitability: B, C, D Pre-requisite: MTH 110**

**MTH 215 (3 Credit) – Social Mathematics [1 ^{st} Semester]**

**Set**

Introduction to sets: definition, subsets, intersection and union. Indices and logarithms: definition of an index for all real numbers, laws of indices, meaning of logarithms: laws of logarithms. Polynomials and inequalities. Idea of a function. Solution of polynomial equations up to quadratic. Inequalities. Absolute values. Solution of inequalities.

Binomial series: The use in approximation.

**Matrices**

Introduction to matrices: addition, multiplication and inverse of a matrix. Use in solving simultaneous linear equations.

**Co-ordinate Geometry**

Cartesian co-ordinates: distance between points, equation of a straight line in the form Identifying m and c from various situation intersection of two straight lines. Use in deriving experimental laws. Plotting graphs, polynomials. Use involving equations. Graphical solutions or linear programming.

**Calculus**

Derivative as slope of a curve at a point. Rules of differentiation. Stationary points and their identification curve sketching. Integration as inverse of differentiation. Indefinite and definite integrals. Areas.

**Suitability: Social Science and Arts Faculties**

**MTH 218 (3 Credits) Mathematical Methods I [1 ^{st} Semester]**

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.

**Suitability A, B, C. D, E, F **

**Pre-requisite: MTH 110, MTH 125.**

**MTH 230 (3credits) Linear Algebra [1 ^{st} Semester]**

Set Theory, Cartestian products. Mappings. Vectors space; basis, dimension, linear mappings. Matrices; algebra of matrices, determinants, inverse, rank. Solvability of system of linear equations, Symmetric and skew-symmetric matrices. Quadratic forms. Eigenvalues.

**Suitability A, B, C. D, E, F**

**Pre-requisite: MTH110 **

**Co-requisite: MTH 210**

**MTH 220 (3Credits) Algebra [2 ^{nd} Semester]**

Groups, Subgroups. Normal subgroups. Permutation groups. Homomorphism, Rings, Integral domains. Fields. Unique factorization domain; Irreducible polynomials. Ideals.

**Pre-requisite: MTH 110 **

**Suitability A, B, C. D, E, F**

**MTH221 (3 Credits) Ancillary Mathematics II [2 ^{nd} Semester]**

Simple series; Taylor binomial exponential; logarithmic and trigonometric. Simple 1^{st} and 2^{nd} order differential equations with constant coefficients. Complex numbers algebra of complex numbers, the Argand diagram. Introduction to probability Binomial, Poisson and Normal distributions. Introduction to large sample estimates and tests using normal distribution. Linear regression and correlation.

**Suitability: Biochemistry, Pharmacy, Botany, Zoology and Microbiology.**

**MTH 222 (3 Credits) Real Analysis II [2 ^{nd} Semester]**

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

**Co-requisite: MTH 212. **

**Suitability A, B, C. D, E, F**

**MTH 223 (3 Credits) Dynamics of a Particle [2 ^{nd} Semester]**

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

**Pre-requisite: MTH 123, MTH 125 **

**Suitability: A, E, F**

**MTH 227 (3 Credits) Introductory Numerical Analysis [2 ^{nd} Semester]**

Introduction to numerical computation; Solution of non-linear equations. Solution of simultaneous linear equation, direct and iterative schemes; Finite difference operators. Interpolation and approximation; Numerical differentiation and quadrature, Numerical solution of ordinary differential equations. Curve fitting and least squares. Introduction to linear programming

**Pre-requisite: MTH 110, MTH 112**

**Suitability: B, C, D**

**MTH 228 (3 Credits) Mathematical Methods II [2 ^{nd} Semester]**

Differential equations; Exact differential equations, in homogeneous 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..

Separations of variables. Fourier Method of solution.

**Suitability A, B, C. D, E, F**

**Pre-requisite: MTH 110-125**

**MTH 240 (3 Credits) Number Theory [2 ^{nd} Semester]**

Prime numbers. Theory of convergence. Quadratic resides. Reciprocity theorem. Arithmetical functions. Partitions.

**Pre-requisite: MTH 110**

**MTH 242 (3 Credits) Further Analysis [2 ^{nd} Semester]**

The Real number system. Dedekind Cut, bounds of real number. Archimedean property of real numbers. Extended real number system. Topology of the real line. Absolute and conditional convergence of series, brackets real-arrangements. Cauchy multiplication. Lim inf criterion for convergence. BolzamWeierstrass theorem. Completeness of real numbers. Lim inf and lim. Sup of subsets of real numbers. Power series. Enumerable and non-enumerable sets.

**Co-requisite: MTH 212 **

**Suitability A**

**MTH 310 (3 Credits) Abstract Algebra I [1 ^{st} Semester]**

Group. Legrange’s theorem. Isomorphism theorem. Cayley’s theorem Sylow theorems. Direct products. Fundamental theorem of abelian groups. Extension of fields.

**Pre-requisite: MTH 220 **

**Suitability: A,**

**MTH 311 (3 Credits) History of Mathematics [1 ^{st} Semester]**

Mathematics in ancients civilizations, Babylonian, Egyptian and Greek mathematics. Development of mathematics in Europe. Solution of cubic and quadratic equation. Invention of the calculus and coordinate geometry. Non-Euclidean geometry. Biographical sketches of famous Mathematicians. Present day trends in mathematics.

**MTH 312 (3 Credits) Real Analysis III [1 ^{st} Semester]**

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.

**Pre-requisite: MTH 212 ****Suitability: A, B, C. D, E, F**

**MTH 313 (3 Credits) Complex Analysis I [1 ^{st} Semester]**

Functions of a complex variable polynomials, rational, trigonometric, logarithmic functions and their inverses. Branch points. Riemann surface. Convergence of sequences and series absolute and uniform convergence. Limit and continuity of a complex-valued function of a complex variable. Differentiation, complex derivative. Cauchy-Riemann equations. Analytic functions. Introduction to conformal mapping.

**Pre-requisite: MTH 222 Suitability: A, B, C. D, E, F**

**MTH314 (3 Credits) Operations Research[1 ^{st} Semester]**

Phases of Operations Research study. Classification of operations research models. Linear. Programming Simplex, Big M. two phase Simplex. Dual simples and the Revised Simplex Methods, Integer Linear Programming Pure and Mixed cases by Gomory Algorithm and Branch and Bound Dynamic Programming Decision Theory. Inventory Models. Critical Path Analysis and Project Controls.

**Pre-requisite: MTH 214 ****Suitability: B, C. D, E, F**

**MTH 315 (3 Credits) Dynamics of a Rigid Body[1 ^{st} Semester]**

General motion of a rigid body as a translation plus a rotation. Moment and products of inertia in 3 diamension. 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, Precession.

**Suitability: A**

**Pre-requisite: MTH 223**

**MTH 316 (3 Credits) Electricity and Magnetism [1 ^{st} Semester]**

Electronstatics; the electrostatic field of force conductivity, Conductors and condensers, Continuous distributions. Method of images. Dielectrics, electro-static stress and energy. Direct current circuits. Magnetism; magnetic materials.

The energy and interaction between two dipoles. Induced magnetism, Magnetostatics, Origin of magnetic field. Magnetic interaction of currents. The vector potential. Biot Savart law. Solenloid. Magnetic field of current sheets. Magnetic energy Coefficients of self and mutual inductions, energy of assembly of circuits. Electro-magnetism.electro-magnetic induction in one or two circuits involving condensers. Maxwell’s equations.

**Suitability: A,**

**Pre-requisite: MTH 213**

**MTH 317 (3 Credits) Numerical Linear Algebra [1 ^{st} Semester]**

Introduction to basic concepts of linear algebra. Pivoting strategies Gaussian elimination. Compact schemes for Caussian elimination. Special matrices; symmetric positive-definite matrices, banded matrices. Error analysis for linear systems. Iterative methods. Over-determined linear systems. Computation of eigen-values and eigenvectors.

**Suitability: A, B, C. D, E, F**

**Pre-requisite: MTH 110, MTH 112**

**MTH 330 (3 Credits) Mathematical Logic [1 ^{st} Semester]**

Rules of inference. Propositional calculus. Quantifiers; Abstract objects. Axiomatic methods. Proof writing. Problem solving. Truth tables. Tautologies. Logic circuits. Axiomatization, the deduction and completeness theorems. Predicate logic Interpretations. Truth models. First order theories. Skolem-Lowenhein theorem. Equality.

**Pre-requisite: MTH 210**

**MTH 332 (3 Credits) Topology I [1 ^{st} Semester]**

Metric space. Topological spaces, open and closed sets, closure, interior, boundary and exterior points of a set. Neighborhoods, subsurfaces and induced topologies. Coarser and finer topologies. Bases and subbases. Continuity and homeomorphism. Separation axions. Hausdorff, regular, normal spaces.

**Pre-requisite: MTH 212 **

**Suitability: A**

**MTH 336 (3 Credits) Vector Field Theory [1 ^{st} Semester]**

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 notion of tensors. The use of tensor notation.

**Pre-requisite: MTH 213**

**Suitability: A**

**MTH 320 (3 Credits) Abstract Algebra II [2 ^{nd} Semester]**

Splitting fields, Galois group solvable groups, Fundamental theorem of Galvis theory, solution by radicals.

**MTH 322 (3 Credits) Real Analysis IV [2 ^{nd} Semester]**

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 Weirestrass approximation theorem.

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

**Suitability: A, B, C. D, E, F**

**Pre-requisite: MTH 222**

**MTH 323 (3 Credits) Complex Analysis IV [1 ^{st} Semester]**

Integration; curves, Jordan curve Theorem, Riemann integration along smooth curves. Csuchy’s theorem (proof for any closed polygon) and consequences e.g. Cauchy’s integral formulae and related theorems; Morera’s theorem, Cauchy’s inequality. Liouville’s theorem. Singularities; classification of isolated singularities, Laurent’s theorem, residue theorem and application to evaluation of integrals and summation of series. Maximum modules principles. Schwartz’s lemma, the Argument theorem, Rouche’s theorem, the fundamental theorem of algebra. Introduction to analytic continuation.

**Suitability: A, B, C. D, E, F**

**MTH 324 (3 Credits) Mathematical Modeling [1 ^{st} Semester]**

Methodology of model building; Identification, formulation, and solution of problems, cause-effect diagrams. Equation Types; Algebraic, Ordinary differential equations, partial differential equations, difference, integral and functional equations, Application of Mathematical Models to Physical, Biological, social and Behavioral Sciences.

**Suitability: B, C. D, **

**MTH 325 (3 Credits) Analytical Dynamics [2 ^{nd} Semester]**

Degrees of freedom. Holonomic and non-holonomic constrains. Generalized coordinates. Legrange’s equations for holonomic system, force dependent on coordinates only, force obtainable from a potential.

Impulsive multiplier ariation for non-holonomic systems

Lagrangian multipliers. Variation principles. Calculus of variation, Hamilton’s principle. Legrange’s equation from Hamilton’s principles. Canonical transformations. Normal modes of vibrations. Hamilton-Jacobi equations.

**Suitability: A Pre-requisite: MTH 213, MTH223**

**MTH 326 (3 Credits) Fluid Dynamics [2 ^{nd} Semester]**

Real and ideal fluids. Differentiation following the motion of fluid particles. Equations of motion and continuity for incompressible inviscid fluids. Velocity potentials and Stoke’s stream functions. Bermoulli’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.

**Suitability: A, Pre-requisite: MTH 213.**

**MTH 328 (3 Credits) Mathematical Methods III [1 ^{st} Semester]**

Special operators: Hermitian, projection and unitary operators. Eigenvalues and eigenvectors; use of net and bra-notation. Infinite dimensional vector space; the classical orthogonal polynomials (Legendie, Hermite and Laguerre polynomials) Rodrigue’s formula. Special Functions; gemjna 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 operators. Special theory functions of operators, intergral and differential operators.

**Suitability: A, B, C. D, E, F Pre-requisite: MTH 218.**

**MTH 340 (3 Credits) Differential Geometry I [2 ^{nd} Semester**

Vector functions of real variable. Boundedness ; Limits, continuity and differentiability Functions of class C-Taylor’s theorem and inverse function theorem. Concept of a surface parameteric representation, tangent plane and normal lines. Topologial properties of simple surfaces.

**Pre-requisite: MTH 212**

**MTH 342 (2 Credits) Topology II [2 ^{nd} Semester**

Separation axions. Hausdorff, regular, completely regular and normal spaces. Compactness, local compactness, Connectedness. Product spaces. Completeness in metric spaces.

**Pre-requisite: MTH 212 Co-requisite: MTH 332. **

**Suitability: A**

**MTH 399 (3 Credits) Industrial Training [2 ^{nd} Semester**

An industrial experience in an establishment to practice theoretical training relating to industries and management under the direction and supervision of a lecturer

**Suitability: B**

**MTH 410 (4 Credits) Advanced Linear Algebra [1 ^{st} Semester]**

Minimal polynomials, Cayley-Hamilton theorem. Nilpotent transformation. Normal and unitary matrices. Rational and Jordan normal forms. Inner products. Duel spaces. Hermitan orthogonal operators.

**Suitability: A ,B**

**Pre-requisite: MTH 212, MTH 310.**

**MTH 412 (4 Credits) Lebesgue Measure and Integration [1 ^{st} Semester]**

Lebesgue measure outer measure, measurable and non-measurable sets, regularity, measurable functions.

Lebesgue integral; integration of non-negative functions, the general integral, convergence theorems, Fubini’s theorem

**Suitability: A Pre-requisite: MTH 310**

**MTH 415 (4 Credits) Quantum Mechanics [1 ^{st} Semester]**

Particle-wave duality. Quantum postulates. Schroedinger equation of motion. Potential steps and wells in 1-dim. Heisenberg formulation. Classical limits of quantum mechanics. Commutator brackets. Linear harmonic oscillator. Angular momentum. 3-dim. Square well potential. The hydrogen atom. Collision 3-dim. Approximation methods for stationary problems.

**Pre-requisite: MTH 316. Suitability: A**

**MTH 416 (4 Credits) Viscous Flow [1 ^{st} or 2^{nd} Semester]**

The Navier-stokes equations for an incompressible flow. Exact solutions; radial flow between plane walls, axi-symmetric jet, stagnation point flows. Rayleigh problems. Boundary layer theory, similarity solutions, the momentum integral methods. The Reynolds stresses, flow in parallel channels and shallow water areas.

**Pre-requisite: MTH 326 Suitability: A**

**MTH 417 (4 Credits) Advanced Numerical Analysis [1 ^{st} Semester]**

Existence of solution. One-step schemes and theory of convergence and stability. Linear multistep methods. Development, theory of convergence and stability. Extrapolation processes.

Intergral equation and boundary-value problem.

**Pre-requisite: MTH 217 or MTH 317 Suitability: A, B, C**

**MTH 418 (4 Credits) Mathematical Methods IV [1 ^{st} Semester]**

Calculus of variation; Lagrange’s functional and associated density. Necessary condition for a weak relative extremum. Hamilton’s principles. Lagrange’s equations and geodesic problems. The Du Bois-Raymond equation and corner conditions. Variable and points and related transforms. Laplace, Fourier and Hankel transforms. Complex variable methods. Convolution theorems. Application to solution of differential equations.

**Pre-requisite: MTH 328 Suitability: A, B , E, F**

**MTH 419 (4 Credits) Probability Theory and Stochastic Processes**

**[1 ^{st} Semester]**

Probability, random variables, probability distribution, expectation probability generating functions. Convolutions and compound distributions. Branching processes. Random walks. Markov chains. Poission, birth, birth-and-death processes. Queuing theory.

**Pre-requisite: MTH 319. Suitability: B, C, D**

**MTH 432 (4 Credits) Modules [1 ^{st} Semester]**

Modules, projective and injective modules. Noetherian and Arthimian modules. Quotient modules. Tensor products. Exact sequences. Theory of categories. Algebras.

**Pre-requisite: MTH 310 Suitability: A**

**MTH 435 (4 Credits) Special Relativity [1 ^{st} Semester]**

Inertial frames, simultaneity, Einstein’s postulates. Intervals proper time and proper length. The Lorentz transformation. Transformation of velocities. Covariant notation. 4-vectors, 4-velocities, 4-acceleration, and 4-force. Relativistic mechanics; energy conservation. Decay of particles. Kinematics of 2-body collisions. Motion of a changed particle in electromagnetic field. Transformation of the electromagnetic field. Covariance of electrodynamics. The energy momentum tensor of EM fields. The Viral theorem. Radiation by moving changes. Lienard-Wiechert potentials and fields.

**Pre-requisite: MTH 316 Suitability: A, E, F**

**MTH 436 (3 Credits) Electromagnetism [1 ^{st} or 2^{nd} Semester]**

Maxwell’s field equations. Electromagnetic waves and electromagnetic theory of light Plane electromagnetic waves in non-conducting media, reflection and refraction at plane boundary. Wave guides and resonant cavities. Simple radiating systems. The Lorentz-Transformation of (E,H.) field. The Lorentz force.

**Pre-requisite: MTH 316 Suitability: A, E, F**

**MTH 420 (4 Credits) Finite Group Theory [2 ^{nd} Semester]**

Normal and composition series. Schreier’s theorem. Jordan-Holder theorem Chrematistic subgroups, Commentators. Derived series. Nilpotent groups. Application of Sylow’s theorem; groups; Linear groups, Representation of groups; Maschk’s theorem.

**Pre-requisite: MTH 310 **

**Suitability: A, E, F**

**MTH 422 (4 Credits) Normed Spaces (Functional Analysis I [1 ^{st} Semester]**

Linear topological spaces, definition, subspaces, quotient spaces, Conditions for metrizable, normable, and finite dimensional linear topological spaces. Examples of such spaces.Linear operator on linear spaces. The Hahn-Banach theorem in normed linear spaces. The dual spaces of a normed linear space.

**Pre-requisite: MTH 312 **

**Suitability: A, E, F**

**MTH 424 (4 Credits) Systems Theory [2 ^{nd} Semester]**

Lyapunov theorems. Solution of lyapunov stability equation

Controllability and observability. Theorem on existence of solution of linear systems of differential equations with constant coefficients.

**Pre-requisite: MTH 227 or MTH 317**

**MTH 426 (4 Credits) Wave Theory [1 ^{st} or 2^{nd} Semester]**

Surface waves. Linear and long-wave approximation, effect of friction and turbulence. Theory of wave generation by winds. Kelvin-Helmholtz instability, models of Philip and Miles. Non-linear wave characteristics and related events. Variational approach to wave characteristics, Introductions to waves in a thermally driven fluid; acoustic and gravity waves in atmosphere and geophysical effects.

**Pre-requisite: MTH 218 or MTH 228 **

**Suitability: A, D, E**

**MTH 427 – Optimization Theory (4 Credits)**

Linear programming models. The simplex methods: formulation and theory. Duality, 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 428 (4 Credits) Mathematical Methods V [2 ^{nd} Semester]**

Elementary notion and theorems of generalized functions with support on the real line. Application; differentiation and integration of generalized functions. General linear and ordinary differential equations of second order with stipulated boundary conditions. Integral equations methods of successive approximation. Necessary conditions for convergence in the norm and uniformly. Collocation and least squares methods. Integral equations with symmetric kernels, Fresholm alternatives. Green’s function, introduction, general theory and various boundary conditions. Eigen function expansion of green’s functions. Helmholtz equation. Wave equation and diffusion equation for all space and the case of finite and infinite media. Classifications and solution of p.d.e. of first and second order

**Pre-requisite: MTH 218, MTH 328 MTH 418Suitability: A, B, E, F**

**MTH 440 (4 Credits) Topological Groups (Functional Analysis II [2 ^{nd} Semester]**

The open mapping theorem, the closed graph theorem and the Banach-Steinhaue theorem in complete metric linear spaces. Elements of Hibert-space theory; the geometry of a Hilbert space, parallelogram law, subspaces, orthogonal complement, direct sums, orthonormal sets. Fourier expansions, linear functionals on a Hilbert spaces. Riesz representation theorem, operators on a Hilbert space. Introduction to Banach Algebras.

**Pre-requisite: MTH 422. Suitability: A, E, F**

**MTH 442 (4 Credits) Measure Theory [2 ^{nd} Semester]**

Abstract integration L^{P}-space

**Pre-requsite: MTH 420 Co-requisite: MTH 412 Suitability: A, E, F**

**MTH 445 (4 Credits) General Relativity [2 ^{nd} Semester]**

Particles in a gravitational field curvilinear coordinates intervals. Covariant differentiation. Christoffel symbol and metric tensor. The constant gravitational field. Rotation. The curvature tensor. The action functions for the gravitational field. The energy momentum tensor. Newton’s law. Motion in a centrally symmetric gravitational field. The energy momentum 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 red shift.

**Pre-requisite: MTH 435 Suitability: A, E, F**

**MTH 446 (4 Credits) Elasticity [2 ^{nd} Semester]**

Analysis of stress and strain, stress and strain relations and the elastic energy constraints; equations of equilibrium, strain energy, solution of simple problems such as thick cylinders and sphere, torsion, bending and stretching of plates. Airy stress function and simple two-dimensional problems.

Elastic waves in solids, Waves of pressure and rotation. Surface waves. Rayleigh. Love and Stoneley waves. Concept of group and phase velocity.

**Pre-requisite: MTH 325; MTH 326 Suitability: A, E, F**

**MTH 499 (6 Credits) Reading Course (Project)[1 ^{st} and 2^{nd} Semester]**

The student undertakes a course of reading under the supervision of a lecturer. There will in general not be formal lectures. The student consults the supervisor as often as necessary. At the end of the course, the student submits a written report on the topic and gives a talk before a departmental evaluation board.

**Suitability: A, B, C. D, E, F**

## Recent Comments