**Area of Specialization**

- Pure Mathematics
- Applied Mathematics

Core Courses

**Generic Course Code Course Title Credit Units**

SCI 801: Mathematics and Entrepreneurship 2

SCI 802: ICT and Research Methodology 2

**Programme Core Courses **

**Course Code Course Title Credit Units**

MAT 800 Research Projects 6

MAT 801 Algebra 3

MAT 802 Topology 3

MAT 803 Real Analysis 3

MAT 804 Complex Analysis 3

MAT 805 Partial Differential Equation 3

MAT 824 Seminar 3

**Elective Courses **

**Pure Mathematics **

**Course Code Course Title Credit Units**

MAT 806 Group Presentation Theory 3

MAT 807 Number Theory 3

MAT 808 Category Theory 3

MAT 809 Lie Groups 3

MAT 810 Differential Manifolds 3

MAT 811 Theory of Integration 3

MAT 812 Integral Equations 3

MAT 813 Theory of Distributions 3

MAT 814 Introduction to Mathematical Modelling 3

**Applied Mathematics **

**Course Code Course Title Credit Units**

MAT 815 Quantum Mechanics I 3

MAT 816 Fluid Mechanics 3

MAT 817 Elasticity 3

MAT 818 Electromagnetic Theory 3

MAT 819 Quantum Mechanics II 3

MAT 820 Visco Elasticity and Plasticity 3

MAT 821 Control Theory 3

MAT 822 Finite Elements Method 3

MAT 823 Biomathematics 3

**MAT 801 Algebra (3 Credits Unit)**

Sylow theorems, direct products, fundamental theorems of finite Albelean groups, fields of quotients, Euclidean rings, Polynomial rings over, commutative rings, inner products spaces, theory modules, sub-modules, quotients modules, modules over principal idea domains, Applications finitely generated Albelean group fields, extension fields, elements of Galois theory, solvability radicals.

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**MAT 802 Topology (3 Credits Unit)**

Review of categories and functors. Homology, fundamental groups, covering transformation, simplecial complexes, singular homology, Universal co-efficient theorem for homology and cohomology.

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**MAT 803 Real Analysis (3 Credits Unit)**

Measures and integration, outer measure, lesbeque measure, basic properties of Banach and Hilbert spaces, Duality. Basic theorems in functional analysis. Classical Banach. Spectral theory of Operators in Hilbert Spaces, *L, *Space as a Hilbert space, Banach algebras, Gelfand theory, compact operation, Examples and applications to classical analysis.

**MAT 804 Complex Analysis (3 Credits Unit)**

Periodic functions, weiestrass functions, elliptic curves, Modular forms, Algebraic functions, Reimann surfaces. Covering surfaces, covering transformation. Discontinous groups of linear transforms, automorphic equations.

**MAT 805 Partial Differential Equation I (3 Credits Unit)**

Basic examples of linear partial differential equations and their fundamental equations and their fundamental solutions. Existence ad regulatory of solutions (Local or Gobal) of the Cauchy problems; boundary value problems and mixed boundary value problems. The fundamental solutions of their partial differential equations.

**MAT 824 Seminar (3 Credits Unit)**

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**MAT 806 Group Presentation Theory 3 Credits Unit)**

Representations of groups by linear transformations; group algebras, character theory and modular representations. Representation theory of algebra groups; representation of finite groups ; representation of compact and locally compact groups; representation of Lie groups Unitary representation theory.

**MAT 807 Number Theory (3 Credits Unit)**

Algebraic integers, completions of the different and discriminant; cyclotomic fields, parallelotopes, class-number, ideles and Adeles. Elementary properties of Zeta-functions. L-functions.

**MAT 808 Category Theory (3 Credits Unit)**

Categories, functions natural –transformation. Functor categories, limits, products and corporducts, pushbacks and pushouts, adjoin functors, Normal and exact categories, Abelia categories, quotient categories.

**MAT 809 Lie Groups (3 Credits Unit)**

Lie groups and their Lie algebras, subgroups, Matrix groups, One-parameter groups, expondential map, Campbell-Hasudorff formula, Lie algebra of matrix griyo, integration on matrix groups, Abstract Lie groups.

**MAT 810 Differential Manifolds (3 Credits Unit)**

General manifolds, topics such as smooth mappings, immersions, submersions, trasnversality, intersection theory, vector fields of manifolds, orientation of manifolds, Gausian curvature, Riemannian manifolds, differential forms, integration on manifolds tensors and connections are included.

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**MAT 811 Theory of Integration (3 Credits Unit)**

The theory on closed and bounded intervals; Gauges and integrals. Basic properties of the integral, The fundamental theorems of calculus. The saks-Henstock Lemma. Measureable functions. Absolute integrability, Convergence theorems. Integrability and mean Convergence. Measure, Measureability and multipliers. Mode of convergences, substitution theorems. Applications. The theory on infinite intervals: General insight into integration on infinite intervals.

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**MAT 812 Integral Equations (3 Credits Unit)**

Basic existence theorems: Equation with L_{2} kernels, Fredholm theory, Non-linear equations, Schauder fixed point theorem, Dual integral and series equations. Wiener-Hope equations and techniques. Singular Integral equations. Applications.

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**MAT 813 Theory of Distributions (3 Credits Unit)**

Opological vector spaces and generalized functions, Distribution calculus and topology; convolution, Tempered distributions and their Fourtier transforms. Integral transforms of mathematical Physics Application.

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**MAT 814 Introduction to Mathematical Modelling (3 Credits Unit)**

Mathematical Modelling. The Art of Transforming Real Life Situations into Mathematical Statements, Examples will be drawn from areas such as Biology, Business, Deformable Media, Industry and other dynamical system. Case Studies.

**MAT 815 Quantum Mechanics I (3 Credits Unit)**

Background of the axiomatic approach of Nul et al. Axioms of continuum and Basic Concepts, Constitutive Relations. Equations of Motion and other Equations. Equations of Motions and Equations of Balance. The place of classical theories.

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**MAT 816 Fluid Mechanics (3 Credits Unit)**

Thermodynamics Compessible flow, waves. sheeks, supersonic flow, Boundary layer theory, stability, Turbulence.

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**MAT 817 Elasticity (3 Credits Unit)**

Formulation of the Linear theory, General theorems, plane strain and generalized Plane stress. Ary’s solution: Papkovich Neuber representation, Basic singular solutions Boundary value and boundary-initial value problems.

**MAT 818 Electromagnetic Theory (3 Credits Unit)**

Maswell’s Equations, Electromagnetic potentials, Tensor Calculus, Stree and Energy; Electrostatic, plane waves, cylindrical and spherical waves, Boundary Value problems, relativistics and Lorentz Transformation; Electrodynamics.

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**MAT 819 Quantum Mechanics II (3 Credits Unit)**

Schrodinger equations; Stone’s Theorem and its application. Unitary transformations: Helsenberg representation: Measurement: Quantum Theory of Scattering; Angular Momentum. Motion in an eternal field. Base and Fermi Statistics; Perturbation Thoery.

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**MAT 820 Visco Elasticity and Plasticity (3 Credits Unit)**

Charatersistcis of various vicco-elastic and plastic materials material, Basic euations. Boundary value orobems, Elastic-pattern problems.

**MAT 821 Control Theory (3 Credits Unit)**

Dynamical systems in the state space, Reachability. Stabilizability and Detectability. Equivalence of Contollability and Pole Assignability. The Calculus of Variations. Generalized Huygen’s Principle. The Algebraic Riccati Equation. Lyapunov Stability Applications to Economic Stabilization, Manpower, Manpower Development, Resource Allocation under Constraints, etc Case Studies.

**MAT 822 Finite Elements Method (3 Credits Unit)**

Introduction to the finite Element Method: formulation of the Finite Element Method Using the Principle and Virtual Displacement. General Isoparametric Formulation, and Variation Techniques. Generalized of the Theory. Application of the Finite Element Method to the Solution of Engineering Problems. e.g., in Solid Mechanics, Heat Transfer, Fluid Dynamics and Mass Transfer. Development of appropriate Computer Programme. Case Studies.

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**MAT 823 Biomathematics (3 Credits Unit)**

Mathematical Methods of Deterministics or Stochastric aspects of Biological Systems e.g. Population dynamics, species interaction malaria epidemic, etc.