M. Sc. Mathematics

Department of Mathematics Master of Science in Mathematics

M. Sc. Mathematics

List of Academic Staff

Name	Status and Qualification	Research Interests
K. Rauf	Professor & Head of Department B.Sc. (Ilorin); M.Sc., PGDC (OAU, Ife); M.Sc., Ph.D. (Ilorin)	Functional Analysis, Complex Analysis and Inequalities
T. O. Opoola	Professor M.Sc. (Karkov); Ph.D (Ilorin)	Complex Analysis and Functional Analysis
O. M. Bamigbola	Professor B.Sc. (Ed), M.Sc., Ph.D. (Ilorin)	Optimisation, Numerical Analysis
M. O. Ibrahim	Professor B.Sc., M.Sc., Ph.D. (Ilorin)	Fluid Mechanics, Mathematical Modelling
O. A. Taiwo	Professor B.Sc., M.Sc., Ph.D. (Ilorin)	Numerical Analysis
R. B. Adeniyi	Professor B. Sc., M.Sc., Ph. D. (Ilorin)	Numerical Analysis
A. S. Idowu	Professor B.Sc. (Ed), M.Sc., Ph.D. (Ilorin)	Analytical Dynamics, Fluid Mechanics
K. O. Babalola	Professor B.Sc., M.Sc. (OAU, Ile-Ife); Ph.D. (Ilorin)	Complex Analysis
M. S. Dada	Professor B.Sc. (Ed), M.Sc., Ph.D. (Ilorin)	Fluid Mechanics, Analytical Dynamics.
Olubunmi A. Fadipe-Joseph	Professor B.Sc., M.Sc. (Ibadan); Ph.D. (Ilorin)	Complex Analysis, Operator Algebra
E. O. Titiloye	Reader B.Sc. (Ed), M.Sc., Ph.D. (Ilorin)	Analytical Dynamics. Fluid Mechanics
Yidiat O. Aderinto	Reader B.Sc. (Ed), M.Sc., Ph.D. (Ilorin)	Optimisation, Complex Analysis
Catherine N. Ejieji	Reader B.Sc. (UNN), M.Sc., Ph.D. (Ilorin)	Optimisation
B. M. Yisa	Senior Lecturer B.Sc., M.Sc., Ph.D. (Ilorin)	Numerical Analysis
J. U. Abubarkar	Senior Lecturer B.Sc., M.Sc., Ph.D. (Ilorin)	Numerical Analysis, Fluid Mechanics
K. A. Bello	Senior Lecturer B.Sc., M.Sc., Ph.D. (Ilorin)	Numerical Analysis
Gatta N. Bakare	Senior Lecturer B.Sc., M.Sc., Ph.D. (Ilorin)	Algebra
B. M. Ahmed	Senior Lecturer B.Sc., M.Sc., Ph.D. (Ilorin)	Algebra

O. A. Uwaheren	Lecturer I B.Sc., M.Sc., Ph.D. (Ilorin)	Numerical Analysis
Idayat F. Usamot	Lecturer I B.Sc., M.Sc., Ph.D. (Ilorin)	Functional Analysis, Algebra
O. T. Olotu	Lecturer I B.Sc., M.Sc., Ph.D. (Ilorin)	Analytical Dynamics
O. Odetunde	Lecturer I B.Sc. (LAUTECH, Ogbomoso), M.Sc., Ph.D. (Ilorin)	Mathematical Modelling
T. L. Oyekunle	Lecturer II B.Sc., M.Sc., Ph.D. (Ilorin)	Fluid Mechanics
A. Y. Ayinla	Lecturer II B.Sc. (ABU, Zaria), M.Sc., Ph.D. (Ilorin)	Mathematical Modelling

B. Introduction

The programme is to concentrate on Mathematics and its applications. The programme is delivered with quality teaching and supervision in various aspects of pure and applied Mathematics including Algebra, Complex Analysis, Functional Analysis, Inequalities, Analytical Dynamics, Fluid Mechanics, Optimization, Numerical Analysis and Modelling.

C. Philosophy

The philosophy of the programme is to focus on training graduates who are well-equipped in

their area of specialisation and all facets of Mathematics with the purpose of meeting both national and global needs in the area of technological advancement.

D. Aim and Objectives

The aim of the programme is to train students to attain academic excellence and competence in mathematical reasoning and problem-solving through the use of logics and computational skills.

Objectives:

training students to be self-reliant in their chosen field of Mathematics;
produce students who are adequately prepared for further research work;
producing mathematicians who can readily impart their knowledge to students at higher levels of education;
developing students self-confidence in handling problems with minimal or no supervision;
training students to develop confidence in appreciating and solving problems in general;
producing students with good educational foundation for a range of career in public services, industries and commerce; and
producing mathematicians that can be self-employed.

E. Admission Requirements

Candidates seeking admission to the M.Sc. Mathematics programme are required to have:

‗O‘ Level Credits passes or their equivalents in five subjects including Mathematics, Physics, Chemistry, English Language, and any other relevant subject;
Bachelor of Science degree of the University of Ilorin with at least a Second Class (Upper Division) Honours or equivalent;
Bachelor of Science degree in Mathematics from the University of Ilorin or any other approved university with at least a Second Class (Lower Division) and a minimum score of 55% in a qualifying Examination administered by the university;
Postgraduate Diploma in Mathematics from University of Ilorin or any other approved university and with a score of at least 3.50 CGPA or 60%.

F. Duration of the Programme

The Full-time programme shall run for a minimum of 18 calendar months and a maximum of 24 calendar months. Candidate may apply for an extension of not more than 12 calendar months, after the expiration of the maximum periods.

G. Detailed Course Description

SCI 801 Management and Entrepreneurship 2 Credits

Feasibility studies. Entrepreneurship skills development. Organisation and management of business. Sourcing for funds. Financial management. Patency. Marketing and management problems. 30h (T); C

SCI 802 Scientific Research Methodology 2 Credits

Principles of scientific research. Data collection. Processing and analysis. Statistical packages. Precision and accuracy of estimates. Hypothesis formulation and testing. Organisation of research. Report writing and presentation. Research ethics and grants. 30h (T); C

MAT 801 Algebra and Topology 3 Credits

Sylow theorems. Direct products. Fundamental theorem and application of finite Abelian groups. Field of quotients. Euclidean rings. Polynomial rings over commutative rings. Inner product spaces. Modules and modules over principal ideal domains. Fields. Elements of Galois theory. Solvability radicals. Review of categories and functions. Homology and universal co-efficient theorem for homology and cohomology. Spectral sequence. 45h (T); C

MAT 802 Analysis 3 Credits

Spectral theorem. Compact operators and applications to classical analysis. Periodic functions. Weierstrass functions. Elliptic curves. Modular forms. Algebraic functions. Riemann surface. Covering surfaces. Covering transformations. Discontinuous groups of linear transforms. Automorphic forms. Discontinuous groups of linear transforms. Automorphic forms. 45h (T); C

MAT 803 Mathematical Methods 3 Credits

Expansion Methods. Properties of transforms. Fourier Series and integrals. Special functions: hyper-geometric, Legendre. Bessel, Gamma, Beta. Factorial functions. Green‘s functions. Euler and Laplace transforms. Perturbation methods. Methods for linear systems. Convergence and stability of these methods. Sparse matrix techniques. Tridiagonalization and orthogonal factorisation. Matrix eigenvalue problems. Over-determined systems. Solutions of non-linear equations. One point iterative methods. Newton‘s and Brown‘s methods. Gradient methods. Bracketing methods. Convergence and stability of these methods. Special methods. 45h (T); C

MAT 805 Partial Differential Equations 3 Credits

Basic examples of linear partial differential equations. Fundamental equations. Existence and regularity of solutions: local or global of the Cauchy problems. Boundary value problems and mixed boundary value problems. Fundamental solutions of their partial differential equations. 45h (T);C

MAT 806 Star-like and Convex Univalent Functions 3 Credits

Analytic representations of star like and convex univalent functions. Introduction to the class of functions with position real parts. Some geometric properties of star like and convex functions. Namely coefficient inequalities. Covering theorems. Growths. Distortions. Integral representations and construction of examples. 45h (T); EMAT 807Univalent Functions and Conformal Mappings I 3 Credits Theory of conformal mappings. Examples of conformal mappings. Rouche‘s theorem. Univalent functions as conformal mappings. Sequences of univalent functions. Riemann mapping theorem. Univalent functions in the unit disk. Normalisation of univalent mappings. Sufficient univalence conditions. 45h (T); E

MAT 808 Univalent Functions and Conformal Mapping II 3 credits

Transformations preserving the class of normalised univalent functions. Area theorem. Some geometric properties of normalised univalent functions. Namely coefficient inequalities. Covering theorems. Growth. Distortions. Integral means and arc length of the range of univalent mapping of the unit disk. 45h (T); E

MAT 809 Maximum Modulus Theorem 3 Credits

Real and imaginary parts of analytic functions. Modulus of analytic functions. Maximum modulus theorem for analytic functions. Schwartz‘s theorem. Mean values of modulus of analytic functions. Applications of the maximum modulus theorem in the theory of geometric functions. 45h(T);E

MAT 811 Optimisation I 3 Credits

Single variable and multivariable classical optimisation problems. Linear programming. Simplex method. Duality principle. Sensitivity analysis. Transportation algorithm. Non-linear programming. Lagrange multipliers and Kuhn-Tucker‘s methods. Integer programming. Game theory. Dynamic programming. Multi-objective optimisation. 45h (T); E

MAT 812 Optimisation II

Search methods. Dichotomous. Fibonacci‘s and Golden-selection methods. Powell Hooke‘s and Jeeves and Rosenbrock‘s methods. Heuristics cutting plane and projection methods. Penalty functions. Trust region methods. Interpolation methods. Coggins method. Quasi Newton methods. Gradient methods. Steepest decent and conjugate gradient methods. Convergence analysis. 45h (T); E

MAT 813 Optimisation III 3 Credits

Optimisation problems. Statement of optimisation problems. Classes of optimisation problems and their corresponding properties. Problem formulation. Mathematical programmes. Convex and concave minimisation. DC programming. Lipschitzian optimisation. Convexity and coercivity. Contraction mapping principle. Least squares method. 45h (T); E

MAT 814 Optimisation IV 3 Credits

Introduction to modern control theory. Stability controllability. Observability and optimal control. Discrete optimal control problems. Extremization of integral. Hamiltonians and Pontryagin‘s principle. Bang-Bang control. Function space and extended conjugate gradient algorithms. Fletcher-Reeves and Polak-Ribiere algorithms. Applications of control theory. 45h (T); E

MAT 841 Algebra I Commutative Ring 3 Credits

Rings and ideals. Rings and modules. Modulus of fractions. Primary decomposition. Integral dependence. Chain conditions. Noetherian rings. Discrete valuation. Rings and Dedekind domains. Completions dimensions theory. Fields. Finite and algebraic closure. Finite fields. Primitive element. Separable extensions and purely inseparable extension. 45h (T); E

MAT 842 Algebra II Algebraic Semigroups 3 Credits

Definition and properties of semigroups: zero and identity elements, left and right-zero semigroup, idempotent and nilpotent elements. Examples: monogenic semigroup, free semigroup and null semigroup. Ordered of sets. Binary relations. Congruences in semigroup. Ideals and Rees congruence. Green‘s relations. Regularities. Regular semigroups. Bands and union of groups. 45h (T); E

MAT 843 Algebra III Group Theory 3 Credits

Fundamental concepts. Conjugates of group. Centre of a group. Centraliser and normaliser of a group. Generated set. Permutation groups. Transitive and Intransitive group. Regular and semiregular groups. Frobenris groups and Frobenrim theorem . Primitive and imprimitive groups. Half transitivity. Multiple- transitivity and regular normal subgroups primitivity. 45h (T);E

MAT 817 Graduate Seminar 2 Credits

Two seminars to be given on approved topics 90h (P); C

MAT 818 Algebra IV Semigroup Theory 3 Credits

Inverse semigroups. Fundamental inverse semigroups. Simple and bisimple inverse semigroups. W-semigroups. Orthodox semigroups. Special topics in semigroup theory: order semigroup, adequate semigroup, transformation semigroup, use of graph in semigroup. Applications of semigroup theory to other areas. Example: formal languages and automata theory. 45h (T); E

MAT 819 Functional Analysis I 3 Credits

Hilbert spaces. Banach spaces. Baire category theorem and its Applications. Open mapping theorem. Closed graph theorem and uniform boundedness principle. Bounded and unbounded operators. Banach and C–algebras. Applications: fourier series and integral equations. 45h (T); E

MAT 820Functional Analysis II 3 Credits

Continuous linear transformation. Hahn Banach extension theorems and introduction to convex conjugation. Topologies on vector spaces. Weak and weak topologies. Frechet separable and reflexive spaces. Application to partial differential equation. 45h (T); E

MAT821 Functional Analysis III 3 Credits

Measure and measurable functions. Properties of measurable function. Concept of convergence and Fubini‘s theorem. ◻◻-Spaces. Duality. Polar sets and representation theorems. Orthogonality. Orthonormal and conjugate space and their applications. 45h (T); E

MAT822 Functional Analysis IV 3 Credits

Spectral analysis of linear operator. Compact operators. Spectral analysis in Hilbert spaces. Symmetric. Unitary. Normal and self-adjoint operators. Projections and matrices. Determinants. Spectrum on an operator. Completion of metric space and its applications. 45h (T); E

MAT 823 Inequality I 3 Credits

Some inequalities with graphs and basic techniques. Geometrical interpretations of Holder‘s and Minkowski‘s inequalities. Theorem of Hadamard. Modulus of a matrix. Maxima and minima in elementary geometry. Some useful inequalities in elementary analysis. Inductive proofs of the fundamental inequalities and Tchebychef‘s inequality. 45h (T); E

MAT 824 Advanced Mathematical Modelling Techniques 3 Credits

Perturbation methods. Introduction to modelling concepts. Dimensional analysis. Perturbation techniques. Matched Asymptotic. Introduction to stochastic analysis. Brownian motion. Hitting problems. PDES and SDES. Application of complex variables. Conformal mapping. Non-linear dynamics. Climate modelling. Environmental related phenomena biomedical modelling. Industrial case studies. Social dynamics 45h (T); E

MAT 825 Mathematical Ecology 3 Credits

Population models for a single species. Malthusian models of resource limitation. Simple age-structured models. Discrete time population models. Logistic map. Demography. Stable age-structure. Euler-Lotka demographic equation. Two species interactions. Competition and Niche-theory. Predator-prey models. Models of disease transmission: epidemics. General Lotka-Voltera models. Application of Lyapunov functions. Many species interaction. 45h (T); ; E

MAT 826 Non-Linear Systems 3 Credits

Continuous dynamical systems. Equilibria. local and global stability. Liouvilles theorem. Conservative and dissipative mechanical systems. Periodic solutions and point care. Bendixson theorem. Discrete dynamical systems. Equilibria. Cycles and their stability. Period doubling bifurcations. Simple random properties of discrete trajectories. Elementary properties of maps in two dimensions. Lyapunov exponents. Attractors and the butterfly effect. 45h (T); E

MAT 827 Biomathematics 3 Credits

Application of mechanics to the understanding of the structure and functioning of animals. Theory of scaling. Mechanics of bones: muscles and other organs of the body. Fluid mechanics of the heart: particularly left ventricular ejection. Problems of microscopic dimensions: diffusion through membranes. Real life applications. 45h (T); E

MAT 828 Numerical Analysis II 3 Credits

Partial differential equations. Parabolic equations. Solution techniques by explicit and implicit methods. Stability and convergence analysis. Elliptic equations. Solution techniques by finite difference methods. ADI methods. Stability and convergence analysis. Hyperbolic equations. Solution techniques by methods of characteristics and finite difference. Lax-Wendroff explicit and implicit methods. convergence and stability analysis. 45(T); E

MAT 829 Numerical Analysis III

Ordinary differential equations. Numerical approximation of solution. Higher order one step methods. Taylor series. R-K methods. Convergence and stability of these methods. Multi-step methods. Adams methods. Stability and convergence of these methods Lanczos and Ortiz Tau methods. Shooting methods. Topics in approximation: least-squares, approximation by series, rational approximation. 45h(T); E

MAT 830 Numerical Analysis IV 3 Credits

Weighted residual methods. Sub-domain. Collocation. Bubnov-Galerkin. Least squares. Moments. Integral domain and orthogonal collocation. Variational methods. Functionals. Minimisation of quadratic functions. Raleigh-Ritz methods. Nagume‘s lemma. Introduction to finite elements methods. Chebyshev polynomial approximation: min-max approximation, power series economisation. Applications. 45h (T); E

MAT 831 Advanced Analytical Dynamics 3 Credits

Principle of dynamics. Structural dynamics. Analysis of a dynamical behaviour of structures. Strain energy. Virtual work. Variational principle. Lagrange‘s equation. Lumped parameter model. Discrete systems. Eigenvalue problem. Natural mode of vibration. Approximate methods for finding natural modes and frequencies. 45h (T); E

MAT 832 Methods of Applied Mathematics in Dynamics 3 Credits

Regular and singular perturbation theory. Method of matched asymptotic expansions. Two timing: methods of multiple scales. WKB approximation. Averaging methods. Differential transform method (DTM). Adomian decomposition method (ADM). Variational iterative method (VIM). All these in context of application in dynamics. 45 (T); E

MAT 833 Dynamics of Distribution Parameter 3 Credits

Dynamics of continuous elastic system: strings, rods, beams, membranes and plates, formulation and solution of the boundary value problems. Rayleigh‘s energy methods. Ralyeigh-Ritz methods. Galerkin‘s methods. Elastic system on a foundation: Winkler, Pasternak. 45h (T); E

MAT 834 Non-linear and Random Analysis Dynamics 3 Credits

Non-linear systems. Conservative and non-conservative single-degree of freedom systems. Stability of equilibrium. Isocline. Delta. Perturbation. Iteration and Runge-Kutta methods. Continuous systems: including strings, plates. Introduction to random vibrations. Random processes. Stationary ergodic processes. Autocorrelation function for stationary processes. 45h (T); E

MAT 835 Fluid Mechanics I

Navier stokes equations and exact solutions energy equation. Flow at small Reynold‘s number. Stokes and Oseens‘ flows. Boundary layer theory. Appropriate methods of solution. Unsteady boundary layers. Boundary layer separation and control. 45h (T); E

MAT 836 Fluid Mechanics II 3 Credits

Introduction to the theory of hydrodynamics stability. Thermal instability of a layer of fluid heated from below. Instability due to an adverse gradient of angular motion. Inviscid couette flow. Viscous couette flow. Synge‘s theory. Rayleigh Taylor instability of superposed fluids. Kelvin-Helmholtz instability. OrrSommerfeld equation. 45h (T); E

MAT 837 Fluid Mechanics III 3 Credits

General features of oblique shocks. Centred expansion of homentropic flow. Hypersonic small disturbance theory. Hypersonic analogy and blast wave solutions. Newtonian flow. Freeman‘s theory of hypersonic flow part place and axis-symmetric blunt bodies. Constants/density solution. Newtonian slender body theory. Optium power law body. 45h (T); E

MAT 838 Fluid Mechanics IV 3 Credits

Review of magnetohydrodynamic (MHD) theory. Two phase problems. Two phase MHD problems. Radiative two-phase MHD problems. Solution of some radiative two-phase MHD problems. Reactive flows. Non Newtonian fluids: second and third grade fluids. 45h (T); E

MTH 801 Axiomatic Set Theory 3 Credits

Algebra of sets. Consistency. Truth-table models. Relations. Functions and inverses peano axioms. Existence in the theory of sets. Axioms of extension of specifications of replacement of choice of power set. Order well-ordering. Transfinite recursion. Zorn lemma. Ordinal arithmetic. Cardinal numbers. 45h (T); E

MTH 802 Point Set Theory 3 Credits

Topological spaces. Continuous functions and homeomorphisms. Topologizing of sets. Identification topology. Weak topology. Artesian products. Connectedness. Separation axioms. Covering axioms. Compact-open topology metric spaces. Metisation of topological space. Hausdolf spaces. Properties of Hausdolf spaces. Strong topology. 45h (T); E

MTH 803 Algebraic Topology Loop space.

Homotopy fundamental group (x) homotopy groups. Homotopy extension properties. Triangulation of compact space. Quotient spaces. Identification space topology. Covering spaces. Homology. Polynomial rings. Polynomials on fields. Factorisation of polynomial rings. 45h (T); E

MTH 804 Function spaces 3 Credits

Compact open topology. Evaluation map. Convergence. Metric topologies and topology. C (Y) spaces. Stone-weierstrass theorem. Ring C (Y). Complete spaces. Baire‘s theorem for complete metric spaces. Fixed-point theorem for complete spaces. 45h (T); E

MTH 805 Advanced Topology 3 Credits

Topics from homotopy. Cohomology. Free group and free products of groups. Theorems of fundamental group of union of two spaces. Applications to group theory. Singular homotopy and properties of uniform topology. Kernels of topology. 45h (T); E

MTH 806 Inequality II 3 Credits

Inequalities of a definite arithmetical character. Theory of primes. Bounds for integral variables. Inequalities to the algebraical theory of quadratic forms. Bessel‘s inequality for theory of orthogonal series. Inequalities on functiontheory: Hadamard‘s three circle theorem and geometrical inequalities. 45h (T); E

MTH 807 Inequality III 3 Credits

Inequalities. Young‘s Inequalities for Lp norms. Proof of the elementary case and standard form: MacLaurin‘s, Muirhead‘s, Chebyshev‘s, Clarkson‘s, Sobolev, Friedrichs‘, Poincare, Landau-Kolmogorov, Ky-Fan, Newton‘s, Hermite Hadamard, Borell-Brascamp-Lieb. Inequalities of arithmetic and geometric means. 45h (T); E

MTH 808 Inequality IV 3 Credits

Generalisation of Young‘s inequality using Legendre transforms. Jensen‘s, Karamata, Carleman‘s and Bernoulli inequalities. Elements of convex analysis. Convex sets. Convex functions. Duality. Jensen‘s. Inequality. Power means. Majorization inequality and supporting line inequality. 45h (T); E

MTH 809 Numerical Analysis I 3 Credit

Solution of algebraic equations; direct and systematic iterative methods for linear systems, convergence and stability of these methods. Sparse matrix techniques. Tridiagonalization and orthogonal factorization. Matrix eigenvalue problems. Over-determined systems. Solutions of non-linear equations: one point iterative methods, Newton‘s and Brown‘s methods, gradient methods, bracketing methods; convergence and stability of these methods. Special methods. 45h (T);

839 Dissertation 6 Credits

Research dissertation on a topic approved by the department. 270h (P); C

G. Graduation Requirements

To obtain M.Sc. degree in Mathematics, the candidate must pass at least 39 Credits comprising 23 Credits of Core courses, 4 Credits of Required courses and 12 Credits of Elective courses. in the chosen option.

I. Summary

Core Courses: MAT 839 (6), 801 (3), 802 (3), 803 (3), 804 (3), 805 (3), 817 (2), 23 Credits

Required Courses: SCI 801 (2), SCI 802 (2) 4 Credits

A. Algebra Option

Electives Courses: MAT 814 (3), 815 (3), 816 (3), 818 (3), 806 (3), MAT 807 (3),

808 (3), 809 (3) 12 Credits

Total of (C+R+E) Courses = 39 Credits

B. Analytical Dynamics Option

Electives Courses: MAT 831 (3), 832 (3), 833 (3), 834 (3), 829 (3), MAT 830 (3), 835 (3), 836 (3), 837 (3)
12 Credits
Total of (C+R+E) Courses = Complex Analysis Option Electives Courses:

MAT 806 (3), 807 (3) 808 (3), 809 (3), 814 (3), 815 (3), 39 Credits
MAT 816 (3), 818 (3)12 Credits
Total of (C+R+E) Courses = Fluid Mechanics Option Electives Courses:

MAT 835 (3), 836 (3), 837 (3), 838 (3), 828 (3), 829 (3),39 Credits
830 (3), 831 (3), 832 (3) 12 Credits
Total of (C+R+E) Courses = Functional Analysis Option Electives Courses:

MAT 819 (3), 820 (3), 821 (3) 822 (3), 806 (3), 807 (3), 39 Credits
814 (3), 815 (3), 823 (3) 12 Credits
Total of (C+R+E) Courses = Inequality Option Electives Courses:

MAT 819 (3), 820 (3), 821 (3), MAT 822 (3), 823 (3) MTH 806 (3), 807 (3), 808 (3)39 Credits

12 Credits
Total of (C+R+E) Courses =39 Credits

Modelling Option Electives Courses: MAT 824 (3), 825 (3), 826 (3), 827 (3), 810 (3), 811 (3),
MAT 828 (3), 829 (3), 830 (3)12 Credits
Total of (C+R+E) Courses =39 Credits

D. Numerical Analysis Option

Electives Courses: MAT 828 (3), 829 (3), 830 (3), 810 (3), 811 (3), 812 (3),

MAT 813 (3), 827 (3) 12 Credits

Total of (C+R+E) Courses = 39 Credits

E. Optimisation Option

Electives Courses: MAT 810 (3), 811 (3), 812 (3), 813 (3), 828 (3), 829 (3),

MAT 830 (3), 827 (3) = 12 Credits

Total of (C+R+E) Courses 39 Credits

F. Topology Option

Electives Courses: MTH 801 (3), 802 (3), 803 (3), 804 (3), 805 (3), 807 (3),

814 (3), MTH 815 (3), MAT 816 (3), 820 (3) 12 Credits

Total of (C+ R+E) Courses = 39 Credits

M. Sc. Mathematics

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