### Special Course Description – Level I

**MSP311β: Group Theory (30 lecture hrs + 15 tutorial hrs) Same as MAT311β (Credit Value 2.5)**

**MSP312β: Real Analysis-III (30 lecture hrs + 15 tutorial hrs) Same as MAT312β (Credit Value 2.5)**

**MSP313β: Mathematical Statistics-II (30 lecture hrs+15 tutorial hrs) Same as MAT313β (Credit Value 2.5)**

MSP314β: Mathematical Methods in Physics and Engineering I (30 lecture hrs+15 tutorial hrs) Same as MAM313β (Credit Value 2.5)

MSP3144: Mathematical Methods in Physics and Engineering II(60 Lecture hrs) (Credit Value 4)

Part A:

Same as AMT313β.

Part B:

Applications of Laplace Transforms to Differential Equations, Fourier Transforms, Legendre Functions, Hermite Equation, Functions and Polynomials, Laguerre Equation and Polynomials, Riccati’s Differential equation, The

Dirac-Delta function,

*Method of assessment: end of semester examination*

MSP316β: Applied Statistics II (30 lecture hrs+15 tutorial hrs)- Same as MIM313β (Credit Value 2.5)

**MSP3174: Topology (60 hrs) (Credit Value 4)**

Topological Spaces, Basis for a Topology, The Subspace Topology, Closed Sets, Limit Points, Continuous Functions, The Product Topology, The Metric Topology, Connected Spaces, Compact Spaces

*Method of assessment: end of semester examination*

**MSP3184: Measure Theory with Applications (60 hrs) (Credit Value 4)**

Borel – Algebra, Borel subsets, Lebesgue outer Measure, Lebesgue measurable subsets, Lebesgue measure, Lebesgue measurable functions. Properties that hold almost everywhere, Lebesgue Integral, Lebesgue integrable functions, Monotone Convergence Theorem, Dominated Convergence Theorem, Fatou’s Lemma, Relation of Riemann and Lebesgue Integrals, Modes of convergence (topics are discussed with applications example probability theory),Introduction to martingales

*Method of assessment: end of semester examination*

MSP3193: Bayesian Inference and Decision Theory (45 hrs) (Credit Value 3)

Fundamentals of the Bayesian theory of inference, probability as a representation for degrees of belief, the likelihood principle, the use of Bayes Rule to revise beliefs based on evidence, conjugate prior distributions for common statistical models, methods for approximating the posterior distribution. Graphical models for representing complex probability and decision models by specifying modular components. Concepts in decision analysis, including influence diagrams, decision trees, and utility theory or/and special topics in advanced Bayesian inference and decision theory.

*Method of assessment: end of semester examination*

**MSP3b9β Mathematical Computing (90 project hrs) (Credit Value 2.5) Same as IMT2b2β;**

The symbolic/numerical mathematics package Mathematica is introduced to solve mathematical problems on the computer. In particular special attention will be given to functional programming aspects of symbolic and numerical computations in Mathematica.

*Method of assessment: Practical examination/assignments/project report and the end of semester oral examination and/or presentation*

**MSP321α: Linear Algebra (23 hrs) (Credit Value 1.5)**

Advanced Group Theory: Isomorphism Theorems, Series of groups, sylow theorems, applications of the sylow theorem, free groups.

*Method of assessment: end of semester examination*

**MSP322α: Real Analysis IV (23 hrs) (Credit Value 1.5)**

Implicit functions: definition, derivative of implicit functions, Implicit function theorem Jacobians, stationary values under subsidiary conditions . More on Integration on R2 : Green’s theorem, Change of Variables in a double

integral.

*Method of assessment: end of semester examination*

**MSP323β: Complex Variables (30 lecture hrs + 15 tutorial hrs)**

– Same as MAT322β

**MSP324α: Complex Analysis (23 hrs) (Credit Value 1.5)**

Review of elementary complex analysis topics from vector analysis: Morera’s Theorem, Liouville’s Theorem, Rouche’s Theorem, Winding numbers, the generalized version of Cauchy’s theorem, Morera’s theorem, the fundamental theorem of algebra, the identity theorem, the Riemann sphere and Weierstrass-Casorati theorem, meromorphic functions, Rouche’s theorem, integration by residues, Conformal mappings and its Physical applications.

*Method of assessment: end of semester examination*

**MSP3254 Numerical Methods with Applications (60 hrs) (Credit Value 4)**

Solving Linear Systems: Matrix notation, direct methods, Gauss, Jordan, Aitken Method etc.Iterative methods: Jacobi, Gauss-Seidel, SOR method etc.Numerical Solution of Ordinary Differential Equations: Euler and modified Euler methods and Runge-Kutta methods, convergence Criteria, errors and error propagation. Numerical Solution of Partial Differential Equations: parabolic type, Elliptic type and Hyperbolic type.

*Method of assessment: end of semester examination*

**MSP3263: Regression Analysis (45 hrs) (Credit Value 3)**

Introduction: Regression and model building, use of regression, role of the computer.

Simple Linear Regression: simple linear regression model, least-square estimation of the parameters, hypothesis

testing on the slop and intercept, interval estimation in simple linear regression, prediction of new observations,

coefficient of determination, estimation by maximum likelihood.

Multiple Linear Regression: Multiple linear regression models, Estimation of the parameters, Hypothesis

testing in multiple linear regression, Confidence interval in multiple regression, prediction of new observations,

Multicollinearity.

Model Adequacy Checking: Residual analysis, Lack of fit of the regression model. Indicator Variables, Variable

Selection and Model Building, Introduction to Nonlinear Regression, Introduction to Generalized Linear Models.

*Method of assessment: end of semester examination*

**MSP3274 Differential Geometry and Tensor Analysis (60 hrs) (Credit Value 4)**

Unit tangent vector, Principal normal, binormal vector and curvature of a curve, Serrate-ferret formula, surfaces, parametric curves, surfaces of revolution, metric, directional ratios and coefficients, Gauss and Mean curvature, Orthogonal trajectories, families of dual curves, Geodesics. Transformation of coordinates, summation convention, the Kronecker-delta, contravariant and covariant vectors, contravariant, covariant and mixed tensors, symmetric and skew- symmetric tensors, tensor algebra, metric tensor, conjugate metric tensor, Christoffel’s symbols of first and second kind, covariant derivatives, Riemann and Ricci tensors.Theory of Manifolds, Commutators or Lie Derivatives, Forms and Dual bases, The wedge product, Exterior and Covariant differentiation, First and Second Carton equations, The Ricci Tensor and the Einstein Tensor.

*Method of assessment: end of semester examination*

**MSP3283 Special Topics in Statistics (eg. Multivariate Data Analysis) (45 hrs) (Credit Value 3)**

Multivariate data and multivariate statistics: Introduction, Types of data, Basic multivariate statistics,The aims of multivariate analysis. Exploring multivariate data graphically: scatterplot, scatterplot matrix, checking distributional assumptions using probability plots.Cluster analysis, Principle component analysis, Logliner and logistic models for categorical multivariate data,Models for multivariate response models, discriminant analysis and factor analysis.

*Method of assessment: end of semester examination*

**MSP3293:Applied Statistics III (30 hrs) (Credit Value 2)**

One-Factor Experiments: Analysis of Variance Techniques,One-Way ANOVA, Completely Randomized De-

sign, Two-way ANOVA, Randomized Block Design.

Chi-squared Tests: Goodness of Fit Test, Categorical Data, Test for Independence, Test for Homogeneity,

Nonparametric Tests: Sign test, Signed-Rank test, Rank-Sum test, Kruskal-Wallis test, Runs test, Rank Cor-

relation Coefficient.

Applied Nonparametric Regression: Introduction, Basic idea of smoothing, Smoothing techniques, Choosing

the smoothing parameter.

*Method of assessment: end of semester examination*