**ALPHA SEMESTER 400 LEVEL**

**MAT411: Topology (3 Units)**

Topological spaces; neighbourhoods and neighbourhood systems. Subspaces, induced topology. Bases, continuity, Metric and normed spaces. First countable, second countable, separable spaces. T1, T2, T3, T4 spaces. Compactness. Product spaces. Connectedness.

**MAT412: Differential equations II (3 Units)**

General linear ordinary differential equations of second order with stipulated initial and boundary conditions. Integral transforms: detail treatment of Laplace transforms, Fourier transforms and Hankel transforms for general solution of IVPs and BVPs. General theory of operators: finite dimensional representation of operators, diagonalization operators, Special theory of function of operators. Integrals and differential operators.

**MAT413: Probability Theory and Stochastic Process (3 Units)**

Probability, random variables, probability distributions, expectation probability generating functions. Convolution and compound distributions. Recurrent events. Branching processes, random walks (unrestricted and restricted). Gamblers ruin problems. Markov process in discrete and continuous time, Poisson, birth and death processes. Queuing processes: M/M/I, M/M/s, M/a/I queues and their waiting time distributions..

**MAT414: Numerical Analysis II (3 Units)**

Finite difference equation and operations; Discrete variable methods for solution of IUPS – ODES. Discrete and continuous Tan methods for solving IUP – ODES, error analysis. Partial differential equation. Finite difference and finite elements methods. Stability convergence and error analyses.

**MAT415: Experimental Design (3 Units)**

Basic principles of experimentation, Randomization, replication and blocking. Local control. Design and analysis of experiments: replication and randomization, completely randomized, randomized blocks and Latin square designs, Balance incomplete blocks, split plot. Missing values. Relative efficiency. Estimation and test of variance components. Multiple comparisons. Departure from underlying assumptions. Factorial experiments. Yates – Algorithm confounding and fractional replication. Diallel Cross Analysis. Further split designs, 2’’ factorial designs. Analysis of treatment effects: Orthogonal contracts and multiple comparisons. Investigation of assumptions and theory of tests. Application to Agriculture, biology and industry. Introduction to response surface methodology.

**MAT416: Advanced Algebra (3 Units)**

Lattice theory, Notherian and Artinian modules and rings. Hilbert basis theorem. Chinese remainder theorem. Semi-simple modules and rings. Prime spectrum of a commutative ring.

**MAT417: Functional Analysis (3 Units)**

Banach spaces and Hilbert spaces. Bounded linear functionals and Operators on Banach Spaces. Introduction to Topological Vector spaces. Introduction to Banach Algebras and Gelfand theory.

**MAT418 : Complex Analysis II (3 Units)**

Integration: curves, Jordan Curve Theorem, Riemann integration along smooth curves. Cauchy’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 singularities, isolated singularities. Laurent’s theorem, residue theorem and application to evaluation of integrals and summation of series. Maximum modulus principles. Schwartz’s lemma, the Argument theorem, Rouche’s theorem. Introduction to analytic continuation.

**Statistical Inference II (3 unit)**

Fisher’s information. Cramer-Rao inequality. Interval estimation. Tests of hypotheses. Neyman-Pearson theorem. Methods of estimation: Mini-max, MLE Optimum properties of estimators Sufficiency and factorization theorem. Rao-Blackwell theorem. Testing of hypotheses. Discussion of Optimality properties of tests. Decision theory: Elements of the theory of Games and Decision theory. Criterial of preference of decision procedures. Estimation theory: Minimax, Bayes and other decision procedures.

**Elementary Categorical Data Analysis (3 Units)**

Probability models for 2 x 2 tables. Hyper geometric, product Binomial, Multinomial models. Fisher’s exact test Measure of association for 2 x 2 tables: Odds ratio, Log-odds ratio, correlation coefficient type statistics. Measure of sensitivity, specificity, and predictive accuracy. Some models under dichotomous response: logistic, probit and complimentary log-linear models.

**MAT434: Classical Mechanics I (3 Units)**

Frame of reference, Inertial frames, Forces, Velocity, Acceleration, Linear momentum, Angular velocity, Angular acceleration, Angular momentum, motion of a particle (Newton laws), motion of a system particles, Rotating coordinate systems, moments and products of inertia. Parallel axes theorem, perpendicular axes theorem for moments and products of inertia. Principle axes and principle moments of inertia of a system of particles, Rotating coordinate systems, Infinitesimal rotation, Euler equations, Generalized coordinates, Lagrange’s formulations, Hamiltonian functions, Theory of small oscillation, Impulsive motion.

**CSC 413: Algorithms and Complexity Analysis (3 Units)**

Basic algorithmic analysis: Asymptotic analysis of upper and average complexity bounds; standard Complexity Classes Time and space trade-offs in algorithms analysis recursive algorithms. Algorithmic Strategies: Fundamental computing algorithms: Numerical algorithms, sequential and binary search algorithms; sorting algorithms, Binary Search tress, Hash tables, graphs & its representation.

**CSC 415: Artificial Intelligence (3 Units)**

Introduction to artificial intelligence, understanding natural languages, knowledge representation, expert systems, pattern recognition, the language LISP.

**EDS411: Entrepreneurial Development Studies VII (1 Unit)**

Issues in Entrepreneurship & Management of SMEs (Part 1). Objective: To expose the students to more issues in entrepreneurship. Topics covered include the following: Various functions of Entrepreneurship – such as financing, production, marketing and personnel management. Entrepreneurial succession, issues in succession: challenges and prospects. Taking Entrepreneur to the stock market. International Entrepreneurship.Funding of Entrepreneurial activities. Term paper on Entrepreneurship from some selected areas of SMEs (Small And Medium Scale Enterprise) operations.

**TMC411: Total Man Concept VII (1 Unit)**

Leadership Development (Part 1). This course examines the building blocks for leadership development in the context of providing an overview of the broad dimensions of leadership. The course also explores the enhancement of leadership traits and how power and influence qualifies the dynamics of leadership.

**TMC412: Total Man Concept - Sports (0 Unit)**

Game (Soccer & Volleyball): This centres on the mastery of basic skills, game situation as well as rules and regulation governing the various sports that will be attempted. Focuses are also being on appreciation of various sports and the spirit of sportsmanship that is ‘win or loss’ taking it in good fate. Aerobics exercise: This is said to be any activity that can get the heart rate going and keeps it at a sustained rate over a period of time. Eg twenty minutes. An aerobic activity helps to increase cardiorespiratory fitness which is one of the fine essential components of physical fitness. Being aerobically fit you can feel it as you go about. Muscle tone improves as you work on the proper running techniques.

**OMEGA SEMESTER**

**MAT421: Optimization Theory (3 Units)**

Linear programming models. The simplex method: 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.

**MAT422: Differential Equations III (3 Units)**

Introduction to Partial Differential Equations. Partial Differential equations of the first order: Langrange method, Standard method, Charpits method. Partial Differential equations of the second order: method by inspection, Monge’s method, Monge’s method of integration. Solution to general Linear Partial Differential Equations of higher order. Solutions to special types of partial differential equations: Hyperbolic, Parabolic, Elliptic equations, Diffusion equation, Wave equation. Methods of solution: Separation of variables, D’Alembert’s method.

**MAT423: Theory of Measure (3 Units)**

Lebesgue measure for subsets of Rn. Lebesgue integration of real and complex-valued functions defined on subsets of Rn. General measure space (X, µ, ϕ) and Lebesgue integration with respect to of real ϕ and complex-valued functions on X. The Classical Banach spaces.

**MAT424: Survey Methodology & Quality Control (3 Units)**

Quality control acceptance sampling, control charts, cumulative sum techniques. Survey methodology: planning of surveys, simple random, stratified, cluster and systematic scenes. Sampling for means, totals and proportions. Sample size allocation in stratification. Comparison of precisions. Ratio and regression estimation, two stage sampling.

**MAT425: Systems Theory (3 Units)**

Lyapunov theorems. Solution of Lyapunov stability equation ATP+PA=Q. controllability and observability. Theorem on existence of solution of linear systems of differential equations with constant coefficients. Uniqueness theorems, theory of stability, elementary type of rest points. Stability under constantly operating perturbation. Test for stability. Lyapunov theorems. Solution of Lyapunov stability

**MAT428: Classical Mechanics II (3 Units)**

Theory of Forces and Couples Basic definitions, Force acting at a point, Resultant of a system of Forces acting at a point, Condition for equilibrium of a system of Forces acting at a point, Vector moment of a Force, Couple, Moment of a Couple, Resultant of a system of Forces in 3D, Invariants, Wrench, Coplanar Systems of Forces, Varignon’s Theorem of Moments, Parallel Systems, Conjugate forces. Bending of Beams: Shear and Bending moment in a beam, Relations among Load, Shear and Bending Moment, Thin Elastic Beams, Bernoulli-Euler Law, Macaulay’s Notation, Clapeyron’s equation for three moments. The Catenary: Flexibility, The common catenary, Parabolic chain, suspension bridge, Catenary of uniform strength, General equations of equilibrium of a string in one plane under given forces, Strings on rough curves, Variable chain hanging under gravity.

**MAT429: Research Project (6 units)**

The student undertakes a research project approved by the Department and Supervised by a Lecturer. The student consults the supervisor as often as necessary. At the end of the session, the student submits a written report on the topic and defends same before a Departmental evaluation board.

**MAT440: Control Theory and Project Management**

Introduction: definition, examples of control systems. Open-loop and closed-loop control systems. System modeling: Signal flow graph, block diagram. Network flow problems. Basic concept of projects, tasks, events, etc.; project planning and execution; critical path method (CPM); project evaluation and review technic (PERT)

**MAT441: Demography (3 Units)**

Types and sources of demography data. Methods of collection of population census, sample surveys and vital registration. Evaluation of the quality of demographic data. Measures of fertility, mortality, nuptiality and migration. Standardization and Decomposition. Life tables: construction and application. Framework for developing demographic information systems.

**MAT442: Time Series Analysis (3 Units)**

Estimation and Isolation of components of time series. Non-stationary and stationary processes: theoretical moments, auto-correlation and partial auto-correlation; sample moments: auto-correlations; partial auto-correlations; Univariate Time Series model: identification and estimation – Auto-regressive (AR), Moving (MA) and Auto regressive Moving (ARMA). Diagnostic checking of models, Linear prediction and forecasting spectral (Harmonic) analysis.

**CIS 421: Computer Security (2 Units)**

Introduction: Objectives, privacy and ethics, risk analysis in computer security, threats and security, security measures, physical protection (natural disaster, physical facility, access control), hardware and software security control, viruses (Trojan horses, worms and logic bomb), encryption and cryptography techniques. Development Secured Computer.

**CSC 423: Concept of Programming Languages (3 Units)**

Language definition structure. Data types and structures, Review of basic data types, including lists and tress, control structure and data flow, Run-time consideration, interpretative languages, lexical analysis and parsing. Pre-requisite – CSC 211, 221, 214, 312.

**EDS421: Entrepreneurial Development Studies VIII (1 Unit)**

Issues in Entrepreneurship & Management of SMEs (Part 2). Topics covered include the following: Reviewing/appraising various strategies and skills for:

Poverty Alleviation

Employment through SMEs

Entrepreneurial Environments: types, appraisal and contending with the environment in Nigeria, Africa/Third World countries.

Incorporating the company: practical steps and issues involved, translating the four phases of business into reality (Micro, Small, Medium and Large).A greater depth of the practical issues in launching, growing and harvesting of entrepreneurial outfits. Issues involved in Partnership and Corporation Formation. Final Project presentation (On the dream business) and feasibility studies on Entrepreneurship etc.

**TMC421: Total Man Concept VIII (1 Unit)**

Leadership Development (Part 2). This is a continuation of TMC411. This second part of the course on leadership development examines the biographical details and leadership traits or styles of some biblical and historical figures and identifies some specific lessons for developing leadership traits and sensitivity. Specific character studies will examine the leadership style of Jesus, Moses, Joshua, Gideon, Alexander the Great, Nelson Mandela, NnamdiAzikwe etc.

**TMC422: Total Man Concept - Sports (0 Unit)**

Jogging: This helps in many ways, our focus here on the benefit of jogging is for physical fitness that reduced risk of Osteoporosis. Osteoporosis is the condition when the bones become increasingly porous and brittle. It can result to bone fractures and deformities.

Game (Basketball & Handball): This centres on the mastery of basic skills, game situation as well as rules and regulation governing the various sports that will be attempted. Focuses are also being on appreciation of various sports and the spirit of sportsmanship that is ‘win or loss’ taking it in good fate.