**MA 141 Basic French I (1, 1, 1)**

Establish one’s identity: Greetings and polite expression, introducing oneself and other. The Francophone World: The place of French in the world; Francophone countries and La Francophone. Time and Weather: Days of the week, months of the year; telling the time of the clock. Telling the weather, weather forecast. The Family/Professions: Members of the family, one’s place in the family; professions/trades of parents. Health and Sport; Parts of the body stating where one is suffering from; common diseases and medications; Heath facilities.

**MA 151 Applied Electricity (2, 2, 3)**

Circuit laws. Circuit theorems. Electrostatics. Electromagnetic. Magnetic circuits. Inductance. Alternating voltage and current. Signal waveforms. Introduction to transformers, DC machines, Induction Machines and Synchronous machines.

**MA 157 Communication Skills I (2, 1, 2)**

Introduction to communication: methods and systems of communication. Pre-writing skills: developing listening skills, note-taking and note-making, developing reading skills, developing writing skills (I): Sentence level (the sentence as an ordered string of words, the simple sentence, basic sentence patterns, common grammatical errors). Coordination and parallelism. Ambiguity and Conventions of usage.

**MA 159 Introduction to Computing (1, 2, 2)**

Introduction to PCs. Windows Operating System, Internet usage, Word Processing, using MS Word. Spreadsheet using MS Excel. Introduction to Programming using Visual Basic Applications (VBA).

__MA 163 Introduction to Programming with C++ (1, 4, 2)__

Understanding and using the basic programming constructs of C/C++ such as operators and expressions, standard C/C++ preprocessor, standard C/C++ library and conditional program execution and program looping and iteration. Manipulating various C/C++ data types, such as arrays, strings, and pointers and isolating and fixing common errors in C/C++ programs. Using memory appropriately, including proper allocation/de-allocation procedures, Appling object oriented approaches to software problem in C++ programs using the above skills.

__MA 171 Basic Algebra and Trigonometry (2, 1, 2)__

Indices. Logarithms. Surds. Polynomials. Rational functions. Partial fractions. Sequences and finite series. Complex numbers. Principles of induction. Binomial theorem for a positive integral index. Trigonometric functions: addition and factor theorems, applications of Trigonometry, circular measure. Equations of lines and circles. Hyperbolic functions.

__MA 173 Vectors and Coordinate Geometry (2, 2, 3)__

Vectors in Euclidian spaces, especially in dimensions 1, 2, and 3. Positive vector. Dot product (scalar product). Cross product (vector product). Composition and resolution of vectors. Vector equation of a line. Vector equation of a plane. The straight line and the plane. The angle between a line and a plane. The angle between two lines and between two planes. Scalar triple products. Conic sections: Parabola, ellipse and hyperbola. Parametric representation of curves.

__MA 175 Discrete Mathematics and Theory of Proofs I (2, 1, 2)__

Multinomial coefficients. Finite difference equations. The z-transform approach to solution. Difference equations with characteristic polynomial which have complex roots. Boolean algebra. Basic Boolean functions. Elements of proof theory. Type Theory. First Order Predicate Calculus. Peano Arithmetic.

Year One Semester Two |

__MA 142 Basic French II (1, 1, 1)__

Movement and Travel: Using adverbs of place to locate places; asking one’s way around, giving direction to places. Transportation: means and types of transport; local and foreign travel, identifying travel schedules. Problems of transportation. Making Purchases/shopping: Saying what one wants to buy; asking the price of items, bargaining and mode of payment. Life in the University: Identifying places on campus. Academic activities; administrative activities. Culinary Art /French cuisine: Art of cooking; kitchen/cooking utensils. Types of meals in a day

__MA 158 Communication Skills II (2, 1, 2)__

Communication skills. Oral presentation. Formal speech making. Conducting interviews and meetings. Communication process. Skill in communication. Channels in communication in an organization. Preparation of official documents such as letters, memos, reports, minutes and proposals.

__MA 170 Discrete Mathematics and Theory of proof II (2, 2, 3)__

Relations in a set. Partial ordering. Zorn’s lemma. Digital logic gates. Minterm and maxterm expansions. Second Order and Infinite Order Systems. Infinity Logic. Predicate logic, Extension of Predicate logic. Cut elimination in predicate logic.

__MA 172 Calculus of a Single Variable (2, 2, 3)__

Limits. Differentiation of a composite function. Implicit differentiation. Maxima and minima. Applications of derivatives: Curve sketching. Integration as the inverse of differentiation. Application of integration to: trigonometry, polynomials, hyperbolic and exponential functions, areas and volumes. Integration techniques: integration by substitution, by parts and by resolution into partial fractions. Taylor’s and Maclaurins series.

__MA 174 Linear Algebra I (2, 1, 2)__

Matrix algebra. Systems of linear equations. Algebra of linear transformations and their representation by matrices. Eigenvalues and eigenvectors. Cayley – Hamilton’s theorem. Add

__MA 176 Statistical Methods (2, 2, 3)__

Descriptive statistics: summarizing data graphically (bar graph, box-plots, stem-and-leaf plots) and summarizing data numerically (measure of location and dispersion), Normal distribution, inference for single population (point/interval estimation; hypothesis testing), Inference for two populations (interval estimation; hypothesis testing), Introduction to Regression and correlation analysis, introduction to Analysis of Variance.

__MA 178 Vector Applications (2, 1, 2)__

Vector mechanics: Statics and Dynamics. Velocity, momentum and moments. Equilibrium and conservation laws. Introduction to vector-valued functions. Differentiation of vector-valued functions. Coordinate-free definitions of gradient, curl and divergence. Scalar and vector potential. Notion of orthogonal curvilinear coordinates and bases. Motion in plane: projectiles, circular motions.

__MA 180 Fundamentals of Economics (2, 0, 2)__

The Economic Problem; Production Possibility Frontiers, Specialization and Trade, Comparative Advantage. Mathematical Techniques in Economics (Interpretation of Graphs, Algebra or functions). Microeconomics: Market Demand and Supply, Elasticities. The Theory of Consumer Behaviour, the Theory of the Firm. Macroeconomics: Measurement of national output and income, Aggregate Demand (AD) and Aggregate supply (AS). Money and Banking. Inflation, Interest Rate, Exchange Rate and Unemployment.

Year Two Semester One |

__MA 251 Literature in English I (1, 1, 1)__

Introduction to literary terms and devices. Specific texts: prose, drama, poetry. Vocabulary and language use. Literature as a reflection of contemporary way of life or society (the text as mirrors). Literature and morality (the text as examples). Literature as a form of entertainment. African Writers Series.

__MA 261 Linear Algebra II (2, 1, 2)__

Vector spaces and subspaces. Basis dimension and coordinates. Change of basis. Annihilating polynomial. Linear functional, Dual spaces. Multi-linear forms. Inner product spaces. Orthogonalisation process. Hermitian, bilinear and quadratic forms. Reduction to a canonical form. Unitary and normal transformations.

__MA 271 Calculus of Several Variables (2, 2, 3)__

Partial differentiation of a function of several variables. Differentiation of implicit functions. Jacobians. Differentiation of a vector functions of several variables. The tangent vector. Curvilinear co-ordinates. Plane polar, cylindrical and spherical co-ordinates. Multiple integrals. Line integrals, multiple, surface and volume integrals. Cartesian tensors and their transformations.

__MA 273 Introduction to Real Analysis (2, 2, 3)__

Introduction to the theory of real numbers. Least upper bound, greatest lower bound of a set. Convergence of sequences. Upper and lower limits. The Bolzano-Wierstrass theorem and the Cauchy principles of convergence. The notion of a function, limit and continuity. Inverse and composite functions. Derivatives of a function. Mean value theorem. Rose’ theorem.

__MA 275 Introduction to Numerical Methods (2, 2, 3)__

Sources and types of error; round-off errors, truncation error, Basic error analysis. Evaluation of functions. Numerical solution of non-linear algebraic equation; one-point methods; simple iteration, secant and Newton-Raphson methods. Acceleration and relaxation. Bracketing methods; Bisection and false-position methods. Numerical Integration: Trapezoidal Method, Simpson’s Method and Gaussian Quadrature. Use of computer essential.

__MA 277 Probability Theory (2, 2, 3)__

Probability: definition and main properties, counting techniques (Permutation and combination), Conditional probability. Independent random events, Main Laws of Probability, Discrete distributions (binomial, geometric, Poisson, hyper-geometric), Expectation and variance. Continuous distributions (uniform, normal, exponential, gamma, chi-square), Expectations and variance. Multivariate distributions, Functions of random variables, The Law of Large Numbers, The Central Limit Theorem.

__MA 279 Basic Physical Chemistry (2, 2, 3)__

Atomic theory, Bonding and Periodicity. Properties of gases, solids and liquids. Chemical equilibrium, Ionic equilibrium, Radioactivity.

Year Two Semester Two |

__MA 252 Literature in English II (1, 1, 1)__

Reading and appreciation. Literary terms. Specific texts: prose, drama, poetry. Vocabulary and language use. Literature as a reflection of contemporary way of life or society (the text as mirrors). Literature and morality (the text as examples). Literature as a form of entertainment. Shakespearean and modern classics.

__MA 256 Field Trip and Technical Report Writing I (1, 1, 1)__

Field trips to the area of interest. Students will be expected to present reports upon which they will be assessed for their credits.

__MA 270 Chaos, Fractal and Dynamical System (2, 2, 3)__

Fractals and chaos in discrete dynamical systems; Fixed points, periodic cycles, stability, Cantor set, the tent map, chaos, Sierpinski triangle, Newton’s method, Julia sets. Dimension of fractals; the Koch curve, the box and Hausdor dimensions. The logistic map; period-doubling bifurcations; Sarkovskii’s theorem; the U-sequence; renormalization. Julia sets and the Mandelbrot set. Mathematical theory, Universality of the Mandelbrot set and Julia sets, Newton’s method revisited. Strange attractors. Continuous dynamical systems and chaos.

__MA 272 Regression Analysis (2, 2, 3)__

Simple Linear Regression, Correlation, Multiple Regression, Test of Goodness-of-fit, Heteroscedasticity and Autocorrelation, Model Selection, Introduction to Logistic Regression.

__MA 274 Ordinary Differential Equations__**(2, 2, 3)**

Ordinary differential equations of first order: Separable, Homogeneous, Linear, Exact. Integrating factors. Linear differential equations of the second order with constant coefficients. Systems of first order equations. Solution of ordinary differential equations of second order using methods of variation of parameters. Reduction of nth order equation to a system of first order equations. Series solution of differential equations. D-operator methods for particular integrals. Laplace transforms and its applications.

__MA 276 Numerical Methods and Scientific Computing (2, 2, 3)__

Numerical solution of sets of linear algebraic equations: elimination back substitution. Matrix inversion. Instabilities and pivoting. Gaussian elimination. Iterative methods for linear systems: Gauss-Jacobi, Gauss-Siedel and successive over relaxation (SOR). Convergence and error analysis. Order of an iterative process. Flowcharts and algorithms. Practical solutions of problems using a computer.

__MA 278 Theoretical Mechanics (2, 2, 3)__

Principles of Newtonian mechanics, single particle under the action of variable forces (F(x), F(t), F(v)). Motion in 1-dimention. Potential energy. Stable, unstable and neutral equilibrium. Free, damped and forced harmonic oscillator. Resonance. Motion in 2, 3 dimensions. Force fields. Conservation theorem of energy. Linear and angular momentum.

__MA 280 Programming with Matlab and Python (2, 2, 3)__

Introduction to the MATLAB programming environment MATLAB basics: Variables and Arrays, Displaying Output Data, Data Files, Operations, Built-in MATLAB Functions, Branching statements and Loops. Flowcharts and Pseudocode, User-defined functions. Introduction to Plotting: Two-Dimensional, Three-Dimensional, Multiple Plots and Animation. Python datastructures: lists and dictionaries. Functions and modules. Input/Output: files and serialization. Basic tools for parallel programming.

Year Three Semester One |

__MA 371 Classical Mechanics (2, 2, 3)__

Central forces. Effective potential. Kepler’s laws and planetary motion. 2-3 dimensional harmonic oscillators. General theorems on the motion of a system of particles with applications to the motion of a rigid body. Variational principles. Lagrange and Hamilton’s equations. Normal coordinates.

__MA 373 Partial Differential Equations (2, 2, 3)__

Definition of a partial differential equation of the first order. Cauchy problem and its characteristics. Method of Lagrange. Classification of second order equations (parabolic, hyperbolic, elliptic). Laplace’s and Poisson’s equations. Separation of variables. Fundamental solution of potentials and their properties. The wave and heat equations. Method of eigen function expansions. Solution of systems of partial differential equation.

__MA 375 Mathematical Modelling ____(2, 2, 3)__

Introduction to modeling and dynamical systems. Chemical Kinetics. First order linear dynamical systems. Introduction to nonlinear dynamical systems. Stability and bifurcation behaviour for nonlinear dynamical systems. Chaos.

__MA 377 Numerical Methods for Ordinary Differential Equations (2, 2, 3)__

Methods for first-order differential equations: Taylor’s method, Euler methods, Runge-Kutta methods, multi-step methods. Methods for higher-order differential equations: Taylor’s, Euler and Runge-Kutta methods.

__MA 379 Elements of Topology (2, 2, 3)__

The concept of a topology: open sets, closed sets, interior, closure, derived sets and boundary of a subset. Continuous mapping. Metric spaces. Uniformly continuous mapping homeomorphism. Dense sets. Separable spaces. Connectedness. Compactness. Hausdorff space

__MA 381 Non Parametric Statistics (2, 2, 3)__

Scale of measurement, rank correlation, other measures of associations in ranked data, rank tests to compare two treatments, Tests to compare more than two treatments, Blocked comparisons.

Year Three Semester Two |

__MA 352 Public Relations (2, 0, 2)__

Scope and importance of Public Relations (PR): ** **the business of PR, definitions of PR, the publics of PR; PR distinguished from other forms of communication; the five images in PR; the qualities of a good PR officer. Planning PR programmes: the four reasons for planning PR programmes; the six-point planning model; the PR transfer process. The PR department; the size of PR department; the PR consultant and manager. The news media; the created private media; press relations. PR in developing countries. Crisis management PR.

__MA356 Field Trip and Technical Report Writing II (0, 4, 1)__

Field trips to the area of interest. Students will be expected to present reports upon which they will be assessed for their credits.

__MA 372 Special Mathematical Functions (2, 2, 3)__

Series solution of certain linear differential equations of second order (example Legendre’s equation and Bessel’s equation). Special functions: Legendre polynomials. Bessel functions, Hermit and Chebychev polynomial, Laguerre and hypergeometric functions. Gamma and beta functions: Sterling’s formula, asymptotic expansions. The method of steepest descent. The method of stationary phase. Recurrence relation. Watson’s Lemma. The error function. The exponential integral.

__MA 374 Elements of Abstract Algebra (2, 2, 3)__

Relations, functions, Permutations, Rings and fields: Definitions, examples and properties. Polynomial rings. Euclidean algorithms. Ideal and quotient rings. The homomorphism theorems. The field of quotients of an integral domain. Principal ideal domains. Factorization in principal ideal domain. Groups. Examples of groups such as cyclic groups. Groups of permutations and dihedral groups. Subgroups, cosets and Lagrange’s theorems for groups.

__MA 376 Optimization Techniques (2, 2, 3)__

Description of the problem of optimization and geometry of R^{n}, n>1. Convex sets and convex functions. Solution of systems of algebraic and transcendental equations. Matrices. Farkas lemma, gradient and Hessian of a function on R^{n}. Unconstrained and constrained problems in R^{n}. Derivative of subjective function available or unavailable, algorithms of Davies, Swann and Campey (DSC), Powell and Goggin (DSC-Powell). Simultaneous search and sequential algorithms. Constrained linear problems in R^{n}, n>1.

__MA 378 Complex Analysis (2, 2, 3)__

Algebra of complex numbers. Convergence of series. Uniform convergence of sequences and functions. Power series. Functions defined by power series. Analytical functions. Differentiation. Cauchy-Riemann equations. Cauchy’s theorem. Cauchy’s integral formulae. Harmonic functions. Conformal mapping. Calculus of residues. Elements of analytical continuation. Maximum modulus principle. Rouche’s theorem and fundamental theorem of algebra.

__MA 380 Statistical Inference (2, 2, 3)__

Estimation: Properties of point estimators. Uniformly minimum variance estimators. Cramer Rao lower bound. Sufficient statistics. Likelihood functions and methods of estimation. General methods of interval estimation. Means and variances of normal distributions, properties. Tests of hypotheses: Power and operating characteristic curves. Sample size estimation: Neyman-Pearson lemma. Likelihood ratio tests and applications.

Year Four Semester One |

__MA 451 Research Methods and Ethics in Science (2, 0, 2)__

Definition and concepts of research. Research process. Research design. Literature review. Sampling. Reliability and validity of data. Qualitative and quantitative research methods. Research reporting. Definition of ethics. Definition of science. Definition of ethics in science. What is a profession? How ethics and values intersect with professionalism. Ethical theory and applications. Standards of ethical conduct in science. Common ethical principles in science. Fraud in science. Whistle blowing. Conflict of interest. Case studies.

__MA 473 Continuum Mechanics (2, 2, 3)__

Continuum mechanics: Lagrangian and Eulerian description of motion. Equation of continuity. Deformation: deformation gradient tensors. Strain tensors. Stress tensors. Cauchy’s equations of motion or conservation of momentum. Hook’s law for elastic media strain-rate tensor. Newtonian viscosity. Viscous flow. Navier-Stokes equations. Bernoulli’s flow in 2 dimensions. Complex potential. Blasuis theorem, Milne-Thompson theorem. Waves. Electrostatics. Electric field equations.

__MA 475 Sampling Theory (2, 2, 3)__

Population and Sample, questionnaire development, Simple random sampling, stratified random sampling, proportional allocation, sample size determination, systematic sampling, cluster sampling and multistage sampling, Nation-wide surveys, Non-probability sampling techniques.

__MA 477 Mathematical Economics I (2, 2, 3)__

Theory of Consumer Behavior: Budget Constraint, Consumer Preference, Maximization of Utility function. Substitution and Income Effects (Slutsky Equation). Theory of the Firm: Production Function, Optimizing Behavior. Market Equilibrium: Assumption of perfect competition, Demand and Supply Functions, Comparative Statics, Effect of Taxes on Equilibrium, Pareto Efficiency, and Dynamic Adjustment. *Introduction to Linear Programming Concepts and Solutions.

__MA 479 Time Series Analysis (2, 2, 3)__

Review of Statistical Expectations, Trend Analysis, Smoothing techniques, Decomposition techniques, Seasonal adjustments, Stationary process, Estimation of Auto-covariance and Autocorrelation functions, Autoregressive (AR) process, Moving Average (MA) process, ARMA models, Forecasting and prediction.

__MA 481 Linear Optimisation (2, 2, 3)__

Linear Programming: Basic Concepts, Solution Methods and Application problems in Transportation, Assignment problems, etc. Duality Theorem and Complementary Slackness Principle. Unconstrained optimization problems: unidirectional search techniques, gradient, conjugate direction, quasi-Newtonian methods; introduction to constrained optimization using techniques of unconstrained optimization through penalty transformation, augmented Lagrangians. Network Analysis, Inventory Control, Queuing Theory.

Year Four Semester Two |

__MA 450 Project Works (0, 12, 4)__

Students select topics on various areas in Mathematics for their project work.

__MA 452 Colloquium/Seminar (1, 1, 1)__

Students will prepare a paper on a selected topic and present it in a seminar under supervision.

__MA 454 Business Entrepreneurship (2, 0, 2)__

Introduction to business entrepreneurship: Definitions and theories of business entrepreneurship. How to identify new business opportunities. Forms of business ownership. Starting a business in Ghana. Writing a business plan. Management of business enterprises: Financial management, Insurance, Taxation. Risks in business. Entrepreneurship as a strategic practice.

__MA 458 Principles of Management (2, 0, 2)__

Introduction: Some developments in management thought, functions of managers. Managerial planning and decision-making. Orgnanising: The formal organizational structure, organizational levels and span of management, departmentation, power, authority, responsibility and accountability, Decentralisation and delegation of authority. Staffing or human resource management. The human factor, motivation and leadership, Controlling, Application of the principles of management through case studies.

__MA 460 Corporate Social Responsibility (2, 0, 2)__

The concept of sustainable development. The evolution of Corporate Social Responsibility (CSR): Drivers and definitions. Theories to analyse and explain Corporate Social Responsibility. Guide to Corporate Social Responsibility in Ghana. Compensation, relocation/resettlement and alternative livelihood issues. Case studies

__MA 470 Designs and Analysis of Experiments (2, 2, 3)__

Principles of Experimental design, Analysis of variance (ANOVA), Completely randomized design (CRD), Randomized complete block design (RCBD), Latin Square, Split-plot design, Mean Separation Techniques, Analysis of covariance (ANACOVA), Factorial experiments, confounding in 2^{n} factorial experiments.

__MA 472 Mathematical Economics II (2, 2, 3)__

Simple model of income determination, consumption and investment, the IS curve. Monetary equilibrium, the LM curve. Labour wages and price (inflation) models. Full employment equilibrium models of income determination. Aggregate demand and supply analysis. Balance of trade (payments), model of income determination. Stabilization policy, comparative statistics, analysis of monetary fiscal policy, the Harold Domar growth model, the neo-classical growth model.

**5 POSTGRADUATE PROGRAMMEs**

- MSc/MPhil Mathematics

PhD Mathematics and Statistics