Syllabus

MA350 Engineering

MA351 Graph Theory

• Introduction to graph theory
• Colouring of graphs
• Eulerian and Hamiltonian graphs
• Trees, minimum spanning trees
• Heap sorting
• Planar graphs, networks and flows

Texts

• N.L. Biggs, "Discrete Mathematics" (Oxford)

References

• A. Gibbons, "Algorithmic Graph Theory" (Cambridge)
• R.J. Wilson & I.J. Watkins, "Graphs" (Wiley)

MA352 Math Methods

• Functions of a complex variable
• Theory of residues
• Conformal mappings

Texts

• E. Kreyszig, "Advanced Engineering Mathematics" (Wiley)

References

• A.J.M. Spencer et al, "Engineering Mathematics" (van Nostrand)

MA355/356 Numerical Methods

• Iterative methods in matrix analysis: Jacobi's method, the Gauss-Seidel method, successive over-relaxation
• Eigenvalues and eigenvectors, tridiagonal matrices, reduction of symmetric matrices to tridiagonal form, the QR method
• Systems of nonlinear equations: Newton's method, Broyden's method, the method of steepest descent
• Ordinary differential equations: finite difference methods for boundary value problems, Runge-Kutta methods, multistep methods
• Partial differential equations: finite difference methods for Laplace's equation

Texts

• L.V. Atkinson, P.J. Harley & J.D. Hudson, "Numerical Methods with FORTRAN 77" (Addison Wesley)

References

• I. Jacques & C. Judd, "Numerical Analysis" (Chapman & Hall)
• C.F. Gerald & P.O. Wheatley, "Applied Numerical Analysis" (Addison Wesley)

MA337 Statistics (part one)

[The syllabi for MA337 and 338 are approximate, and more topics may be added depending on the students' interests and the instructor's preference. Assessment of students is usually based on homework assignments (for most of which use of statistical software is required), and a final examination.]
 

Explanation of the difference between probability and statistics. The role of probability in statistical decision making.

Review of basic probability and statistical inference

Review of techniques of data presentation and summarisation.

 Discussion of several probability models, including binomial, geometric, Poisson and normal. Moments of distribution.

Statistical inference: concepts of point and interval estimation, and of hypothesis testing, P-value and power of tests.

One- and two-sample inference (parametric and non-parametric). Analysis of enumerative data.

MA338 Statistics (part two)

• Simple linear regression, including inferences about parameters, prediction, procedures for checking model inadequacy, etc.
• Multiple linear regression, including model assumptions, global and partial F-tests, step-wise regression, etc.
• Analysis of Variance, including its relation to regression analysis, one-way ANOVA, randomized block and Latin square designs.

Texts

• R.L. Ott, "An Introduction to Statistical Methods and Data Analysis"
• Ryan & Joiner, "Minitab Handbook" (Duxbury)

References

• J.E. Freund, "Modern Elementary Statistics" (Prentice Hall)
• P.G. Hoel & R.J. Jesson, "Basic Statistics for Business and Economics" (Wiley)
• T. Sincich, "Business Statistics by Example" (Dillon/Macmillan)