- Mathematical Analysis and its Applications I
(MAED 5021)
This course is an introduction to analysis and its applications. Topics
will be selected from countable and uncountable sets, metrics, norms,
open sets, closed sets, continuity, homeomorphisms, connectedness,
complete metric spaces, totally bounded sets, fixed points, compact
metric spaces, uniform continuity, category, the Baire Category
Theorem, sequences of functions, pointwise and uniform convergence, the
space of bounded functions.
- Algebra and its Applications I (MAED 5121)
This course is an introduction to abstract algebra and it
applications. Topics include: Groups, rings, homomorphisms, quotients,
group actions, polynomial rings, chinese remainder theorem,
applications to encryption and codes, field extensions geometric
constructions.
- Classical and Modern Geometry (MAED 5211)
This course is about important ideas in the development of geometry.
Topics include logic and axiomatic systems, projective geometry,
Hilbert’s axioms, and hyperbolic models, geometric transformations,
hyperbolic trigonometry.
- Probability and Statistics (MAED 5421)
This course serves those who want to use statistics in their careers or
teach statistics/probability (or topics related to statistics and
probability). Topics include: descriptive statistics, examples of
commonly-used probability distributions and their applications, main
techniques for estimating and testing model parameters,
and regression modeling. Statistical and probabilistic techniques will
be illustrated by using the open-source statistics package "R" to
analyze data in education.
- Problem Solving Strategies (MAED 5731)
This course covers strategies and techniques for solving mathematical
problems that appear in high school or university-level mathematics
competitions. Topics include algebraic transformation, inequalities,
functional equations, coordinate geometry, the use of complex numbers
in geometry, combinatorics and generating functions etc. Students will
have opportunities to present solutions to selected interesting
problems, so that they can compare the strengths and weaknesses of each
method, and apply these key approaches into teaching.
- Applications of Geometry and Analysis (MAED
5032)
This course shows how mathematics can be appropriately applied into
investigating a variety of physical phenomena in daily life. It first
begins with fundamental knowledge of Linear Algebra and Applied
Analysis, followed by the use of Differential Geometry and the
discussion of Kepler’s laws of planetary motion. Local and global
properties of curves and surfaces will also be illustrated. Additional
topics will be other historically significant uses of Differential
Equations and Fourier Series.
- Classical and Abstract Algebra (MAED 5111)
This is a course on real numbers and polynomials. Topics include real
and complex number systems, Dedekind cuts, fundamental theorem of
algebra, cubic and quartic equations, conics, symmetric polynomials,
and special polynomials.
- Combinatorics (MAED 5321)
This course provides students with general knowledge of useful
principles in combinatorics. Topics will be selected from graph theory,
systems of distinct representatives, flows in networks, Latin squares,
Hadamard matrices, Reed-Muller codes, combinatorial designs, and
projective geometries.