- 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.
- 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.