MAED Courses

 Four core courses are offered every year

• 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.
  
  
  

  At least five elective courses are offered every year on a rotational basis from:

• 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.
  

• Complex Analysis for Mathematics Educators (MAED 5033)
  
  This course is about analysis of functions in a complex variable. Topics include holomorphic functions, line integrals in the complex plane, Cauchy integral formula, isolated singularities, Taylor series and Laurent series, residues, conformal mappings, Weierstrass factorization, and the Riemann Zeta function. Applications of these ideas will lead to a broader and deeper understanding about topics in secondary school mathematics, including plane geometry, roots of polynomials, trigonometry, evaluation of series and integrals, and the study of prime numbers.
  

• 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.
  
  
  

• Classical and Modern Geometry (MAED 5211)
  
  This course is about important ideas in the development of geometry. Topics include logic and axiomatic system, projective geometry, Hilbert’s axioms, hyperbolic models, geometric transformations, hyperbolic trigonometry.
  
  
  
• 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. 

• Methodology of Mathematics(MAED 5322)
  
  This course is about mathematical thinking in mathematics. One purpose is to show how mathematical concepts, terminologies, formulas, equations, and theories are developed through examples of calculus, analysis, algebra, geometry, combinatorics, and probability, etc. The other purpose is to provide a global picture of mathematics by discussing its foundations, structures, internal relations, crises, and envisions. It is a combination of history, pedagogy, methodology, and philosophy of mathematics. 

• Teaching Mathematics in the Digital Age(MAED 5511)
  
  This course is about the use of various digital tools to produce interactive teaching materials for mathematics and the pedagogical framework of designing mathematics lessons using digital tools that can enhance the effectiveness of students’ learning.

• Pedagogy in Mathematics Teaching (MAED 5611)
  
  This course focuses on intricate teaching methods and best practices in mathematics education. It delves into effective teaching strategies, the application of advanced technology in mathematics instruction, current trends and challenges in mathematics education, and the integration of cultural diversity in the classroom. Designed for educators and those aspiring to specialize in mathematics education, this course aims to enhance their teaching proficiency. Upon completion, participants will have a full grasp of effective strategies for math instruction and will be equipped to design compelling math lessons for their students.
  
  
  
• Topics in Mathematics (MAED 5821)
  
  This course in which students are shown how mathematical theories are applied to various disciplines. It consists of four modules chosen from mathematical physics, mathematical biology, game theory, image processing, and traffic flow. 

• Topics in Applied Mathematics for Mathematics Educators (MAED5841)
  
  This course introduces a selection of topics in Applied Mathematics, with focus on the integration of mathematical knowledge and the latest advancement of technologies. It aims at equipping math educators with necessary techniques in modern Mathematics curriculum, for example, Data Analytics and Visualization, Ordinary Differential Equations (ODE) and Partial Differential Equations (PDE). Through understanding both analytical and numerical perspectives of these branches in mathematics, one can formulate real-life scenarios as mathematical models, solve and analyze these scenarios, then interpret the numerical results and associate with different physical disciplines.
  
  
  
• Scientific Computation (MAED 5851)
  
  This course introduces case studies drawn from different areas of science to illustrate the use of computers as a problem-solving tool. Each integrates physical principles and mathematical models, as well as numerical techniques and computer implementations, into a coherent perspective. Topics include damped-driven pendulum, phase space, Fourier series, spectral analysis, visualization, fractals, and computational fluid dynamics (CFD).

• MSc Project (MAED 6980)
  
  This course requires students to complete a project in an area of mathematics or mathematics education under the guidance of an MAED instructor. The project theme should be within one of the following 3 categories: 

1. Survey a topic of mathematics / mathematics education, i.e., reading course; 
2. Develop a lesson plan and relevant supporting platforms or e-learning tools for a topic selected from Grades 10-12 Mathematics curriculum or from Undergraduate Level Mathematics; 
3. Conduct a mini-project in a branch of mathematics / science and describe the investigation.

• Independent Study (MAED 6981)
  
  This course is for independent study under the guidance of an MAED instructor. The topic offered should not appear in any other Core or Elective courses of the MAED curriculum.
  

Typical two-year part-time study sequence

  Typical one-year full-time study sequence

• Fall
  MAED 5021 - Mathematical Analysis and its Applications I
  MAED 5121 - Algebra and its Applications I
  MAED 5731 - Problem Solving Strategies 
  1st elective course
  2nd elective course


• Spring
  MAED 5421 - Probability and Statistics
  3rd elective course
  4th elective course
  5th elective course