Teaching at Singapore Polytechnic
A lecturer at Singapore Polytechnic, I teach Engineering Mathematics to the freshman and junior years.  Part of the syllabus is on geometric transformations, matrices and their inverses.  One of the components of the modules is Problem Based Learning.  For this component, I set up two problems that tests on geometric transformation and inverse matrices.

Robotic Vision - a slightly more difficult problem that looks at projection from 3D to 2D using the Mars Rovers robotic vision as an illustration. 

Mosaicking - image mosaicking is the process of aligning and stitching several images together to form a composite image.  Finding a global transformation through projection, scaling, translation, and rotation tests the students on their concepts of geometric transformation.

I also teach statistics, probability and decision theory.  For decision theory, here's a
simple problem to be solved with rubrics attached.

I am currently developing a General Elective Module on optimization, covering Network Routing, Linear Programming, Queuing Theory, and Multiobjective Programming.  Since the module's name is "Decision Making in Daily Life," the module will feature problems which are close to the students' life such as decision in train routes, their study scheduling etc.
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