MATH3052-Learning Outcomes

At the end of this course you will be able to:

  1. Develop a deep understanding of geometry and create your own geometric questions, conjectures, and projects.
  2. Take core geometric concepts, (point, line, angle, sum of angle in a triangle, congruency, similarity, transformations) and ‘unpack’ the concepts through presentations with multiple representations and appropriate examples on different geometric surfaces.
  3. Explain the primitive terms (objects, relations, and functions), common notions, and axioms used in different axiomatic geometries.
  4. Construct, analyze, and interpret different geometric axiomatic models and understand the value and limitations of these models, such as Euclidean and non-Euclidean (Lobachevski’s Hyperbolic Geometry Model, Spherical, Cylindrical, Poincare disk, etc.,).
  5. Work with transformations such inversion, reflections, rotations, projections of a sphere and a cylinder onto a plane.
  6. Develop a deep understanding of congruency and similarity of two geometrical objects on different geometrical surfaces such as Euclidean plane, Sphere, cylinder, Hyperbolical plane, etc.
  7. Critically analyze the fifth postulate and develop a supporting argument of equivalent statements with the fifth postulate, i.e., Parallel transport postulate.
  8. Join in group work regularly in class and some group work outside of class.
  9. Work with and build physical models in class (such as plastic spheres for spherical geometry, plastic "polydron" for polyhedral models, kaleidoscopes), and use these for reasoning and communication.
  10. Work with a dynamic plane and spherical geometry program, i.e., Geometer's Sketchpad, GeoGebra 3D, GeoGebra Geometry, Desmos, MatLab, Maple, etc.
  11. Explore the use of visual material in the learning and communication of mathematics (including geometry);
  12. Prepare and present some material in class, and in a written project; while the topic of this project must be discussed with the instructor, we encourage you to take your own questions and ideas seriously. Propose a project that is significant to your own learning and possible career plans.