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

of geometry and create your own geometric questions, conjectures, and projects.**Develop a deep understanding**(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.**Take core geometric concepts**,the primitive terms (objects, relations, and functions), common notions, and axioms used in different axiomatic geometries.**Explain**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.,).**Construct, analyze, and interpret**with transformations such inversion, reflections, rotations, projections of a sphere and a cylinder onto a plane.**Work**of congruency and similarity of two geometrical objects on different geometrical surfaces such as Euclidean plane, Sphere, cylinder, Hyperbolical plane, etc.**Develop a deep understanding**the fifth postulate and develop a supporting argument of equivalent statements with the fifth postulate, i.e., Parallel transport postulate.**Critically analyze**regularly in class and some group work outside of class.**Join****in group 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.**Work**plane and spherical geometry program, i.e., Geometer's Sketchpad, GeoGebra 3D, GeoGebra Geometry, Desmos, MatLab, Maple, etc.**Work****with a dynamic**the use of visual material in the learning and communication of mathematics (including geometry);**Explore**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.**Prepare and present**