Geometry courses are usually available through bachelor's, master's and doctoral degree programs in mathematics and math education. College courses in geometry cover much more than basic shapes and formulas. Students taking geometry courses will be exposed to fractal geometry, computational geometry, differential geometry and calculus and projective geometry. Math education majors learn to teach the subject of geometry to students at the 7-12 levels.
Here are common concepts explored in geometry courses:
- Fractal dimension
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List of Courses
A fractal is a geometric object that can be split into parts to create smaller copies of the original object. Students in this class study the principles and concepts of fractal geometry, such as common fractal sets and the Iterated Function System. They analyze how different behaviors, such as chaos and multifractals, can cause small changes which can have large effects. Exercises may include applying the study of random fractals to the stock market to search for patterns within the randomness.
In this course, students see geometry through a practical light as they apply each of the concepts to a specific group or incident. They explore linear and nonlinear equations. They also study geometry in projective space. Students apply different concepts, such as points at infinity, to the different dimensions. Projective geometry does not use angles because angles do not exist in all of the other planes.
Education majors taking this course examine practical methods for teaching geometry to elementary students, middle school students and high school students. They explore resources available to teachers and use technology that can make learning basic, intermediate and advanced geometry fun and effective. Future teachers can also explore web-based methods of teaching and learning. Often, students complete a lesson plan that incorporates the different methods of teaching geometry.
Differential Geometry and Calculus
This course familiarizes students with the history and multiple applications of calculus in physics, chemistry, biology, the social sciences, statistics and economics. Students apply calculus concepts to geometry, examining vector functions, derivatives and limits. They examine theorems and methods including Newton's method, divergence theorem and Stokes' theorem, analyzing their practical applications and their uses. Through this course, students examine the role of calculus in a number of sciences and see its practicality.