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Perspectives in Mathematics, Fall 2013: Educational Goals

Math 103: Perspectives in Mathematics is a course which satisfies Science and Quantitative Reasoning Category B requirement. Thus, the educational goals of this course are largely centered around symbolic reasoning.

  • Goal 1:
    To further students’ ability to think and work with abstract objects by means of their symbolic (at times algebraic) forms. Working towards this goal gives you an opportunity to liberate yourself from thinking solely in terms of concrete tangibles. In this class you will have an opportunity to use concrete examples to develop an inductive understanding of abstract objects, relationships and ideas which are usually inaccessible to mathematically untrained minds. Specifically, in this course the students will:

      Work with abstract shapes represented in symbolic form; the corresponding assessment will be based on student performance on assignments from weeks 1, 8, 9 and 10.
      Work with higher dimensional objects in symbolic/algebraic form; the corresponding assessment will be based on student performance on assignments from weeks 2, 7 and 12.
      Execute arguments based on algebraic manipulations; the corresponding assessment will be based on student performance on assignments from weeks 3, 10 and 11.
      Analyze functional relationships between geometric quantities; the corresponding assessment will be based on student performance on assignments from weeks 4 and 5.
  • Goal 2:
    To further students’ ability to recognize the abstract concepts discussed above as they manifest themselves in our physical world. The extent to which this goal is achieved will be determined based on assignments which explore the concept of curvature and possible geometries of our universe (e.g weeks 5, 6 and 15).
  • Goal 3:
    To develop a basic understanding of what modern practice of mathematics is about. The extent to which this goal is achieved will be determined based on assignments which explore the distinction and interaction between geometry and topology (e.g weeks 3 and 13).
  • Goal 4:
    To situate the practice and communication of mathematics within its larger intellectual and social context. Specifically, this course presents an opportunity to learn about a currently active area of mathematics research, as well as its historical and philosophical underpinnings. The extent to which this goal is achieved will be determined based on assignments having to do with developments which lead to the discovery of hyperbolic geometry and the proof of the Poincaré conjecture (e.g weeks 7 and 15).
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