{"id":552,"date":"2016-12-14T17:27:23","date_gmt":"2016-12-14T17:27:23","guid":{"rendered":"http:\/\/sites.msudenver.edu\/jcarte11\/?page_id=552"},"modified":"2017-08-15T17:12:29","modified_gmt":"2017-08-15T17:12:29","slug":"spring-geometry-from-an-advanced-perspective","status":"publish","type":"page","link":"https:\/\/sites.msudenver.edu\/jcarte11\/past-courses\/spring-geometry-from-an-advanced-perspective\/","title":{"rendered":"Spring 2017 – Geometry from an Advanced Perspective"},"content":{"rendered":"

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YEAR COURSE OFFERED: 2017
\nSEMESTER COURSE OFFERED: Spring
\nDEPARTMENT: Mathematical and Computer Sciences
\nCOURSE NUMBER:
\nNAME OF COURSE:\u00a0Geometry from an Advanced Perspective
\nNAME OF INSTRUCTOR: John Carter
\nCONTACT EMAIL*: jcarte11@msudenver.edu
\nOFFICE: SCI 1050<\/p>\n

WEBSITE: http:\/\/sites.msudenver.edu\/jcarte11<\/a><\/p>\n

*My office phone is the absolute worst way to contact me, don\u2019t use it. I will not answer email on weekends, after 5pm, or before 10 am. Feel free to email me outside of those times, I will get to it, just don\u2019t expect an immediate answer.<\/p>\n

***************************************************************************<\/p>\n

The information contained in this class syllabus is subject to change without notice. Students are expected to be aware of any additional course policies presented by the instructor during the course.<\/p>\n

Office Hours:<\/h3>\n

Monday thru Thursday\u00a011am-12:30 pm, or by appointment<\/p>\n

Course Description:<\/strong><\/h2>\n

This course will treat the traditional content of an upper level geometry course through the lens of Felix Klein\u2019s Erlangen Programm. The primary focus will be on transformations of the plane both in the form of rigid motions and similarities. These will be explored on both the level of their usefulness as tools in proving theorems regarding geometric objects (triangles, circles, lines, etc.) and through Klein\u2019s dictum of \u201ca geometry is determined by its symmetry group.\u201d<\/p>\n

Required Reading Materials:<\/strong><\/h2>\n

Continuous Symmetry: From Euclid to Klein William Barker and Roger Howe Publication Year: 2007 ISBN-10: 0-8218-3900-4 ISBN-13: 978-0-8218-3900-3<\/em><\/p>\n

Specific Measurable<\/em> Student Behavioral Learning Objectives:<\/strong> (format<\/em> – 1, a, i, ii, etc.)<\/p>\n

Upon completion of this course the student should be able to:<\/p>\n

    \n
  1. Distinguish between traditional synthetic and transformational geometry.<\/li>\n
  2. Relate the notion of a symmetry group and a geometry.<\/li>\n
  3. Use the notion of transformations to prove classical theorems from geometry<\/li>\n
  4. Describe the classification of discrete groups of plane isometries \u2013 rosette groups, frieze groups, and wallpaper groups.<\/li>\n<\/ol>\n

    Detailed Outline of Course Content<\/strong>:<\/h2>\n

    Detailed outline of course content:<\/p>\n

      \n
    1. Foundations of Geometry in the Plane<\/li>\n
    2. Isometries in the Plane: Products of Reflections<\/li>\n<\/ol>\n

      III.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Transformations in the Plane.<\/p>\n

        \n
      1. Isometries in the Plane: Classification & Structure<\/li>\n
      2. Conjugacy and Geometric Equivalence<\/li>\n
      3. Applications to Plane Geometry<\/li>\n<\/ol>\n

        VII.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Symmetric Figures in the Plane<\/p>\n

        VIII.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Frieze and Wallpaper Groups<\/p>\n

          \n
        1. Area, Volume, and Scaling<\/li>\n<\/ol>\n

          Evaluation of Student Performance; <\/strong><\/h2>\n
            \n
          1. Attendance and participation<\/li>\n
          2. Daily individual homework<\/li>\n
          3. Group participation and presentation<\/li>\n
          4. Written and\/or oral responses to readings.<\/li>\n
          5. Midterm and final exams<\/li>\n<\/ol>\n

            Official Syllabus:<\/h3>\n

            https:\/\/mcs.msudenver.edu\/syllabi<\/a><\/p>\n

            IMPORTANT DATES FOR SPRING 2017:<\/h3>\n