Spring 2017 – Geometry from an Advanced Perspective

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YEAR COURSE OFFERED: 2017
SEMESTER COURSE OFFERED: Spring
DEPARTMENT: Mathematical and Computer Sciences
COURSE NUMBER:
NAME OF COURSE: Geometry from an Advanced Perspective
NAME OF INSTRUCTOR: John Carter
CONTACT EMAIL*: [email protected]
OFFICE: SCI 1050

WEBSITE: http://sites.msudenver.edu/jcarte11

*My office phone is the absolute worst way to contact me, don’t 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’t expect an immediate answer.

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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.

Office Hours:

Monday thru Thursday 11am-12:30 pm, or by appointment

Course Description:

This course will treat the traditional content of an upper level geometry course through the lens of Felix Klein’s 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’s dictum of “a geometry is determined by its symmetry group.”

Required Reading Materials:

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

Specific Measurable Student Behavioral Learning Objectives: (format – 1, a, i, ii, etc.)

Upon completion of this course the student should be able to:

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

Detailed Outline of Course Content:

Detailed outline of course content:

  1. Foundations of Geometry in the Plane
  2. Isometries in the Plane: Products of Reflections

III.                 Transformations in the Plane.

  1. Isometries in the Plane: Classification & Structure
  2. Conjugacy and Geometric Equivalence
  3. Applications to Plane Geometry

VII.               Symmetric Figures in the Plane

VIII.             Frieze and Wallpaper Groups

  1. Area, Volume, and Scaling

Evaluation of Student Performance;

  1. Attendance and participation
  2. Daily individual homework
  3. Group participation and presentation
  4. Written and/or oral responses to readings.
  5. Midterm and final exams

Official Syllabus:

https://mcs.msudenver.edu/syllabi

IMPORTANT DATES FOR SPRING 2017:

  • Mon. Jan 16 Martin Luther King Jr. Day (Campus Open, No Classes)
  • Tue. Jan 17 Classes begin
  • Mon. Jan 23 Last day to drop full-term courses with 100% refund
  • Fri. Feb 3 Census Day
  • Fri. Feb 3 Last day to drop full-term courses with 50% refund and have classes deleted from your record.
  • Fri. Feb 3 Last day to request a Pass/Fail
  • Fri. Feb 3 Deadline to file Spring 2017  Application for Graduation
  • Fri. Feb 3 Deadline for application for certification
  • March 20-26 Spring Break (Campus Open, No Classes)
  • Wed. April 5 Last day to withdraw from full-semester classes and receive a ‘W’
  • Sat. May 6 Last day of classes
  • May 8-13 Finals Week
  • Fri. May 12 Commencement
  • Thu. May 18 Grades due from faculty by noon
  • Fri. May 19 Grades available online

IMPORTANT University Policies:

Students are responsible for full knowledge of the provisions and regulations pertaining to all aspects of their attendance at MSU Denver, and should familiarize themselves with the following policies:

  1. GENERAL UNIVERSITY POLICIES
  2. GRADES AND NOTATIONS including WITHDRAWAL FROM A COURSE, ADMINISTRATIVE WITHDRAWAL, and INCOMPLETE POLICIES Students should be aware that any kind of withdrawal can have a negative impact on some types of financial aid, including scholarships.
  3. ACADEMIC DISHONESTY
  4. PROHIBITION ON SEXUAL MISCONDUCT
  5. ACCOMMODATIONS TO ASSIST INDIVIDUALS WITH DISABILITIES
  6. CLASS ATTENDANCE ON RELIGIOUS HOLIDAYS
  7. ELECTRONIC COMMUNICATION (STUDENT EMAIL) POLICY For a complete description of these policies go to https://mcs.msudenver.edu/policies