Course Syllabus

Course Prefix and Number: MATH 361

Course Title & Credit Hours: Modern Geometry Syllabus, 3 credit hours

Dakota State University

Academic Term, Year: Fall 2009 (August 31 – December 18)

Course Meeting Time and Location:  Internet Course, final must be taken during finals week or the week before finals week (between December 7th and December 18th).

 

Instructors Contact Information:

Dr. Richard Avery

208b Lowry Hall

Telephone: 256-5188

E-mail: rich.avery@dsu.edu



Office Hours:  I will respond to email every working day and I will respond on most weekends as well.   Please send me an email (preferably through Desire2Learn email) and I will get back to you as soon as possible (expect 24 hour turn around during the week, no guarantees on the weekends).  The hours listed below are the times I am scheduled to be in my office on the DSU campus and my phone number is listed above if you would like to call me during these times (you can call at any time, but I may not be in the office – email is usually the best way to contact me).

 

                                   

                                    Monday:          10:00-11:50

Office Hours:             Tuesday:          9:00-11:50

Wednesday:    10:00-11:50

                                    Thursday:        9:00-11:50

 

Additional office hours by Discovery or Appointment.

 

 

Course Description: In this course topics will be chosen from: axiomatic systems, finite geometries, Euclidean plane geometry, transformational geometry, three dimensional geometry, and Non-Euclidean geometries.  (2009-2010 DSU Catalog)

 

Course Prerequisites:

Prerequisites: MATH 125 or Consent of the Instructor

Technology Skills: Desire2Learn (D2L) will be used to deliver course files and video lectures as well as serving as a communication tool between students and instructor.  The Geometer’s Sketchpad will be used to create dynamic sketches.  The Geometer’s Sketchpad is available on the DSU Citrix Server (www.citrix.dsu.edu) which will be discussed in the opening lecture.  Students are expected to have the necessary plug-ins, players and software installed on their computer and have the technology skills to use them in order to complete this course.  If your computer passes the browser check at http://support.dsu.edu/d2l/browsercheck/ and you have a suitable internet connection (ability to work on the Citrix server online and watch videos online) then you have the ability to complete this internet course (you will need to download the Citrix client to use the Citrix Server as discussed in the first course video).

     

Description of Instructional and Course Delivery Methods: Students learn mathematics by doing mathematics. Lessons and assignments are developed to engage students and facilitate learning.  (ACTIVE LEARNING)  This is an Internet course!  Students will watch video lectures (pdf presentations with audio saved as MP4 videos), work through guided sketches (pdf files with step by step instructions to complete Geometer Sketchpad sketches), then complete both written assignments and Geometer Sketchpad sketches and send them to the instructor for comments and grading (email sketches and preferably written assessments as well but you can send paper copies in the mail if necessary).  Exams will have both a written component and a Geometer Sketchpad component. 

 

                                                                                                                       

Course Requirements:

 

Required Textbook(s) and Other Materials: Barbara Reynolds and William Fenton, College Geometry Using the Geometer’s Sketchpad (Preliminary Edition), (Pearson Education, Inc, New York, 2007).  Students are required to purchase the textbook.

 

 

Selected Bibliography:

§  Coxeter and Greitzer, Geometry Revisited  (MAA, Washington DC, 1967).

§  Greenberg, Euclidean and Non-Euclidean Geometries (W.H. Freeman and Company, New York, 1993).

§  Gustafson and Frisk, Elementary Geometry (John Wiley and Sons, New York, 1991).

§  Isaacs, Geometry for College Students (Brooks/Cole, Pacific Grove - CA, 2001).

§  Smart, Modern Geometries (Brooks/Cole, Pacific Grove - CA, 1998).

§  Thomas, Modern Geometry (Brooks/Cole, Pacific Grove - CA, 2002).

 

            University Deadlines:

 

            Add/Drop Deadline (Census Day): September 10th is the last day to add this course or drop this course and receive 100% refund. 

 

            Withdraw Deadline: November 16th is the last day to withdraw from this course and receive a grade of “W”.

 

            DSU Student Information and Help Links:

 

Student Handbook: http://www.departments.dsu.edu/studentaffairs/handbook/

DSU Catalogs: http://www.departments.dsu.edu/registrar/catalog/

DSU Student Resources Center: http://www.support.dsu.edu/

 

 

Course Goals:

      • Students will create dynamic sketches utilizing the Geometer’s Sketchpad.
      • Students will analyze dynamic sketches utilizing the Geometer’s Sketchpad and apply the Drag Test to make conjectures.
      • Students will justify conclusions applying rules of logic.
      • Students will write proofs in paragraph form and in the two column (T) format.
      • Students will use and prove triangle congruence theorems.
      • Students will use and prove quadrilateral theorems.
      • Students will justify compass and straightedge construction techniques.
      • Students will apply and justify area formulas for triangles and quadrilaterals.
      • Students will apply an prove similar triangle theorems.
      • Students will explore the foundation of Non-Euclidean Geometries.

 

Evaluation Procedures: Course grade will be based on a 500-point scale. 

                                                           

                                                                        Sketches                                  100 points

                                                                        Homework                              100 points                  

Midterm                                  150 points

Final                                       150 points

Total                                       500 points

 

Your grade will be calculated using your accumulated point total. The grade scale is:

 

A         450-500

B         400-449

C         350-399

D         250-349

F          < 250

 

 

Students near a cutoff may receive the higher grade at the discretion of the instructor.  There are ten assignments on the D2L site for this course.   Each assignment has a collection of homework exercises and a collection of Geometer Sketchpad exercises (ten points for each, so each assignment is worth a total of twenty points).  Send your Geometer sketchpad sketches to me as an attachment (gsp file type) in an email message and you can either send me your homework completed using a tablet pen electronically (as a jnt file or scanned if you have it saved as a word document, but not other file types) or in the regular mail (print and complete using a pen then put in the mailbox).

 

 

Classroom Policies:

 

Class Attendance-Completion Policy: Students are expected to meet the course deadlines.  An email message will be sent to you on D2L at least one week before the deadline for each assignment for the course as well as the deadline for completing the midterm and the final exam.

 

Homework/Test Completion Policy: Students are expected to complete assignments and exams by the deadlines and there will be no make-up opportunities for missed assessments.  All work must be completed by December 18th.

 

Cheating & plagiarism Policy (Academic Honesty Statement): Academic dishonesty includes giving, receiving or using unauthorized aid on any academic work. The definition of academic dishonesty and the procedure for handling it are described in detail in the current version of the student handbook.  You should read and understand this material.  All forms of academic dishonesty will result in no credit for the corresponding work.  You will not be allowed to have or use any electronic devices during the paper portion of your exam (zero on an exam if you use a cell phone, computer, …. during the paper portion of the exam).  Dakota State Universities policy on academic integrity (DSU Policy 03-22-00) is available online.

 

Make-up Policy: There will be no make-up opportunities for missed exams or assignments.  In the case of an excusable extended illness/absence during the semester contact the instructor to make arrangements for completing the course.

 

ADA Statement:  If there is any student in this course who, due to a disability, has need for accommodations, please contact Dakota State University's ADA coordinator, Keith Bundy, by email at keith.bundy@dsu.edu  or by phone at 605-256-5121, as soon as possible.  Accommodations cannot be given until they have been applied for, and the need confirmed.  Further information can be found at  http://www.departments.dsu.edu/disability_services/ .                 

 

Freedom in Learning Statement:  Students are responsible for learning the content of any course of study in which they are enrolled. Under Board of Regents and University policy, student academic performance shall be evaluated solely on an academic basis and students should be free to take reasoned exception to the data or views offered in any course of study.  It has always been the policy of Dakota State University to allow students to appeal the decisions of faculty, administrative, and staff members and the decisions of institutional committees.  Students who believe that an academic evaluation is unrelated to academic standards but is related instead to judgment of their personal opinion or conduct should contact the dean of the college which offers the class to initiate a review of the evaluation.

 

Internet Course:  This is an internet course and it is expected that any student enrolling in this course has a suitable internet connection and quality (virus free) computer at their disposal to complete the course requirements which will all be done via the Internet.  Moreover, it is the students responsibility to ensure that the computer they are using has the appropriate plug-ins, players and software installed on their computer and have the technology skills to use them in order to complete this course.  If your computer passes the browser check at http://support.dsu.edu/d2l/browsercheck/ and you have a suitable internet connection (ability to work on the Citrix server online and watch videos online) then you have the ability to complete this internet course (you will need to download the Citrix client to use the Citrix Server).

 

The Professor reserves the right to modify this course syllabus to better meet student needs.

 

COURSE OUTLINE :  This course is composed of thirty lessons, ten assignments, a midterm and a final.  Each assignment has a homework component and a Geometer Sketchpad component.  The exams have a written component and a Geometer Sketchpad component.

 

Lesson 1: Introduction to Sketchpad – Drag Test

 

Lesson 2: Axiomatic System – Euclidean Geometry

 

Lesson 3: Proof Techniques

 

Assignment 1

 

Lesson 4: Pasch’s Theorem and the Crossbar Theorem

 

Lesson 5: Congruence Criteria for Triangles

 

Lesson 6: Concurrence Properties for Triangles

 

Assignment 2

 

Lesson 7: Incircles and Excircles of triangles

 

Lesson 8: Ceva’s Theorem and pedal triangles

 

Lesson 9: Menelaus’ Theorem and Napoleon Triangles

 

Assignment 3

 

Lesson 10: Nine Point Circle

 

Lesson 11: Parallel Lines

 

Lesson 12: Convex Polygons and Regular Polygons

 

Assignment 4

 

Lesson 13: Parallelogram properties

 

Lesson 14: Rectangle Properties

 

Lesson 15: Trapezoid Properties

 

Assignment 5

 

Midterm Exam

 

Lesson 16: Properties of a rhombus

 

Lesson 17: Constructions of segments, angles and triangles

 

Lesson 18: Constructions of midpoints and perpendiculars

 

Assignment 6

 

Lesson 19: Area of a rectangle and a parallelogram

 

Lesson 20: Area of a triangle and a trapezoid

 

Lesson 21: Pythagorean Theorem

 

Assignment 7

 

Lesson 22: Special Right Triangles

 

Lesson 23: Proportions – Basic Facts

 

Lesson 24: Similarity of Triangles

 

Assignment 8

 

Lesson 25: Triangle similarity theorems

 

Lesson 26: Applications of similar triangles

 

Lesson 27: Neutral Geometry

 

Assignment 9

 

Lesson 28: Finite Geometries (3 point and 4 point)

 

Lesson 29: Introduction to Hyperbolic Geometry

 

Lesson 30: Introduction to Elliptic Geometry

 

Assignment 10

 

Final Exam