Syllabus
for Math 520, Geometry for High
School Teachers, Summer 2005

Instructor:
Dr. Elizabeth Arnold

e-mail: arnoldea@math.jmu.edu

Phone: 568-6532

URL: www.math.jmu.edu/~arnoldea

Office: Burruss 116

Office Hours: M-F 2:30-4:30pm

Class Meets: M-F 9-11:30am, 12:30-2:30pm. June 20-July 1.

COURSE DESCRIPTION: This course will cover topics from Euclidean and non-Euclidean Geometry. We will use the software Geometry Explorer as a supplement to the text. This software can be installed on Windows, Macintosh or Linux machines. It will be available in the JMU Math computer lab as well. It is understood that the students have as a pre-requisite an in-depth understanding of (high school level) Euclidean geometry. Prior experience with proving mathematical results is highly recommended. Also desirable is some experience with matrix algebra and the notion of a group from abstract algebra. The goal of this class is to expose you to new concepts in geometry and to deepen your understanding of basic concepts in Euclidean geometry. This is NOT a methods course, nor is it a workshop where you will take home worksheets, projects, etc. for your own students. This is a content course where you will deepen your knowledge and hopefully your appreciation of geometry, which should enhance your teaching of your individual curriculum. Topics for this course will include axiomatic geometry, more Euclidean geometry, analytic geometry, transformational geometry, non-Euclidean geometry and fractal geometry. We will cover most of the sections in Chapters 1, 2, 5 and 7 of the text, the first 2 sections only of Chapter 3, and as much of Chapter 9 as we can. A tentative outline is below.

TEXT: Geometry with Geometry Explorer by Michael Hvidsten, Geometry Explorer CD (included with text)

ATTENDANCE: Attendance is mandatory. Missing one class in this summer session amounts to missing over 2 weeks of a regular semester class.

GRADING: The grading will be assigned on a graduate scale: A, A-, B+, B, B-, C, F. A=Excellent, B=Good, C=Poor, F=Fail. Grades will be based on quizzes, computer projects, midterm and attendance/participation.

QUIZZES: Quizzes will be short - 10-15 minutes, and will cover what we have covered through the last quiz including material covered the previous day. Quizzes will be given in the afternoon session and there will be time to ask questions about the previous day's material in the morning session.

HOMEWORK: Homework will be assigned, but not collected. Quizzes will be based on both lectures/readings and homework. Time will be given in each morning session to answer questions and go over some (but probably not all) homework problems. It is recommended that you work on homework problems together and ask questions during office hours.

COMPUTER PROJECTS: There will be 5 computer projects assigned during this course. These projects are designed for you to learn new concepts, solidify concepts covered in class, and, in general, to get exposure to learning techniques using geometric software. The software provided with the textbook is very similar to other commecially available software packages that you can use in your own classroom. You are encouraged to work together on the computer projects, but you must write up your own work to turn in. See "Group Work" below.

MIDTERM: There will be a take home mid-term given out on Friday, June 24 and due on Monday June 27. You may not work together on this, but you may use your notes, your text book and the software. Please do not use any other assistance such as other texts, other people or other computer sites or software.

GROUP WORK: Group work, also called cooperative learning, is an important and effective learning strategy. You are encouraged to work together in class and out of class. However, when turning in projects or homework, you must write up the work yourself. If you turn in work that is not your own, you must have the author's name on it as well. Not crediting the work correctly is a violation of the honor code.

NOTE: This is a very intense class. Plan to work hard, learn a lot and have fun. It is not recommended that you are taking another class or are working during this class. There will be homework assigned at every class and a computer projects assigned at almost every class. I will be available to help you and answer questions during the lunch hour and for 2 hours at the end of each day. I am also available by e-mail in the evening.

e-mail: arnoldea@math.jmu.edu

Phone: 568-6532

URL: www.math.jmu.edu/~arnoldea

Office: Burruss 116

Office Hours: M-F 2:30-4:30pm

Class Meets: M-F 9-11:30am, 12:30-2:30pm. June 20-July 1.

COURSE DESCRIPTION: This course will cover topics from Euclidean and non-Euclidean Geometry. We will use the software Geometry Explorer as a supplement to the text. This software can be installed on Windows, Macintosh or Linux machines. It will be available in the JMU Math computer lab as well. It is understood that the students have as a pre-requisite an in-depth understanding of (high school level) Euclidean geometry. Prior experience with proving mathematical results is highly recommended. Also desirable is some experience with matrix algebra and the notion of a group from abstract algebra. The goal of this class is to expose you to new concepts in geometry and to deepen your understanding of basic concepts in Euclidean geometry. This is NOT a methods course, nor is it a workshop where you will take home worksheets, projects, etc. for your own students. This is a content course where you will deepen your knowledge and hopefully your appreciation of geometry, which should enhance your teaching of your individual curriculum. Topics for this course will include axiomatic geometry, more Euclidean geometry, analytic geometry, transformational geometry, non-Euclidean geometry and fractal geometry. We will cover most of the sections in Chapters 1, 2, 5 and 7 of the text, the first 2 sections only of Chapter 3, and as much of Chapter 9 as we can. A tentative outline is below.

TEXT: Geometry with Geometry Explorer by Michael Hvidsten, Geometry Explorer CD (included with text)

ATTENDANCE: Attendance is mandatory. Missing one class in this summer session amounts to missing over 2 weeks of a regular semester class.

GRADING: The grading will be assigned on a graduate scale: A, A-, B+, B, B-, C, F. A=Excellent, B=Good, C=Poor, F=Fail. Grades will be based on quizzes, computer projects, midterm and attendance/participation.

QUIZZES: Quizzes will be short - 10-15 minutes, and will cover what we have covered through the last quiz including material covered the previous day. Quizzes will be given in the afternoon session and there will be time to ask questions about the previous day's material in the morning session.

HOMEWORK: Homework will be assigned, but not collected. Quizzes will be based on both lectures/readings and homework. Time will be given in each morning session to answer questions and go over some (but probably not all) homework problems. It is recommended that you work on homework problems together and ask questions during office hours.

COMPUTER PROJECTS: There will be 5 computer projects assigned during this course. These projects are designed for you to learn new concepts, solidify concepts covered in class, and, in general, to get exposure to learning techniques using geometric software. The software provided with the textbook is very similar to other commecially available software packages that you can use in your own classroom. You are encouraged to work together on the computer projects, but you must write up your own work to turn in. See "Group Work" below.

MIDTERM: There will be a take home mid-term given out on Friday, June 24 and due on Monday June 27. You may not work together on this, but you may use your notes, your text book and the software. Please do not use any other assistance such as other texts, other people or other computer sites or software.

GROUP WORK: Group work, also called cooperative learning, is an important and effective learning strategy. You are encouraged to work together in class and out of class. However, when turning in projects or homework, you must write up the work yourself. If you turn in work that is not your own, you must have the author's name on it as well. Not crediting the work correctly is a violation of the honor code.

NOTE: This is a very intense class. Plan to work hard, learn a lot and have fun. It is not recommended that you are taking another class or are working during this class. There will be homework assigned at every class and a computer projects assigned at almost every class. I will be available to help you and answer questions during the lunch hour and for 2 hours at the end of each day. I am also available by e-mail in the evening.

520 Summer 2005 tentative outline

June 20 Sections
1.1-1.5

Homework: Section 1.4: 3-10, Section 1.5: 1, 4-10

Project: Project 1 - The Ratio Made of Gold 1.3, pp. 8-18. Due Wednesday, June 22

Project: Project 1 - The Ratio Made of Gold 1.3, pp. 8-18. Due Wednesday, June 22

June 21 Sections
1.6-1.7

Homework: Section 1.6: 2, 3, 5-11

Project: Project 2 - A Concrete Axiomatic System, pp. 40-49. Due Thursday, June 23

Project: Project 2 - A Concrete Axiomatic System, pp. 40-49. Due Thursday, June 23

June 22 Sections 2.1-2.3

Homework: Section 2.1: 1-4, Section 2.2: 4-9, 11, 12

Project: Project 1 Due.

Quiz 1

Project: Project 1 Due.

Quiz 1

June 23 Sections 2.4-2.6

Homework: Section 2.4: 7-10, Section 2.5: 1-4, 7,
2.6: 1-6, 8, 12

Project: Project 4 Circle Inversion, pp. 98-103,

Project 2 Due.

Project: Project 4 Circle Inversion, pp. 98-103,

Project 2 Due.

June 24 Sections 2.7,
5.1, 5.2

Homework: Section 5.1: 3-10; 5.2: 6-11

Quiz 2

Take-home Midterm handed out - Chapters 1 and 2

Quiz 2

Take-home Midterm handed out - Chapters 1 and 2

June 27 Sections 5.3-5.5

Homework: 5.3: 4-6, 8; 5.4: 1,2, 4,5, 7,8,9;

Project: Project 7 Quilts and Transformations pp. 206-211

Midterm Due

Project: Project 7 Quilts and Transformations pp. 206-211

Midterm Due

June 28 Sections 5.6, 7.1

Homework: 5.6: 5-11

Quiz 3

Project 4 DueHomework: 5.6: 5-11

Quiz 3

June 29 Sections7.2, 7.3

Homework: 7.3: 3-6

Project: Project 10 The Saccheri Quadrilateral, pp 286-290

Project 7 Due

Project: Project 10 The Saccheri Quadrilateral, pp 286-290

Project 7 Due

June 30 Sections
9.1, 9.2, 9.3

Homework: 9.3: 1-5

Quiz 4

Quiz 4

July 1
Sections 9.4

Homework: NONE!

Project 10 Due

Quiz 5

Homework: NONE!

Project 10 Due

Quiz 5