Course Information-Math 123H, Fall 2005

Course Information
Math 123H - Symmetry - An Exploration of Connections
Fall, 2005 - M,W,F 10:00-10:50am, PS 302

Professor: Dr. Cathy Kriloff	Office/Phone: PS 316C / 282-3093	Math Dept. Phone: 282-3350
E-mail: krilcath@isu.edu	Web Page: www.isu.edu/~krilcath	Math Dept. Fax: 282-2636

Office Hours: T 10:30am-12:00pm, W 11:00am-12:00pm, and F 9:00-10:00am, and by appointment or e-mail.

You should use office hours (for all your classes) as an ongoing resource to address questions or difficulties that were not addressed in class. Knowing your professor is also a great motivator and a good way to get advice on courses and other education and career related decisions.

Objectives: Mathematics is an important part of a broad education, is used in all science and many social science fields, and is crucial in thinking logically and critically. Mathematical literacy includes not only mastering various technical principles but also being able to use the precise language of mathematics to justify assertions. Both of these can help you in your future career and in daily decisions. Learning these skills can be difficult and frustrating at times. But solving a problem, constructing a rigorous argument, and expressing solutions clearly are all rewarding processes that contribute to becoming a well educated and well rounded person.

The first goal of this course is for you to develop a mathematical understanding of symmetry. In the process you will strengthen your ability to think and read and write clearly by solving mathematical problems and explaining your answers. I also hope that you will obtain a glimpse of how new mathematics is developed. The second goal is to understand how symmetry provides connections both within mathematics and between mathematics and other fields.

By the end of this course you should be able to:

Apply symmetry operations and analyze symmetries of finite figures, strip patterns, and wallpaper patterns.

Use properties of symmetry operations to identify and distinguish between them and to show that symmetries form groups.

Formulate questions, explore and solve open-ended problems involving symmetry, and communicate your questions and solutions clearly and effectively, using logical arguments as appropriate.

Understand the role of experimentation, conjecture, and proof in the development of new mathematics.

Appreciate and describe connections of mathematical symmetry to other areas of mathematics and to other fields, including art, architecture, biology, mineralogy, and physics.

Materials: We will use several texts, for a variety of purposes.
Groups and Symmetry, by Farmer will be our main workbook for learning the mathematics behind symmetry.
Symmetry, A Unifying Concept, by Hargittai and Hargittai will be used throughout the semester to provide brief background descriptions and illustrations of symmetry.
Reality's Mirror, by Bunch, and Symmetry Discovered, by Rosen will be sources for readings on applications of symmetry in other areas and different perspectives on symmetry.
Cut & Assemble 3-D Geometrical Shapes, by Smith will be used for constructing models that will help us explore 3-dimensional symmetry later in the course.

Other supplementary readings or exercises may be used. We will occasionally utilize the mathematical software package Geometer's Sketchpad, some web-based java applets, the Zome building set, and other manipulatives as tools for illustrating symmetry and symmetry operations.

Prerequisites: The prerequisite for this course is Math 025, Elementary Algebra, or equivalent preparation as evidenced by a sufficient score on the Math Placement Exam. Being willing to work hard, explore and ask questions, and learn to think and communicate mathematically will be most valuable.

Format and Evaluation
Class time will usually include a mixture of brief lectures and cooperative group work, videos, or guest lecturers. I expect you to prepare for each class by reading and attempting certain problems before the class period. You are responsible for material covered in all class sessions regardless of whether you have reason to be absent. Participation, through attending regularly and asking questions during class, particularly during guest lectures, will constitute a portion of your grade.

Homework will be of two types. Attempt tasks marked C before the class in which we will discuss them. These may be collected and graded on effort. Part of class time will be spent discussing your solutions to the C tasks and starting others. Each of you will present a solution to a C task or a task assigned during class twice during the semester. Do tasks marked T on your own and turn them in for a grade based on correctness. Please keep all work on both types of tasks, from initial attempts through a final, neatly organized and written solution, on lined paper in a three-ring binder so portions may be turned in periodically. Up to ten percent of the grade on each T homework will be based on the mathematical writing. Writing guidelines and a list of C and T problems with due dates will be updated during the semester on the class web page, http://www.isu.edu/~krilcath/m123Fa05.html. Your lowest T score will not be included in your grade, so late homework will generally not be accepted.

Studying together and discussing problems are encouraged, after you have worked hard on the material or problem yourself, since this can be a very effective and rewarding way to learn mathematics. But you must write up solutions yourself and give appropriate written credit for ideas obtained from other sources. Violations of ISU's plagiarism policy will not be tolerated and will be addressed following ISU policy (see the Student Code of Conduct in the Student Handbook, http://www.isu.edu/references/st.handbook/conduct.html#CONDUCT and the section of the Faculty Staff Handbook referenced there, http://www.isu.edu/fs-handbook/part6/6_9/6_9a.html).

Exams will be closed-book in-class exams. Each will include questions that are closely related to homework and at least one problem that involves applying familiar concepts in a new situation. If an emergency requires you to miss an exam, you should contact me or have someone else contact me before the exam if at all possible and must provide documentation. The exam dates are tentative, but the final date is firm, so please mark it down now.

Grades of A, B, C, D will be guaranteed by earning overall percentages of 90%, 80%, 70%, 60%. Cutoffs for +/- will be determined at the end of the semester, but will be within 3 percentage points of these values.

Participation	5%	Attend regularly and ask questions, particularly for guest lecturers.
Presentations	5%	Present solutions to a task done before or in class (2 required).
Homework	25%	Parts of homework notebook will be turned in periodically.
Project	15%	First draft due Friday, November 11, Final draft due Friday, December 2
Exam I	15%	Monday, September 26, Chapters 1-3 of Farmer
Exam II	15%	Monday, October 24, Chapters 4, 5 of Farmer and applications
Final	20%	Monday, December 12, 10:00am-12:00pm, Cumulative

Philosophy: All of you have the potential to succeed in this course and hard work counts for a great deal. I continue to learn by expanding my knowledge of mathematics and its connections with other subjects, by doing original research, by understanding more about learning and teaching, and by working to teach in ever more effective ways. I expect you will deepen your knowledge of mathematics and its applications, will learn to formulate questions that lead you to construct your own understanding of mathematics, and will know more about the process of problem solving after you complete this course. The most important skill you gain during a college education is the ability to learn independently.

Accommodations: Our program is committed to all students achieving their potential. If you have a disability or think you have a disability (physical, learning, hearing, vision, or psychiatric) that may need a reasonable accommodation, please contact the ADA Disabilities & Resource Center, Room 123 Graveley Hall, 282-3599 as soon as possible.