You should use office hours (for all your classes) whenever you have questions or difficulties.  Knowing your professor is great motivation and a good way to get advice on courses and other education and career related decisions.

Questions: Although the title of this course is Modern Geometry, properties of well known objects such as points, lines, angles, triangles, quadrilaterals, and circles have been studied systematically since 300 BC when Euclid's Elements, one of the most influential books of all time, was first published. Interesting questions considered by Euclid and other ancient Greeks are still of fundamental interest today and some were only fully answered much more recently. For instance: Can we define what a line is or what a rectangle is and if so how? How can you tell when two triangles have exactly the same size and shape - what about two circles or two quadrilaterals? When can a circle be drawn through the vertices of a quadrilateral? When do three lines drawn through the vertices of a triangle all pass through a common point? Is it possible, using only a compass and straightedge, to trisect an angle, or to construct a square with the same area as a given circle? What if other tools or methods are allowed?

Goals: One modern aspect of these questions is whether you can use a computer to help you answer them, help you explain your answer, or help you generate additional questions. In this course you will use a computer, and work you do by hand, for all three of these purposes as we investigate ancient and more recent planar geometry results concerning angles, parallel lines, triangles, quadrilaterals, polygons, and circles. Some results will probably be familiar from previous experience and some will be new. This course will help you learn to develop claims of what is true through experimentation (inductive reasoning), and to then use the precise language of mathematics and a list of assumptions and prior results to justify those assertions (deductive reasoning). If you will be a teacher in the future you will also consider the role of geometry and various approaches to it in mathematics curriculum. We will finish the semester by briefly examining more closely the axiomatic structure of Euclid's Elements - what initial assumptions were made and what happens when you change those assumptions? The latter question is the starting point for the fascinating subject of non-Euclidean geometry, which requires another entire course, Math 344, to even begin to address.

This course will help you:

• Master the fundamental results and understand deeper results of two-dimensional Euclidean geometry related to triangles, parallel lines, quadrilaterals, circles, polygons, area, congruence and similarity, and Ceva's Theorem.
• Use Geometer's Sketchpad as a tool to formulate conjectures, illustrations, proofs, and further questions.
  
• Be able to construct logical arguments to prove propositions involving the fundamental ideas and give clear written and verbal presentations of proofs based on those arguments.
• Know the properties of and be able to use the four rigid motions of the Euclidean plane.
  
• Be aware of connections between geometry and other areas of mathematics.
  
• Learn the history of Euclidean geometry and the axiomatic perspective.

Materials: The main text is College Geometry Using the Geometer's Sketchpad, by Reynolds and Fenton. We will cover most of chapters 1, 2, 3, and 6 and possibly parts of chapters 4 or 8 as time and interests allow. We will regularly use the computer software package Geometer's Sketchpad as a tool to experiment with examples, develop conjectures and proofs, illustrate ideas, and check work. Excerpts from Great Moments in Mathematics Before 1650 by Eves will be used as a supplement when we discuss history and axiomatics. These will be available from the bookstore later in the semester. The online course management system Moodle will likely be used for some online discussion outside of class, particularly the glossary feature.

Other supplies you should obtain and usually bring with you: straightedge, compass, colored pencils or pens, floppy disk, and optionally, protractor and circle template.

Prerequisites: The official prerequisites for this course are Math 287 and Math 230 or Math 330, which are intended to ensure that you possess some familiarity with and ability to utilize abstract mathematical concepts and construct proofs. You will further develop these abilities in this course. Many of the topics are similar to those you may have seen in a high school geometry course, but presented more rigorously, and other topics will be new. As stated in the undergraduate catalog, you must earn a C- or better in Math 343 to use it as a prerequisite for 344.

Format and Evaluation
Class time will include a mixture of brief lectures, cooperative group work, and computer activities in the lab, PS 324. You are responsible for material covered in all classes regardless of whether you have reason to be absent. Material covered in class lectures and group activities will assume that you have read and thought about the material ahead of time or tried some activities on your own before class. To fully succeed in accomplishing the goals above, you will need to take responsibility for and participate actively in your own learning, both inside and outside of class. Things that will help are to read the book both before and after material is presented in class, review class notes and construct your own notes about the material, complete and turn in assigned homework, work extra problems for practice, learn from comments and corrections on returned work, and talk to others (either in the class or not) in person or in the online Moodle forum about what you are learning.

Understanding and being able to do mathematics requires consistently working on problems yourself. But in addition to doing so you are encouraged to study together and discuss problems with others since this can be a very effective and rewarding way to learn mathematics. You must write up solutions yourself and give written credit for ideas obtained from other sources. Violations of ISU's plagiarism policy will not be tolerated and will be addressed according to ISU policy (see the Student Code of Conduct in the Student Handbook, http://www.isu.edu/studenta/2007-2008_Handbook.pdf and the section of the Faculty Staff Handbook referenced there, http://www.isu.edu/fs-handbook/part6/6_9/6_9a.html).

Two or three presentations will be required of each student. Dates and guidelines for these will be discussed in class.

Exams will be closed-book and in-class. Each will require you to give some definitions of key terms and some proofs that are comparable (but not necessarily identical) to homework problems or results in the text. Test problems may require you to apply familiar concepts in new situations. 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 and coverage listed below are tentative. 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 within 3 percentage points of these values.  The grades and comments on individual assignments are intended to provide you with feedback and to help you assess your current state of learning.  Occasional assignments that ask you to reflect on your strengths and weaknesses in various thinking abilities, knowledge, and understanding will provide additional help with both of these purposes and may be used to help determine your grade.  The final course grade will reflect to what extent you have accomplished the first four goals above on what you should be able to do at the end of the course.

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 logical structure, will learn to formulate questions that lead you to construct your own understanding of mathematics, and will know more about the process of learning, solving problems, and writing proofs after you complete this course. The most important skill you gain during a college education is the ability to learn independently.

Accommodations: Idaho State University is committed to equal opportunity in education for all students. If you have a diagnosed disability or if you believe you have a disability that might require reasonable accommodation in this course, please contact the ADA & Disability Resource Center, Room 123 Graveley Hall (282-3599) as soon as possible.