You should use office hours (for all your classes) whenever you have questions or difficulties that were not addressed in class.  Knowing your professor is great motivation 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 helps you think logically and critically.  Mathematical literacy includes not only mastering computational techniques but also using the precise language of mathematics to justify assertions.  The resulting skills obtained are beneficial in most careers and in making daily decisions.  Learning these skills can be difficult and frustrating at times.  But solving a problem, constructing a rigorous argument, and explaining and expressing solutions clearly are rewarding processes that contribute to becoming a well educated person.

This course focuses on non-Euclidean geometry, especially as it compares to Euclidean geometry, and transformation groups.  In addition to strengthening visualization, geometry is one of the best areas of mathematics in which to practice precise logical thinking as well as constructing and understanding proofs.  The course will help you further strengthen these abilities.  

By the end of this course you will:

• Master the fundamental results of two-dimensional hyperbolic non-Euclidean geometry related to the Poincare and Klein models, sensed parallels and ultraparallels, asymptotic and finite triangles, and Saccheri quadrilaterals.
• Be able to use an analytic model of the plane to write and work with isometries, including determining properties, combining them, and finding symmetry groups.
  
• Be able to construct logical arguments to prove propositions about non-Euclidean geometry and transformations and give clear written and verbal presentations of proofs based on those arguments.
• Use Geometer's Sketchpad as a tool to formulate questions and conjectures and to illustrate results.
  
• Be aware of connections between geometry and other areas of mathematics.
  
• Be aware of  the development of non-Euclidean geometry and its impact on the axiomatic perspective.

Materials: The main text is A Course in Modern Geometries, by Cederberg.  We will cover most of chapters 1, 2, and 3 and possibly other sections if time permits.  We will regularly use the computer software package Geometer's Sketchpad as a tool to illustrate ideas, experiment with examples, develop proofs, and check work.  

Other supplies you may want to obtain and sometimes bring with you: colored pencils or pens, straightedge, circle template, compass,  protractor, and floppy disk or USB drive.

Prerequisites: The official prerequisite for this course is Math 343 with a C- or better.

Format and Evaluation
Class time will include a mixture of brief lectures and cooperative group work and will sometimes take place in the computer 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.  To fully understand and succeed you will need to read the book both before and after material is presented in class, review class notes, work extra problems for practice, complete and turn in assigned homework, and learn from comments and corrections on returned homework and exams.

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/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).

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

Exams will include an in-class portion and a take-home portion.  Each in-class portion will be closed-book and 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 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 determined at the end of the semester, but will be within 3 percentage points of these values.

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.