Syllabus :: Geometry

• Dr. Ryan Jensen
• Mathematics Department
• Email: jensenrj@sfasu.edu
• Website: https://mathnotes.cc
• Course Website: https://mathnotes.cc/teaching/geometry/
• Office: 320 Mathematics Building
• Office Phone: (936)-468-1636
• Office Hours:
  • MTWRF 9:00-10:00 in Math 320
  • Zoom link: https://sfasu.zoom.us/my/drjensensfa.
• Course Meeting Time and Place
  • MWF 8:00-8:50 in Math 205
  • Zoom link: https://sfasu.zoom.us/my/drjensensfa.

Survey of topics from classical Euclidean geometry, modern Euclidean geometry, projective geometry, transformational geometry and non-Euclidean geometries.

College Geometry: A Discovery Approach, 2nd ed. Written by David C. Kay and published by Pearson.

This course will probably be very different form other math courses you have taken. You (the students) will be the ones responsible for most of the math, including writing proofs on the board. This instruction method is known to me as the Moore method, but the more contemporary appellation is Inquiry Based Learning.

Each week I will distribute a list of definitions, theorems, propositions, questions etc. for you to work on. Regardless of how they are titled, statements requiring proof should be considered conjectures, i.e. they could be true or false. Your main responsibility is to prove the conjectures as either true or false and present your justification. You may work together in this class, but any work presented or turned in should be your own. On the flip side if you help someone in the class, give them main ideas, but don't give away solutions; let them work it out for themselves. For the first part of the course the material will follow what is in the book, and you are encourage to read the relevant sections. In fact some of the theorems you will be asked to prove may have proofs already given in the book, in which case you are free to use them once you understand them.

You should keep a journal of all things proved in this course, which will be turned in as a final project. Since this will be turned in and graded, you will need to make it nice, hence I suggest you first work out problems and proofs somewhere else, and then put them in your journal when they are more polished.

You will present proofs on the board for your classmates. There will be a take-home midterm, a take-home final, and you will turn in your journal containing all course material you have completed. Your grade will be determined by how many points you earn; you may think of it as a game. The rules of the game are:

1. The object is to collect as many points as possible.
2. Points are awarded by demonstrating you have mastered an idea. Some ways to earn points, and the point values, are:

   Class attendance

   Each week you attend class and actively participate, you earn two points. Actively participating means being to class on time, asking questions when the material is unclear, and commenting on others work. There are 14 weeks and hence 28 possible points in this category.

   Presenting a correct solution in class

   You will have ample opportunity to present solutions to theorems during class. You will earn 5 points per correct solution. A correct solution is one where everyone in the class is convinced of the truthfulness of what you presented.

   Take home midterm

   You will have one take-home midterm exam, worth from 0-50 points depending on your ability to demonstrate an understanding of the problems. The midterm exam is to be done completely on your own; no help from me or any other person or resource.

   Take home final

   You will have a take-home final exam to be turned in on Monday May 4 at 8:00, worth from 0-100 points.

   Final project

   You will have a final project which is worth from 0-100 points, turned in at the time of the final exam. This final project is your work journal. For full points, it should include all work done during the course; so all the definitions and all theorems proved in class or on homework should be included in this document. All proofs should be correct and complete.

   Other ways

   There are other ways to earn points, for example proposing a new nontrivial theorem for inclusion in this course. I'll inform you during class of other opportunities for points.

3. The intent of the course is for you to prove things yourself. As such, if you work with someone the work you present must be your own, and you may not just give someone the solution.
4. Your final grade will be based on the number of points you earn during the course. Since I don't know how many points are possible, I can't at this time tell you how many points correspond to a certain grade. In the end if I feel that an A is \(x\) points, then everyone with points \(>=x\) will receive an A.
5. Have fun!
6. These rules may be changed by the professor during the course.

At one time I was told that I was required to put the following in all my syllabi, hence here it is. The following is an exerpt from SFA Policy 5.4:

The federal definition of a credit hour is an amount of work represented in intended learning outcomes and verified by evidence of student achievement that is an institutionally established equivalency that reasonably approximates:

1. Not less than one hour of classroom or direct faculty instruction and a minimum of two hours out-of-class student work each week for approximately fifteen weeks for one semester or trimester hour of credit, or 10 to 12 weeks for one quarter hour of credit, or the equivalent amount of work over a different amount of time, or;
2. At least an equivalent amount of work as outlined in item 1 above for other academic activities as established by the institution including laboratory work, internships, practica, studio work, and other academic work leading to the award of credit hours.

To this end, all students in courses offered by the Department of Mathematics and Statistics that wish to be successful should plan to spend a minimum of two hours outside of class for every credit hour associated with this course. Expected activities to be completed in the time outside of class include reviewing notes from previous class meetings, reading assigned course resources, completing all assigned exercises and projects, and performing periodic assessment preparation.

See http://www2.sfasu.edu/math/docs/syllabi/MTH140Syllabus.pdf for elements common to all sections.