Office: 321 Zimmermann

Phone: Office: 784-5283; Home 784-6473

- Give an overview of the variety of modern geometries.
- Demonstrate the deductive nature of axiomatic systems.
- Acquaint students with the evolving notion of geometry.
- Introduce the students to reasoning with abstract objects.

- Schedule at least 1 to 2 hours outside of class each day for studying geometry.
- Read each section carefully and write each proof with paper and pencil, endeavoring to fill in any missing steps.
- Look at problems besides those assigned to discover why the author asked the question.
- Prepare homework to hand in before class starts, including putting the name, class, homework number, and date on the outside.
- Come to class on time every day and stay the entire period,
- Have paper and pencil out on the desk at the beginning of class ready to work.
- Sit beside a partner with whom you will discuss geometry during class.
- Turn off electronic communication during class.
- Rest and eat before or after, but not during, class.
- Check all homework answers with the book and others, but write them up without copying.

- Start and end class on time, or within 3 minutes of the scheduled time.
- Be prepared for class every day.
- Grade and return homework and exams within 2 class days.
- Treat every student with respect.
- Learn each student's name.
- Answer every question in a respectful, truthful manner.
- Post homework assignments with clear due dates.
- Be available in my office during office hours, and give priority to anyone signed up.
- Grade all exams myself, completely, equitably, and clearly. Daily homework may be graded by an assistant. Not every homework problem turned in will be graded.
- Make every minute of every class a learning experience.

- Homework (~300) Approximately 17 homework assignments will be given at 20 points each. Homework assignments will typically be due 2 class days from the day they are given. Written homework is due at the beginning of class on the due date. Late homework will not be accepted after the set has been graded. Papers will be returned in the labeled rack beside my office door. After one week, unclaimed papers will be discarded. The two lowest homework scores will be ignored.
- Exams: Exams (300) Two midterm exams and a final (@100)
- You must take the final exam in 114 Science at 8:00 am on Thursday, December 14.
- The final is comprehensive.
- Exams may be taken late provided arrangements are made prior to the exam. If, in the opinion of the instructor, missing an exam would not be unavoidable, 90% of the exam score will be recorded.

- Extra Credit (up to 50 points): Extra credit points will be added to your total before the percentage is figured. Extra credit may be given for successful participation in the weekly math contest (5), math club (5), math contest team (20), quizzes (as announced), etc.

Day | Date | Topic |

1 | 9/3/08 | Geometry Timeline |

2 | 9/5/08 | Axiomatic Systems |

3 | 9/8/08 | Logic |

4 | 9/10/08 | Proof Checklist |

5 | 9/12/08 | Finite Geometry/Affine Plane Proofs |

6 | 9/15/08 | Desargue's Configuration Axioms |

7 | 9/17/08 | Desargue's Configuration Proofs |

8 | 9/19/08 | Euclidean Geometry Propositions 1-30 |

9 | 9/22/08 | 5th Postulate |

10 | 9/24/08 | Pythagorean Theorem per Euclid |

11 | 9/26/08 | Star Geometry |

12 | 9/29/08 | Review |

13 | 10/1/08 | Exam 1: Finite and Euclidean Geometries |

14 | 10/3/08 | 2.2 What did Euclid miss? |

15 | 10/6/08 | 2.3 Hyperbolic Geometry Intro |

16 | 10/8/08 | 2.3 Hyperbolic Geometry Continued |

17 | 10/10/08 | 2.4 Sensed Parallels |

18 | 10/13/08 | 2.5 Asymptotic Triangles |

19 | 10/15/08 | 2.6 Saccheri Quadrilaterals |

20 | 10/17/08 | 2.6 Continued |

21 | 10/22/08 | 2.7 Area of Triangles |

22 | 10/24/08 | 2.8 Ultraparallels |

23 | 10/27/08 | 2.9 Elliptic Geometry |

24 | 10/29/08 | Consistency of Formal Systems |

25 | 10/31/08 | Review |

26 | 11/3/08 | Exam 2 Non Euclidean Geometries |

27 | 11/5/08 | Review of Matrix Multiplication |

28 | 11/7/08 | 3.1-2 Line and Point Reflections |

29 | 11/10/08 | 3.3 Rotations and Finite Symmetry Groups |

30 | 11/12/08 | 3.4 Translations and Frieze Pattern S. G.'s |

31 | 11/14/08 | 3.5 Analytic Model of Euclidean Plane |

32 | 11/17/08 | 3.6 Transformations of the Euclidean Plane |

33 | 11/19/08 | 3.7 Isometries |

34 | 11/21/08 | 3.8 Direct Isometries |

35 | 11/24/08 | 3.9 Indirect Isometries |

36 | 12/1/08 | 5.1 Chaotic Background |

37 | 12/3/08 | 5.2 New Geometric Language |

38 | 12/5/08 | 5.3 Fractal Dimension |

39 | 12/8/08 | 5.4 Iterated Function systems |

40 | 12/10/08 | 5.5 What is a fractal? |

41 | 12/12/08 | Review |

12/16/08 | 10:00 Final Exam | |

- Be neat!
- Use 8.5 x 11 loose leaf paper, one side only.
- Use pencil or a computer.
- Working problems on scratch paper first and recopying is a good strategy for catching mistakes as well as for being neat.

- Fold papers together lengthwise to hand them in. Do not staple or tear, etc. The blank side of the paper is to be out. (See illustration below.)
- On the outside at the top, provide the following information as shown in the illustration.

- Name
- Class (Modern Geometries)
- Homework Number
- Date that you turn it in

- Clearly mark the section and number of each problem from the book.
- Include enough information on each problem so that the reader will know, without refering to the book, (a) what the book asked for, and (b) your response.
- Respect the equal sign "=". Use this sign only when you mean that the expression on one side can be substituted into any statement containing the expression on the other side without changing the truth value of the statement.
- Avoid "Type" errors. Use the equal sign "=" to connect two expressions only when they stand for the same type of expression, e.g. two numbers, two functions, or two sets. Use implies "=>" to connect two statements when the truth of the first guarantees the truth of the second. Sometimes, you will need to use an explanatory phrase such as "Therefore", "Now we can see", or "From equations (1) and (2)... in order to express the relationship between two statements.
- Write using complete sentences whenever possible.

Last Update: September 1, 2008

Ronald K. Smith

Graceland University

Lamoni, IA 50140

rsmith@graceland.edu