Math 4410
Euclidean and Non-Euclidean Geometry (3 hours)
Spring 2017
Instructor: Dr. Darrin Frey
Office: ENS 368
Office Phone: 7643
e-mail: freyd
Office Hours: MW 3:00-4:00, TR 3:30-5:00.
Class Meeting Time and Location: TR 2:00-3:15 ENS 349
Textbook: Euclidean and Non-Euclidean Geometries; Development and History, 4th edition by Marvin Jay Greenberg.
Grading
There will be two mid-semester exams in addition to the final exam. Homework
will be collected weekly and will figure significantly in your grade. Also, we
will be having some in-class work. Each part will contribute as follows:
Exam 1: 20% -------- (Covering the first four chapters)
Exam 2: 20% -------- (Covering chapters 5, 6 and the first parts of chapter 7)
Homework: 25% -------- (See my webpage and/or Moodle for weekly assignments)
final exam (comprehensive) : 30%
other classwork: 5%
(I
reserve the right to adjust these percentages on an individual basis at my
discretion).
If you will miss an exam, you MUST let me know BEFOREHAND. If you do not, you will not be able to make it up unless you are sick. If you are sick, you need to bring a written doctor’s letter. You are expected to read each section of the text before we cover it in class.
Grading Scale:
93-100: A -------- 73-76: C
90-92: A- -------- 70-72: C-
87-89: B+ -------- 67-69: D+
83-86: B --------- 63-66: D
80-82: B- -------- 60-62: D-
77-79: C+ -------- < 59: F
Coverage: We will be covering Chapters 1 through 8 (I hope) with a few forays into Chapter 10 to discuss hyperbolic lengths and area. We will perhaps even go beyond the text on those topics. In more detail, we will discuss Euclid's axioms and their problems, incidence geometry and projective planes, Hilbert's Axioms for Euclidean geometry, Neutral geometry, the history of attempts to prove the parallel postulate, hyperbolic geometry, and Euclidean models of hyperbolic geometry. This will include calculations of hyperbolic area, and some philosophical implications of hyperbolic geometry.
Homework: All homework must be typeset using LaTeX.
Attendance policy: Attendance is not a formal part of your grade. However, if you miss a lot of class, it will take its toll on your grade. Also, when I am determining final grades, if you are a borderline case and you have missed a lot of class, I will almost always choose to give you the lower grade.
Extra Credit: I do not give Extra Credit. Past experience tells me that it hinders rather than enhances learning.
Academic Dishonesty: Anyone who is involved in academic dishonesty is subject to potential grade reduction, course failure or dismissal from Cedarville University. It will be my discretion which punishment I will pursue.
Academic Integrity Statement: The Academic Integrity Pledge is a commitment to live with integrity in all areas of life including the classroom. All forms of academic dishonesty violate this pledge and could result in dismissal from this community.
Academic Integrity Pledge: With my pledge to affirm the Cedarville Covenant I attest that all work I submit is my own and is in accordance with the standards of the Academic Integrity Policy. As a member of the community I will love God and others, live with integrity, and pursue excellence in all that I do.
Academic AccommodationsGroup work: I highly encourage working in groups if you are actually studying or problem solving. However, each required turn in must be your work and not a copy of another person's efforts. If you receive extensive help from someone, then it is appropriate to credit them somewhere on the turn in as a reference. You may work together if you desire. HOWEVER, work that is to be turned in should be your work regardless of how much assistance you had to get before you completed it.
Late papers: Any items turned in late will receive an automatic 5% cut per calendar day (as opposed to per class day). If you have a planned official trip, then turn in any assignment before you depart. If you are sick, then it is due the next time you come to class.
Appeal process: Our commitment as faculty is to provide you with the best possible educational experience this semester. If a concern arises during the semester, I encourage you to discuss the issue with me or, if you wish to remain anonymous, you may share your concern Dr. Dennis Flentge, Chair of the Department of Science and Mathematics. He will work to resolve the issue. If the concern is about grading assignments or exams, your first responsibility is to speak with me. If you believe that the outcome of that meeting did not resolve the issue, you may appeal to Dr. Flentge. The formal grade appeal process can be found at www.cedarville.edu/gradeappealprocess. Dr. Flentge can be contacted by email (flentged@cedarville.edu), by phone (extension 7940) or in his office (ENS 380A).Personal Computers: Students are expected to complete all out of the classroom assignments with the use of the appropriate technology made available to all students. While I will use the computer to demonstrate things in class, you will not be required to have a computer in the classroom.
My Role: Before any exam, my role as your Professor is to help you learn this material. I will do whatever I can to help you, but as with anything, I can only help you if you want to be helped. When I am writing the exams, my role changes from being an instructor who is anxious to help you learn to an impartial evaluator of your progress. Many times students see me as an easy-going, easy-to-talk-to, willing-to-help person, (which I am) and they are surprised when they find that I write demanding exams and am a demanding grader. Sometimes students mistake my demanding grading and exams as evidence that I don't care about their success. That is not true. I am very concerned about the progress each one of you makes. However, I am not doing you any favors if I am too easy on you. Make sure that you are aware that I take my role of impartial evaluator of your progress as seriously as I take my role of helping you to learn.
Your Responsibility: Your responsibility is to come to class every day, take notes, read the text and master both the notes and the text as well as the homework problems I assign. It is your responsibility to get help when you need it. It is your responsibility to know when things are due and to get them turned in to me on time. It is also your role to motivate yourself to learn the material. That is not to say that I don't try to make the course interesting.
Is Math Sacred?: Yes. The Bible talks about special revelation (the Bible itself) and general revelation (the creation). Keep in mind that what we are studying in this class is revelation from God just as much as the scriptures are. I think that adds a bit of sacredness to our endeavors in the classroom. I believe that general revelation has a couple of purposes. One is to help us exercise dominion over the creation. This involves not only using the creation but taking care of it. The other purpose of General Revelation is to show us more vividly and viscerally the wonder and glory of God. (For example, no generation who ever lived has a clearer sense of how big and complex God is than we do since none understood the universe as well as we do.) So, even if you never use some topic we study in your future career, you are studying what He has made and therefore it is valuable at least to tell you more about Him. The fact that it might be difficult for some is no surprise, as God is difficult to understand. Math eventually becomes difficult for everyone, including mathematical geniuses. Keep this in mind as we move through the semester.
How to do well in my class:
0. Be willing to work hard. God wants us to work hard and be skillful and knowledgeable both generally and in our professions.
Psalm 47:7 For God is the King of all the earth; Sing
praises with a skillful psalm.
Exodus 28:3 And you shall speak to all the skillful persons whom I have endowed with the spirit of wisdom, that they make Aaron's garments to consecrate him, that he may minister as priest to Me.
Proverbs 10:14 Wise men store up knowledge, But with the mouth of the foolish, ruin is at hand.
Proverbs 15:14 The mind of the intelligent seeks knowledge, But the mouth of fools feeds on folly.
Colossians 3:23-4 Whatever you do, do your work heartily, as for the Lord rather than for men; knowing that from the Lord you will receive the reward of the inheritance. It is the Lord Christ whom you serve.
Proverbs 14:23 In all labor there is profit but mere talk leads only to poverty.
"Anything Christian should have quality stamped all over it." -- Dr. Paul Dixon
That applies to the quality of your work as a
student.
Remember
that you are here to learn, not to earn grades. In the heat of the semester
that is easy to forget, but superficial learning is short-sighted and will cost
you later. I probably won’t know the difference but the Lord will. To perform
acceptably, a typical well-prepared student should be ready to spend around
five or six hours outside of class for each hour in class.
1. Spend a lot of time reading your class notes and thinking about the material we are covering before you work on the homework. One mistake that is often made in this course is that students worry about getting the homework done because the problems are nontrivial and so they start on them before they have fully digested the section. The material in this course can be deceptively difficult because the information is familiar so make sure you spend time with each of the theorems and see what they mean in the specific examples that you know of. You should also spend time really learning the proofs of some of the theorems. That will give you some tools with which to tackle the problems and although it probably won’t seem like it, it should save you a lot of time.
2. When you run into a difficulty that you cannot overcome by yourself, come see me in my office. Don't hesitate to do this right away, because the longer you put it off, the more you will have difficulty with later material. Also, don’t be afraid to come see me. I enjoy having students in my office.
3. Do all of your homework carefully and completely. When you run into problems you can't solve immediately (and you will), take time to understand the problem and try lots of things to help you make progress. If you try something and it doesn't go anywhere, then try something else. Don't let yourself write solutions you don't understand. Also, make sure that you know what skills and concepts are important in each section and don’t go forward until you know them well.
4. Don't do dumb things like miss class for no reason, or talk to your friends about other things during class, etc. Sit near the front of the room so that you won't be distracted by what other students are doing.
5. A warning about lectures, tutors and office hour help: Just because you follow someone’s explanation of the solution to a problem doesn’t mean you understand the solution. You need to go back and try the problem again on your own to see if you can do it yourself without looking at their solutions. That will highlight any items you may have missed in their explanation. I really think you should memorize the proofs in the book. But don't just rote memorize them, you want to be able to think through the proofs on your own. You really just want to memorize points along the way that keep you from getting stuck.
Other pearls of wisdom:
There are three things I am looking for when I determine grades and how to make up exams.
1. Skills - These are mechanical things. Can you solve the routine problems? Can you solve problems like the ones in the book and the ones done in class? I expect you do be able to do skill problems almost without thinking. They should be automatic. Some things begin as conceptual problems, but after you have done several, they will become automatic.
2. Conceptuals - These are the ideas of the course. Can you explain the ideas of the course to someone who is not in the course? For example, if someone asks you "What is Non-Euclidean Geometry? Is it really true?", you should be able to tell them in a way that they can understand. Also, can you give some idea of why what we’re studying might be of interest to someone else?
3. Mastery - Can you apply your knowledge in unfamiliar situations? Can you recognize in a situation (given in English without mathematical terms) the inherent ideas of geometry even though they are not explicitly stated?
I am really looking forward to teaching this class and I hope it is
enjoyable for you. I know it will be a lot of work, but it is a beautiful
subject and hopefully I can pass my appreciation for it on to you.
Catalog Course Description: Rigorous Treatment of the foundations of
Euclidean Geometry; an introduction to hyperbolic geometry with an emphasis on
its Euclidean models. Prerequisite: MATH 2210 Logic and Methods of Proof.
Course Objectives:
1. Students will understand the role that axioms play in geometry and be able to work with different systems of axioms from memory.
2. Students will learn the basic theorems of neutral geometry and be able to solve problems and generate proofs in neutral geometry from memory.
3. Students will learn the basic theorems of hyperbolic geometry and be able to solve problems and generate proofs in hyperbolic geometry from memory.
Mapping Assignments to Course Objectives:
Exam 1 maps to objectives 1 and 2.
Exam 2 maps to objectives 1 and 3.
The final maps to all three objectives.
Homeworks 1 through 4 map to objective 1.
Homeworks 4 through 6 map to objective 2.
Homeworks 7 through 11 map to objective 3.
The in-class project maps to objective 1.
|
Unit
Outcome |
Program
Outcome |
Decision
Point |
Assessment |
|
2
-- Content Knowledge: |
3
-- Completion of Principles block |
GPA
in course |