MAT 363: Topics in GeometryFall 2008 Syllabus

Professor: Robert Talbert, Ph.D.Office hours: Old Main 128 MF 11:00-12:00, MTRF 1:30-2:30 and by open-door drop-in, appointment, or instant messenger.Voice: 317.738.8268Email: rtalbert@franklincollege.eduAOL instant messenger: rtalbert235Google Talk instant messenger: robert.talbert

Course Materials• Textbook: W. Fenton and B. Reynolds. College Geometry Using the Geometerʼs Sketchpad, Key

Curriculum Press. We will cover Chapters 1--6, Chapter 9, and Appendix A. • Course website: http://mat363.wikispaces.com (Note: This is different and separate from the course

Angel site.) • Additionally, students should have 24/7 access to a computer for class work involving Geometerʼs

Sketchpad and other course software.

Informal Course Description and Course GoalsIn this course, we will take geometry, widely considered the oldest organized mathematical subject -- having its roots in the work of the Greek mathematician Euclid from over 2000 years ago -- and examine it from several different perspectives. • We will consider geometry from the axiomatic perspective, clearly identifying the minimum set of

assumptions that we need to form a well-structured geometric system and deriving many of the theorems you learned in high school as well as many new ones. Especially important to us is what happens if one of those axioms is altered or deleted entirely.

• We will consider geometry from the analytic standpoint, making use of algebra and coordinate systems to establish results, and from the “classical” standpoint where no such contrivances are used.

• We will consider geometry from the static perspective, where geometric figures are thought of as unchanging fixtures, and from the transformational perspective where geometric relationships are thought of in terms of movements and physical motions.

• We will consider geometry from the mathematicianʼs perspective, using dynamic geometry software to make observations to form precise mathematical conjectures, which we then prove using classical logic and theorem-proving methods.

The overall goal of the course is not simply to rehash the geometry you learned (and which some of you will eventually teach) in middle or high school, but to understand on a deep level why the results of geometry are the way they are, how mathematicians from antiquity to the present day use logic and mathematical methods to obtain those results, and what other kinds of geometries are possible than just the one we see with our eyes.

The successful student in MAT 363 will be able to do the following: • Use dynamic geometry software (e.g. Geometerʼs Sketchpad) as an exploratory tool; • Generalize and form conjecrures from geometric examples; • Write clear, correct, complete proofs of geometric concjectures; • Use the vocabulary of geometry with precision; • Explain the role of axioms (or assumptions, presuppositions) in drawing conclusions; • Relate algebra to geometry (and vice versa) through the use of coordinate systems, and derive

geometric results without resorting to geometry; • Describe the role of geometry in the study of trigonometry and use geometry to derive

trigonometric identities;

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• Make constructions and prove theorems in alternative frameworks for geometry such as taxicab geometry and the Poincaré disk model of hyperbolic geometry;

• Explain the role of the Parallel Postulate in Euclidean and non-Euclidean geometry; • Work with confidence and effectiveness as a problem-solver and mathematical practitioner, both

individually and as a member of a working group.

What to ExpectThis class is very active, having very little traditional lecturing on the professorʼs part. Usually, two out of every five class meetings are spent in a laboratory setting with students working in groups to answer questions and solve problems. The remaining time is split between students proving theorems at the board/document camera for the class and students contributing to discussions led by the professor. The professorʼs job is not to dispense answers or knowledge but rather to manage discussions and coordinate coursework (labs, exams, and outside assignments). The studentsʼ job, by contrast, is to prepare diligently for each class meeting and contribute thoughtfully to class activities. This involves: • Reading the textbook carefully and working through questions and problems as you go; • Giving a serious, significant effort to working each of the problems assigned for discussion; • Keeping well-organized records of your notes, questions, graded work, and grades; • Seeking help from the professor as needed; and• Staying on top of work that is due in the future.

Especially important is this rule: DO NOT FALL BEHIND, AND DO NOT PROCRASTINATE. If you do either, even occasionally, you will find that it is extremely hard to catch up. The kind of work we do in MAT 363 is not the kind that can be done in a single hour just before it is due. It takes time, repeated and persistent effort, and patience (and a healthy sense of humor). Falling behind or procrastinating will spell almost certain failure, even if done early in the course. On the other hand, students who have taken MAT 363 in the past and given it the hard work and attention it requires have found this class to be one of the most enjoyable and useful math courses they have taken.

It is appropriate, given the difficulty level of the class, that the professor should extend himself proportionately to the same degree you are being ask to extend yourselves. I hold regular office hours and maintain an open-door policy for unannounced drop-ins; I also make myself available through instant messaging. Please do not hesitate to call on me for help; itʼs my job.

Assessments and GradingYour grade in the course will be determined by the following items of work: • Labs. The focal point of the class meetings are times for working in groups of 2 or 3 on laboratory

activites from the textbook using the software Geometerʼs Sketchpad (included with your book). These lab activities will generally involve using the software to make geometric constructions on the computer and then manipulating your constructions to make observations about a particular kind of behavior, and then forming precise mathematical conjectures about what you see. There are 15 of these labs planned; they are graded on an 8-point scale on the basis of effort and completeness.

• Discussion and Board Work. The periods of lab work (usually two days at the beginning of each chapter we cover in the text) will be followed by three days of discussion over your labs, over exercises assigned specifically for discussion, and over more difficult problems to prove that are assigned for students to work at the board (in that order, starting with simple discussions at first and moving toward student board work by the end of day 3). Students will receive points for participating in discussion and doing problems at the board. Students must accumulate at least 70 points of discussion/board work credit and can receive extra credit for going beyond that minimum.

• Quizzes. The first day of discussion in each chapter will begin with a quiz covering the main points and terminology of the preceding lab work and the reading for the chapter. Quizzes are 10 points each, and there are 8 of them planned.

• Problem Sets. There will be seven problem sets assigned which cover problems to prove and more complicated exercises, worth 20 points each.

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• Tests. There are two tests planned covering basic ideas and terminology as well as problems from the course material. They are worth 100 points each.

• Pythagorean Theorem project. Each student will find two different proofs of the Pythagorean Theorem and write them up in her/his own words. This writing project is worth 20 points; more information is forthcoming.

• Sketchpad project. Each student will choose a topic in geometry which we did not cover in class and write a short lesson on the topic, illustrating it with constructions using Geometerʼs Sketchpad. This project is worth 50 points.

• Final Exam. A comprehensive final exam will be given on Monday, December 8 from 8:00--10:00 AM, worth 120 points.

The points fit together as follows:

Item Points Grade percentage

Labs (15 @ 8 each) 120 15%

Discussion/Board Work* 70 9%

Quizzes (8 @ 10 each) 80 10%

Problem Sets (7 @ 20 each) 140 18%

Tests (2 @ 100 each) 200 25%

Pythagorean Theorem project 20 3%

Sketchpad project 50 6%

Final Exam 120 15%

Total: 800

* Students must earn a minimum of 70 points through a combination of general discussion and doing board work, with a minimum of 25 points from each type of contribution. Students who earn more than 70 points will have the additional points added into their overall totals as extra credit (up to a maximum of 100 points). Students who fail to earn at least 25 points in each type of contribution will receive a grade for discussion no greater than

20 + min(general discussion total, 25) + min(board work total, 25)

Your semester grade will be determined by taking your point total, dividing by 800 to get a percentage, and then assigning letter grades as follows:

Grade Percentage Range Grade Percentage RangeA 93-100 C 73-76A- 90-92 C- 70-72B+ 87-89 D+ 67-69B 83-86 D 63-66B- 80-82 D- 60-62C+ 77-79 F 0-59

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Keep in mind that most students in MAT 363 need a C- or higher to “pass”.

Course Policies

Academic Honesty. All work that is submitted by a student must be the work of that student alone. Submission of work that properly belongs to someone else constitutes plagiarism and is heavily punished by Franklin College. Please see the notes on academic honesty which are appended to this syllabus for more details.

Attendance. The effectiveness of this course depends upon your preparation, attendance, and participation in the class meetings. Each student is expected to attend class every day and participate in an active, well-prepared discussion. You will not receive participation credit for any day that you miss. Absences on a day of a test, quiz, or the final exam must be accompanied by a documented excuse, signed in ink by an adult in charge of the situation (doctor, police officer, etc.) and submitted to the professor within 24 hours of the absence in order to qualify for a makeup. Otherwise a grade of “0” will be given. To receive credit for lab work if you miss, you must submit a documented excuse as above, complete the lab entirely on your own, and submit your writeup to the professor at a time of his choosing

Late Work. Late submissions of lab writeups, problem sets, and projects will not be accepted. This includes handing in preview activities late because a student was late to class. If a student knows in advance that he or she will be missing a class, all work that is due for that day must be submitted in advance (email is good for this) or by proxy (= giving it to another student to hand in).

Students with Learning Disabilities. Students with documented learning disabilities are eligible for alternate exam environments, including extended times and alternate locations. Please see the professor as soon as possible to arrange such accommodations if you are eligible.

Technology. It is assumed that students in MAT 363 have basic proficiency with the operation of a personal computer and with the resources on the campus network. You will be responsible for obtaining and installing Geometerʼs Sketchpad on your computer system and seeing to it that you can access this program at any time. Technological difficulties will not be considered valid excuses for late work. For example, failing to hand in an assignment because “the printer wonʼt work” will result in a grade of 0; the student should instead email the assignment as an attachment to the professor or hand in the writeup on a flash drive. It is assumed as well that you will back up your work to multiple locations besides your personal computer (e.g. your G: drive, a flash drive, as an email attachment to yourself, using a web-based storage service such as box.net, etc.) in the event of a catastrophic computer failure such as a hard drive crash. Students will be responsible for checking their Franklin College email and the course web site at least once per day for announcements and assignments.

Writing. A key element of MAT 363 is effective communication, particularly technical communication and especially as regards mathematical proofs. Even if you never write a proof in your post-college career, you will be called upon to argue logically for or against an idea and to communicate your thoughts (or the thoughts of your employer) with clarity and precision. A large portion of your grades on all the assessments in MAT 363 will be based on the quality of your writing, which in mathematics also includes the correct use of mathematical notation and terminology. Therefore it is implicit in every exercise or problem you work that you must give a complete, correct, and clear explanation of your answer and not just give the answer itself. (For many problems, the “answer” is itself the explanation.) Students are expected to use English correctly, including correct spelling and grammar, and to format their mathematics in a professional way. There are hints in the textbook for how to write mathematics, and you will be expected as part of your daily preparation to absorb and implement these hints.

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Academic Honesty in MAT 363 and at Franklin College

One of the primary, if informal, goals of MAT 363 is to get you to “think like a mathematician”. The overall goal of the course is to develop, within the context of geometry, your problem-solving, proof-construction, and communication skills to the point where you are a confident problem-solver in any context and a fluent lifelong learner of mathematics, having followed your own path toward understanding and appreciating this amazing subject.

As such, all of the work that you complete as part of the requirements for this course must be your own work, or the result of an honest and equitable collaboration among the members of your working group. When I grade your work, I am looking to see your own personal development in the understanding of the material. I must be able to trust that the work that you are handing in reflects this development and understanding accurately, even -- especially -- if there are problems or errors in it. I have no interest in your merely emulating the work of one of your classmates, copying or even paraphrasing work from a web site or textbook, or in any way otherwise passing off someone elseʼs work as your own.

Plagiarism is the term usually given to define the act of handing in work as if it were your own, when in fact it is not. Academic dishonesty is a broaded term that encompasses plagiarism as well as other actions such as using unauthorized implements on a timed exam. Academic dishonesty is so named, and plagiarism is included under its heading, because academically dishonest behavior is intended to mislead the professor into thinking that your work is an accurate reflection of your learning.

To be clear: Academic dishonesty is not a “youthful indiscretion” or something that can be rationalized away because of the stresses of college life or because so many get away with it. It is a deliberate, conscious choice on the part of the student to mislead his or her professor, and it demolishes the mutual trust upon which all of education is predicated. If you plagiarize or commit academic dishonesty, it is not just the one instance that I cannot trust; your entire body of work (past, present, and future, and not just for MAT 363 but for all your college career) becomes untrustworthy. And it is supremely unfair to the students who are struggling but doing so honestly.

The penalties for academic dishonesty in any form are appropriately severe at Franklin College. If a professor suspects academic dishonesty on an assignment, the professor is required to investigate it. (Note: This is not a choice on the professorʼs part but a job-related obligation according to the Faculty Handbook of Franklin College.) If the professor, in his or her professional opinion, finds that academic dishonesty was committed, each student involved receives a grade of “0” on the assignment, and each studentʼs letter grade in the course is lowered by one full letter, after the “0” has been factored in. That is the penalty for the first offense in the studentʼs career at Franklin College. If it is the studentʼs second offense -- or if the student commits a second offense later -- the student is expelled.

While professors do have some leeway in recommending alternative punishments for academic dishonesty, it is my personal policy not to do so, but rather recommend the full force of the penalty in all situations -- whether the assignment in question was a final exam or a 5-point reading assignment.

Given the severity of academic dishonesty and its punishment, it is appropriate to lay out precise guidelines for academic honesty in MAT 363 in various cases.

• On Problem Sets and projects, every sentence that you write should be one that you have generated yourself and that you understand. You are permitted to collaborate with other classmates on overall strategies for solutions and on big ideas and hints. But you must be working alone when you write your solutions. Additionally, all collaboration with other students on Problem Sets must occur with students who are currently at the same stage of the solution as you. For example, if you are making no progress on a solution and find a classmate who had finished the problem, and then get help on how to do the problem, that is considered plagiarism (collaborating with someone not at the same level of progress as you). If you are making no progress on a problem and get together with 2-3 classmates

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who have also made no progress to brainstorm big ideas for the solution, then this is acceptable collaboration. However, if one of those students in your brainstorming group comes up with the correct idea for the solution, and you simply write down their work without working out the details for yourself and without real understanding, then thatʼs plagiarism (using someone elseʼs work as your own).

• Also on Problem Sets, the primary resource you should use is the course textbook and your notes (and the notes that are on the course web site via the daily scribes). However, you may find it helpful sometimes to look up additional reference material (such as other geometry books). If you use such information in a significant way for your solution, you must attribute it properly using the title, author, and page numbers of the resource you used. However: It is plagiarism to use other books or other mateirals to get completed solutions or significant parts of completed solutions; this is using someone elseʼs work as your own.

• Finally for Problem Sets, no contact whatsoever is allowed with past students or the work of past students from MAT 363.

• On Labs, students will be working in groups of 2 or 3. Collaboration may happen freely within the group (also keeping in mind that individuals need to understand the reading for participation opportunities), but groups may not interact with other groups outside the guidelines above.

• Academic honesty specifications for the Pythagorean Theorem project and Sketchpad project will be more restrictive than the above and will be spelled out in more detail as those projects as assigned.

The easiest route to take in order to avoid issues with academic dishonesty is just simply to recognize and avoid the temptation to engage in it. It is much better to turn in work that has problems but honestly reflects your best efforts than to turn in something that, for all practical purposes, lies to the professor about you. You might lose points in the short term, but you will learn better, perform better, and enjoy your mathematical future better if you stay honest.

PS: In order to “walk the walk” here, I should mention that portions of this document were adapted from Ted Sundstromʼs syllabus for his course Communicating in Mathematics, which is available at his web site at Grand Valley State University.

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MAT 363 Course Calendar for Fall 2008

M T R

8/26/2008Overview of Geometerʼs Sketchpad; work together through 1.2 Activities 1--3.

8/28/2008Lab: 1.2 Activities 4-10.

9/1/2008Labor Day

9/2/2008Using the Geometerʼs Sketchpad: Exploration and Conjecture (day 1)

9/4/2008Using the Geometerʼs Sketchpad: Exploration and Conjecture (day 2)

9/8/2008Using the Geometerʼs Sketchpad: Exploration and Conjecture (day 3).

9/9/2008Lab: 2.1 Activities 1--5.

9/11/2008Lab: 2.1 Activities 6--10.

9/15/2008Mathematical Arguments and Triangle Geometry (day 1).

9/16/2008Mathematical Arguments and Triangle Geometry (day 2).

9/18/2008Mathematical Arguments and Triangle Geometry (day 3).

9/22/2008Lab: 3.1 Activities 1--5.

9/23/2008Lab: 3.1 Activities 6--10.

9/25/2008Circle Geometry, Robust Constructions, and Proofs (day 1).

9/29/2008Circle Geometry, Robust Constructions, and Proofs (day 2).

9/30/2008Circle Geometry, Robust Constructions, and Proofs (day 3).

10/2/2008Lab: A.1 Activities 1--3; Review for Test 1.

10/6/2008Test 1 (Chapters 1--3).

10/7/2008Lab: A.1 Activities 4--9.

10/9/2008Trigonometry (day 1).

10/13/2008Trigonometry (day 2).

10/14/2008Lab: 4.1 Activities 1--5.

10/16/2008Fall Break

10/20/2008Lab: 4.1 Activities 6--11.

10/21/2008Analytic Geometry (day 1).

10/23/2008Analytic Geometry (day 2).

10/27/2008Analytic Geometry (day 3).

10/28/2008Lab: 5.1 Activities 1--4.

10/30/2008Lab: 5.1 Activities 5--9.

11/3/2008Taxicab Geometry (day 1).

11/4/2008Taxicab Geometry (day 2).

11/6/2008Taxicab Geometry (day 3).

11/10/2008Lab: 6.1 Activities 1--5.

11/11/2008Lab: 6.1 Activities 6--10.

11/13/2008Transformational Geometry (day 1).

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M T R

11/17/2008Transformational Geometry (day 2).

11/18/2008Transformational Geometry (day 3).

11/20/2008Lab: 9.1 Activities 1--2; review for Test 2.

11/24/2008Test 2 (Appendix A, Chapters 4--6).

11/25/2008Lab: 9.1 Activities 3--5.

11/27/2008Thanksgiving break

12/1/2008Hyperbolic Geometry (day 1).

12/2/2008Hyperbolic Geometry (day 2).

12/4/2008Hyperbolic Geometry (day 3); review for final exam.

Final Exam: Monday, December 8, 8:00--10:00 AM

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