Catalog Description. CRN 23371. Credit Hours: 3.00. This course begins at the high-school level and then moves quickly to intermediate and advanced topics including an introduction to non-Euclidean geometry. Emphasis on proofs.
Overview. The goal of the course is to allow the student to gain mastery over plane geometry so that the student may effectively teach the subject at the high school and college level. The course will cover Book I of Euclid's Elements with the due rigor necessary to achieve this goal.
Meeting Time and Location. MWF, 3:30-4:20, UNIV 129
Textbook. The textbook for the course is "Euclid's Elements" as translated by Thomas L. Heath. A pdf of course notes will also be distributed.
Contact. The best way to contact me is by email. My email address is tsincla(at)purdue.edu. I will usually respond to emails fairly promptly during normal business hours. If you have not received a reply within 48 hours, feel free to follow up.
Office. My office is 744 in the Mathematical Sciences building.
Office Hours. See the course Brightspace page for details. Outside of regular office hours, I am also happy to meet by appointment. Please email me to schedule.
Brightspace. The course page on Brightspace will serve as the main point of contact for announcements, assignments, course policy, and virtual content. Students will be expected to check the course page regularly, at least before every class meeting.
Gradescope. Assignments and quizzes must be uploaded to Gradescope via the course page in Brightspace. (Select "Content" from the top pane in the Brightspace course home page then look for the "Gradescope" tab on the left.) No hard copies of assignments or quizzes will be accepted.
Course Notes. Handwritten course notes will be available in a OneNote Notebook accessible from the course Brightspace page under "Content/Course Notes."
Academic Calendar For ease of reference, here is a link to the academic calendar detailing all breaks, add/drop deadlines, etc.
Lecture. Lectures are held in-person. Due to the interactive nature of the course, attendance is mandatory. Class cancellations and other changes due to a health-related absence on my part will be communicated via the course page in Brightspace.
Accessibility. Purdue University strives to make learning experiences accessible to all participants. If you anticipate or experience physical or academic barriers based on disability, you are encouraged to contact the Disability Resource Center at: drc@purdue.edu or by phone: 765-494-1247, as soon as possible.
If the Disability Resource Center (DRC) has determined reasonable accommodations that you would like to utilize in this class, you must send your Course Accommodation Letter to the instructor. Instructions on sharing your Course Accommodation Letter can be found by visiting: https://www.purdue.edu/drc/students/course-accommodation-letter.php. Additionally, you are strongly encouraged to contact the instructor as soon as possible to discuss implementation of your accommodations.
Exams. There will three in-class exams for the course, two during the regular semester and one comprehensive exam during the final examination period.
Attendance. Attendance will be recorded at several points throughout the course.
Quizzes. There will be 5 quizzes in total for the course. The quizzes will be administered online through Gradescope. There will be a three day window to take each quiz, but quizzes will have a time limit from when they are open to complete and upload solutions. The lowest quiz score will be dropped.
Alternate Examinations. Alternately, you may obtain credit on any or all exams by oral examination. Intent to take such an exam must be communicated at least 3 business days prior to the scheduled exam date. Exam scores obtained by oral examination are final and are not subject to dispute. Makeup exams will not be granted without a legitimate, documented excuse.
Homework. There will be 11 homework sets assigned on a near-weekly basis. Homeworks will be assigned on Fridays and due the following Friday. (See below for details and due dates.) Students are encouraged to collaborate on homeworks as long as: 1) all collaborators are listed at the top of each assignment; 2) each student turns in their own, individual work. Rote copying of solutions from peers, use of internet forums, use of AI to assist in completion of homework problems, or plagiarism of any kind will not be tolerated. Any assignment determined by my personal judgement more likely than not to have been completed with the use of prohibited resources or in a prohibited manner will be given a score of zero. The lowest homework score will be dropped.
Homework Formatting. Homeworks must be typed or neatly written and scanned. Students are encouraged to prepare assignments using LaTeX (see the section on LaTeX below) or other word processing application. There should be no significant cross-outs, rewrites, scratchwork, scribbling, etc. Problems should be clearly indicated and be placed in the correct sequence. Homework should be uploaded to Gradescope by 5:00 pm on the Monday after the due date.
Presentations. Students will be assigned to give in-class presentations over homework problems and selected theorems in Euclid. Presentations will be graded on correctness, clarity, organization, and audience engagement.
Grades. There will be 200 total points. Exams will be worth 30 points each (90 points total). Homework will be worth 5 points per assignment (50 points total). Quizzes will be worth 5 points each (20 points total). Presentations will be worth 30 points total, and Attendance will be worth 10 points total. Grades will be determined by percentage of total points earned. For marginal cases, there will be some discretionary leeway in final grade assignment to account for course participation/engagement or extraordinary effort. Students who get at least 97% of the total points in this course are guaranteed an A+,93% guarantees an A, 90% an A-, 87% a B+, 83% a B,80% a B-, 77% a C+, 73% a C, 70% a C-, 67% a D+, 63% a D, and 60% a D-. The following is a sample cutoff distribution which is fairly typical for courses I have previously taught. The final grade cut-offs may differ slightly. A >92, A- >88, B+ >85, B >78, B- >74, C+>70, C> 65, C- >60.
LaTeX is the language for mathematical typesetting. If you are a CS, Math, or Stats major, I would strongly recommend becoming proficient in LaTeX. Here is the link to A.J. Hildebrand's excellent (archived) collection of beginner LaTeX resources. Another great place to start is Jon Peterson's advice and resources for new researchers. You will probably also frequently need to consult the LaTeX Wiki.
Academic Integrity. See the Academic Integrity webpage from the Office of the Dean of Students. Penalties for academic dishonesty will be, at minimum, a score of zero on the quiz or assignment. Egregious cases will be referred to the Dean of Students and may result in failure of the course or expulsion.
The following is a tentative outline of topics covered and is subject to change. If you are absent from class it is your responsibility to find out what material was covered and to obtain notes from classmates.
Week 1, 8/25 Course Overview. The Use of Proof. Geogebra. Ruler and Compass Constructions.
Week 2, 9/1 LABOR DAY, Course notes, section 1
Week 3, 9/8 Course notes, sections 2 and 3
Week 4, 9/15 Course notes, sections 3 and 4
Week 5, 9/22 Course notes, section 4
Week 6, 9/29 Course notes, section 7
Week 7, 10/6 Course notes, section 8
Week 8, 10/13 FALL BREAK, Leeway/Selected Topics
Week 9, 10/20 Euclid, Selected Topic or Activity
Week 10, 10/27 Euclid, Selected Topic or Activity
Week 11, 11/3 Euclid Selected Topic or Activity
Week 12, 11/10 Euclid, Selected Topic or Activity
Week 13, 11/17 Euclid, Selected Topic or Activity
Week 14, 11/24 THANKSGIVING BREAK
Week 15, 12/1 An Introduction to Non-Euclidean Geometries
Week 16, 12/8 Leeway or Selected Topics
Week 1, 8/25 HW 1 Assigned
Week 2, 9/1 HW 1 Due, HW 2 Assigned.
Week 3, 9/8 HW 2 Due, HW 3 Assigned. Presentations HW 2.
Week 4, 9/15 HW 3 Due, HW 4 Assigned, Presentations HW 3. Quiz 1
Week 5, 9/22 HW 4 Due. HW 5 Assigned, Presentations HW 4.
Week 6, 9/29 HW 5 due. Presentations HW 5. Quiz 2
Week 7, 10/6 HW 6 Assigned. Exam 1.
Week 8, 10/13 HW 6 Due. HW 7 Assigned. Presentations HW 6 and/or Euclid.
Week 9, 10/20 HW 7 Due, HW 8 Assigned. Quiz 3. Euclid Presentations.
Week 10, 10/27 HW 8 Due. HW 9 Assigned. Euclid Presentations.
Week 11, 11/3 HW 9 Due. Quiz 4. Euclid Presentations.
Week 12, 11/10 Exam 2. HW 10 Assigned. Euclid Presentations.
Week 13, 11/17 HW 10 Due. HW 11 Assigned. Euclid Presentations.
Week 14, 11/24
Week 15, 12/1 HW 11 Due. Quiz 5.
Week 16, 12/8 Quiet Period.
Finals Week, 12/15 Exam 3.