2024 Spring Course Syllabus - Mathematics 2061.001

Course: Mathematics 2061.001.

Course Title: Euclidean Geometry.

Credits: 3.

How this course will be taught: In person.

Time: TR 9:30 - 10:50 AM.

Place: Wachman 016.

Instructor: Dumitru Dan Rusu.

Instructor Office: Wachman 550.

Instructor Email: dumitru.rusu@temple.edu

Instructor Phone: Please use my email. Email me directly, not via Canvas.

Office Hours: TR 1:00 - 3:20 pm and by appointment. Please note that the office hours may not be used to cover material missed due to unjustified absences.

Prerequisites: Math 1042 (Calculus II) with a grade of C or better or equivalent transfer credits for Math 1042. It is expected that the student will have some, but not a lot, of experience writing proofs. By taking this course, the student will gain more practice and depth.

Course Materials: All lecture notes and hand-outs for this course will be provided by the instructor. In addition, we will use "Classical Geometry - Euclidean, Transformational, Inversive, and Projective" by I. E. Leonard, J. E. Lewis, A. C. F. Liu, and G. W. Tokarsky, 1st edition, Wiley 2014, ISBN-13: 978-1118679197 (available ONLINE from the Temple University Libraries). This book provides a source for some of the fundamental theorems (with proofs) of Euclidean plane geometry and some interesting homework problems.

Course Goals: Since Euclid's The Elements, a book written around 300 BCE and used in mathematics instruction until the 20th century, geometry has been taught as a deductive science, with definitions, axioms, theorems and proofs. In the words of Ludwig Wittgenstein: "If you want to know what a mathematical proposition says, look at what its proof proves". Rather than trying to discuss in depth the subtleties of the axiomatic system, I will concentrate on the fundamental theorems, their proofs, and their consequences and adopt a problem solver's perspective on a variety of challenging questions. By studying Euclidean geometry students learn how to think, and how to develop and write geometric proofs.

Topics Covered: We will cover methods of proof, axiomatic system, basic definitions and facts, congruence, parallelism, metric relations, area, similarity, circles, geometric locus, concurrency, and the applications of the intrinsic theory of vectors. We will prove fascinating theorems about triangles, circles, and lines that you likely haven't seen before. You will also be introduced to non-Euclidean geometries although we will only scratch the surface of these "other geometries". Geometry can be developed in several fundamentally different ways, and all should be considered if the subject is to be shown in all its multifaceted power. Therefore, in addition to the synthetic (i.e., coordinateless) approach, we will briefly discuss why geometry is entangled with algebra and how sometimes tortuous arguments can be replaced by simple algebraic calculations. Using analytic geometry tools and complex numbers for solving certain geometric problems will develop your ability to approach a mathematical problem from a variety of perspectives.

Course Grading: Your course grade will be computed according to the following scheme: Homework 25%, Exam 1 - 25%, Exam 2 - 25%, Final Exam - 25%. Correspondence between the numerical and letter grades is: 93-100 A, 90-92 A-, 87-89 B+, 83-86 B, 80-82 B-, 77-79 C+, 73-76 C, 70-72 C-, 65-69 D+, 55-64 D, 50-54 D-, 0-49 F. Please notice that you will be graded both on correctness and on quality of exposition since a major focus of this course is the ability to communicate mathematical ideas clearly. Any work that is confusing, ambiguous, or poorly explained will not receive full credit.

Exam Dates: We will have midterm exams, tentatively scheduled for Tuesday, February 27 and Tuesday, April 16. They will be held during regular course hours. The final cumulative exam is scheduled on Thursday, May 2, 8:00 - 10:00 am. Each exam will consist of a take-home part and an in-class part. The in-class part will consist in problems similar to those from the homework.

Attendance Policy: You are expected to attend all classes, and you are responsible for all material covered in class. Attendance in lectures will be recorded and will be taken into account in borderline grade cases. Absence will adversely affect your performance on assignments and exams, and could lead to unsatisfactory performance in the course. If you have an excuse for missing a class, you should let me know as soon as possible (preferably before missing the class).

Attendance and Your Health: To achieve course learning goals, students must attend and participate in classes, according to your instructors' requirements. However, if you feel unwell or if you are under quarantine or in isolation because you have been exposed to the virus or tested positive for it, you should not come to campus or attend in-person classes or activities. Students have the responsibility to contact their instructors to create a plan for participation and engagement in the course as soon as they are able to do so and to make a plan to complete all assignments in a timely fashion when illness delays their completion.

Drawing Tools: In this course, you will not only calculate but will be compelled to draw lots and lots of pictures. Geometry is something for everybody and being able to visualize is as important as being able to reason or to calculate. After all, the constructive approach was Euclid's approach: what good are geometric shapes if we cannot build them? Using a straightedge, a compass, and unlined paper is highly recommended. If after a while you will be able to make your judgments using imperfect figures done by hand, that would be great. Using mathematics software like GeoGebra can also be useful since it allows to quickly draw flexible, accurate pictures that can be easily modified, facilitating further investigation and experimentation. You can download the free of charge GeoGebra on your computer or work on it online: https://www.geogebra.org/geometry?lang=en.

Approaches to Learning: Due to the broad spectrum of this course, you may find the pace fast. Mathematics is not a spectator game and you are going to work hard consistently throughout the entire semester to be successful in this course. Often you will be asked to read in advance the lesson that we plan to discuss in class. Asking questions during class is encouraged and appreciated. Be sure to allocate enough time to stay current and keep up with daily work and homework. Please do not read the material passively or assume that you understand and know a topic just because it makes sense when you see the material explained by someone else. Mathematics can be only learned through practice. Reading a mathematics textbook is different from reading any other kind of textbook. When you see phrases like "you can verify" or "obviously" or "it is easy to see", you should use pencil and paper to do the calculations to be sure what the textbook said is correct. This is not a class you want to fall behind in.

Course Attitudes: It is very important to foster a respectful and productive learning environment that includes all students in our diverse community of learners. Treat your classmates and instructor with respect in all communication, class activities, and meetings. All opinions and experiences, no matter how different or controversial they may be perceived, must be respected in the tolerant spirit of academic discourse. You are encouraged to comment, question, or critique an idea but you are not to attack an individual. Our differences, some of which are outlined in the University's nondiscrimination statement (opens in a new tab/window), will add richness to this learning experience. Please consider that sarcasm, humor and slang can be misconstrued in online interactions and generate unintended disruptions. Profanity should be avoided as should the use of all capital letters when composing responses in discussion threads, which can be construed as "shouting" online. Remember to be careful with your own and others' privacy. In general, have your behavior mirror how you would like to be treated by others.

Homework: A substantial portion of your learning in this course will take place through homework and for this reason it is essential that you be conscientious about doing them. Homework assignments will be assigned on regular basis and will consist of selected problems that I will grade. Your consistent effort will certainly lead to improved understanding, and it will almost certainly lead to you earning high grades. We may go over the most difficult problems at the beginning of each class but it is your responsibility to look for clarification of any other questions during office hours. Your final submission of the assignment for grading must be based solely on your own work and efforts; you are not supposed to copy it or share it with others. Obvious copies of solutions from the work of other students will earn both students 0 points.

Make Up Policy: No make-up midterm exams will be given except under extraordinary circumstances with DOCUMENTED emergencies that prevents a student from taking a test as scheduled. In those cases, the student is supposed to contact the instructor immediately in order to discuss alternative arrangements.

CANVAS: This is a registered CANVAS course. Please check CANVAS daily for important announcements.

Exam Security Policy: We have a zero tolerance policy towards cheating. Under no circumstances is the use of personal electronic devices such as phones, computers, smart watches allowed during exams. All such items must be stowed away and out of sight for the duration of the exam. Any student found with such a device during an exam will not be allowed to complete the test, will receive a score of zero for the test, and will be reported to the Student Code of Conduct Board. In addition, under no circumstances, will students be allowed to bring in any kind of papers for use during the exam. Should a student need extra paper during a test, the proctor will provide it. Any student found using papers that they themselves brought into the exam will not be allowed to complete the test, will receive a score of zero for the test, and will be reported to the Student Code of Conduct Board. This is consistent with the Temple University Academic Honor Code (see https://secretary.temple.edu/sites/secretary/files/policies/03.70.12.pdf ) that states: "Every member of the university community is responsible for upholding the highest standards of honesty at all times. Students, as members of the community, are responsible for adhering to the principles of academic honesty and integrity". More serious penalties are possible and those caught cheating will be reported to the office of student conduct. See also the university's academic honesty statement https://bulletin.temple.edu/undergraduate/about-temple-university/student-responsibilities/#academichonesty.

Academic Support: The Student Success Center (SSC) and the Math TA and CA Consulting Center (MCC) both provide excellent support services for this course throughout the semester. Information regarding the services these centers provide will be posted on the course Canvas page. Students are strongly encouraged to take advantage of these services! Some information can be found here: https://www.math.temple.edu/ugrad/tutoring/MCC.html and here: https://studentsuccess.temple.edu/.

Disability Statement: Any student who has a need for accommodations based on the impact of a documented disability or medical condition should contact Disability Resources and Services (DRS) in Howard Gittis Student Center South, Rm 420 (drs@temple.edu; 215-204-1280) to request accommodations and learn more about the resources available to you. If you have a DRS accommodation letter to share with me, or you would like to discuss your accommodations, please contact me as soon as practical. I will work with you and with DRS to coordinate reasonable accommodations for all students with documented disabilities. All discussions related to your accommodations will be confidential.

Academic Freedom: Freedom to teach and freedom to learn are inseparable facets of academic freedom. The University has adopted a policy on Student and Faculty Academic Rights and Responsibilities (Policy # 03.70.02) which can be accessed here (opens in new tab/window).

Add/Drop Policy: Students will be charged for a course unless dropped by the Drop/Add deadline date. Check the University calendar (opens in new tab/window) for exact dates.

During the Drop/Add period, students may drop a course with no record of the class appearing on their transcript. Students are not financially responsible for any courses dropped during this period. In the following weeks prior to or on the withdrawal date students may withdraw from a course with the grade of "W" appearing on their transcript. After the withdrawal date students may not withdraw from courses. Check the University Calendar (opens in new tab/window) for exact dates. See the full policy by clicking here (opens in new tab/window).

AI Policy: The use of generative AI tools (such as ChatGPT, DALL-E, etc.) is not permitted in this class unless specifically announced for a particular assignment; therefore, any use of AI tools for work in this class may be considered a violation of Temple University's Academic Honesty policy and Student Conduct Code, since the work is not your own. The use of unauthorized AI tools will result in a grade of zero on the assignment; a second offense will be reported to the Student Conduct Board.

Incomplete Policy: The grade "I" (an "incomplete") is only given if students cannot complete the course work due to circumstances beyond their control. It is necessary for the student to have completed the majority of the course work with a passing average and to sign an incomplete contract which clearly states what is left for the student to do and the deadline by which the work must be completed. The incomplete contract must also include a default grade that will be used in case the "I" grade is not resolved by the agreed deadline. See the full policy by clicking here (opens in new tab/window).

Student Support Services: The following academic support services are available to students (all links open in a new tab/window):
    The Math Consulting Center
    Student Success Center
    University Libraries
    Undergraduate Research Support
    Career Center
    Tuttleman Counseling Services
    Disability Resources and Services
If you are experiencing food insecurity or financial struggles, Temple provides resources and support. Notably, the Temple University Cherry Pantry and the Temple University Emergency Student Aid Program are in operation as well as a variety of resources from the Division of Student Affairs.