2021 Fall Course Syllabus - Mathematics 3061.001

Course: Mathematics 3061.001.

Course Title: Modern Geometry I.

Credits: 3.

How this course will be taught: In person.

Time: T R 08:00 - 09:20.

Place: Wachman 010.

Instructor: Dumitru Dan Rusu.

Instructor Office: Wachman 550.

Instructor Email: dumitru.rusu@temple.edu

Instructor Phone: Please use my email.

Office Hours: TBA.

Prerequisites: (MATH 2061 or MATH 2111) and (MATH 2101 or MATH 2103 or MATH 3051) with a grade of C- or higher. Any of these courses may not be taken concurrently with MATH 3061.

Course Materials: "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. This book is available ONLINE from the Temple University Libraries.

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 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 and their consequences and adopt a problem solver's perspective on a variety of challenging questions. By studying geometry students learn how to think, and how to develop and write mathematical proofs.

Topics Covered: We will start with a discussion of the Euclidean geometry, the foundation for what follows. The axiomatic method will be considered but the emphasize will be more on geometric intuition, proofs and problem solving. Topics such congruency, concurrency, similarity and area will be covered. (Please note that a more detailed coverage of Euclidean geometry is done in MATH 2061.) In addition, if time permits, a good number of miscellaneous topics (such as the theorems of Ceva and Menelaus, nine-point circle, Euler line, the circle of Apollonius, etc.) will be considered. Next, we will discuss Euclidean transformations of the plane and properties that are invariant under them, as well as groups and their use in studying these transformations. Rotations, reflections and translations, algebra of isometries, symmetry and groups, homotheties and tessellations will be covered. Inversive and projective geometry will be introduced as natural extensions of Euclidean geometry. The course will continue with a brief introduction to spherical and hyperbolic geometries in two dimensions. The course will conclude with a discussion of the Kleinian unification of geometry using group theory.

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: There will be two in-class midterm exams: Exam 1- Tuesday, October 5, Exam 2 - Thursday, November 11, and a comprehensive Final Exam: Tuesday, December 14, from 8:00 to 10:00 AM. Each exam will consist of a take-home part and an in-class part. The in-class part will consist of problems similar to those of 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.

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. It is the student's 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.

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. You will receive periodically a homework assignment consisting of selected homework 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.

Drawing Tools: In this course, you will not only calculate but will be compelled to draw 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.

Course Attitude: 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.

Make Up Policy: In the case of a DOCUMENTED EMERGENCY that prevents a student from taking a test as scheduled, the student must contact the instructor immediately in order to discuss alternative arrangements.

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

Exam Security Policy: We have a zero tolerance policy towards cheating. Students caught cheating on a problem in a test (receiving outside help, using unauthorized resources or devices such as calculators, online resources, etc.) will receive a score of 0 for the entire test. 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.

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).

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).

Expectations for Class Conduct: The best way to maintain a safe and focused learning environment is for everyone to get vaccinated. Masks must be worn by vaccinated and unvaccinated people in all indoor or in enclosed spaces (including classrooms, the Library, the TECH Center, the Student Center, shuttles/buses, administrative spaces, common areas in residence halls, etc.). For your general health and well-being, hand washing and monitoring your health is still highly recommended.

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.

For courses in remote mode:

Technology specifications for this course: A working computer with a reliable internet connection, a Webcam, and audio capability. Recommended Internet Speed: 8mbps download & 5mbps upload. You can test your connection at https://www.speedtest.net. Please note: Hard-wired connections are more consistent than Wi-Fi for Zoom sessions. A scanning app such as AdobeScan or CamScanner is required as is access to Zoom and Canvas (the Canvas app is also recommended).
Limited resources are available for students who do not have the technology they need for class. Students with educational technology needs, including no computer or camera or insufficient Wifi-access, should submit a request outlining their needs using the Student Emergency Aid Fund form. The University will endeavor to meet needs, such as with a long-term loan of a laptop or Mifi device, a refurbished computer, or subsidized internet access.

Remote proctoring statement: Zoom, Proctorio or a similar proctoring tool may be used to proctor exams and quizzes in this course. These tools verify your identity and record online actions and surroundings. It is your responsibility to have the necessary government or school issued ID, a laptop or desktop computer with a reliable internet connection, the Google Chrome and Proctorio extension, a webcam/built-in camera and microphone, and system requirements for using Proctorio, Zoom, or a similar proctoring tool. Before the exam begins, the proctor may require a scan of the room in which you are taking the exam.

Online Classroom Etiquette: It is expected that each student attends every class on time for the full duration of each class and behaves, in the same professional manner, as if you are in a regular classroom. This refers in particular to your location and attire. It is not appropriate to eat a large meal, drink alcohol, smoke, or get up often during an online class.

Statement on recording and distribution of recordings of class sessions: Any recordings permitted in this class can only be used for the student's personal educational use. Students are not permitted to copy, publish, or redistribute audio or video recordings of any portion of the class session to individuals who are not students in the course or academic program without the express permission of the faculty member and of any students who are recorded. Distribution without permission may be a violation of educational privacy law known as FERPA as well as certain copyright laws. Any recordings made by the instructor or university of this course are the property of Temple University.