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2022 Fall Course Syllabus - Mathematics 4096.001

Course: Mathematics 4096.001.

Course Title: Senior Problem Solving.

Credits: 3 credits.

How this course will be taught: In person.

Time: TR 3:30-4:50.

Place: Wachman 010.

Instructor: Gerardo A. Mendoza.

Instructor Office: Wachman 618.

Instructor Email: gerardo.mendoza@temple.edu

Instructor Phone: 1-5053.

Course Web Page: http://math.temple.edu/~gmendoza

Office Hours: Wednesday, 1:00-3:00. Office hours by appointment are also possible (try to arrange one day in advance). Or just come to my office: if I have time, I'll see you.

Prerequisites: As specified in the Undergraduate Bulletin.

Course Materials: No textbook. When necessary, material will be posted or distributed in class.

Course Goals: The two principal aims are: (i) To develop additional mathematical problem solving skills and knowledge of topics not necessarily covered in a standard undergraduate course, and (ii) to acquire or reinforce good writing and oral communication skills of mathematical topics. The course will provide a working acquaintance with tools of the profession such as using state-of-the art technical typesetting (TeX and the macro package LaTeX), mathematical software such as Mathematica, and online resources and repositories such as MathSciNet, ArXiv.org, and JSTOR.

How to get there: To achieve these goals you will be giving in-class oral (chalk and blackboard) presentations as well as turning in papers of your resolution of individual problems or related problem lists I will be posting online on the course's website throughout the semester on the course's home page. The papers must be written using the TeX typesetting system, for which basic instructions will be available on the course's webpage; if you need additional help come to my office (or ask in class).

The style of the written component of your work will be either in the form of a research paper or of a chapter in a textbook or monograph.

In the case of a research paper, it will consist of a title, abstract, introduction describing the context, stating or describing the problem, and subsequent sections presenting the solution of the problem(s), in the format of theorem (or proposition/lemma/claim) and proofs as needed, ending with relevant bibliography and references.

Papers turned in in the style of a chapter in a textbook will have a title, an introduction describing the problem and its context, and successive sections similar to that of papers (including bibliography and references cited).

The style of a chapter is more relaxed than that of a research paper, but in both cases a good narrative is important: the point of your work (eventually in a professional context) is to make yourself understood. A good guide is to write as if you are telling the story to a classmate, keeping a running dialogue in your mind, with your interlocutor asking you questions or clarification of your statements. When you write, think about the way ideas in your textbooks or in papers you have read are expressed, and mimic their style. Think and write professionally.

It is very important to include references consulted. It is a fundamental component of our discipline (as with any other) to be completely forthcoming about the origin of the ideas, whether they came from the literature, online searches, or through discussions with your classmate or others. You can acknowledge such discussions as a reference to {name, personal communication}, or a generic statement at the end of the introduction or the last section before the references. Only if they are your ideas will you omit a reference.

Typically, you will choose a topic to work on (from the list I provide) and start working on solving the problems. This first part is a paper-and-pencil process where you work on providing proofs of almost every statement you make; if you consult the literature, keep track of the sources you are using. The level of understanding of each problem should already be so that you can explain to your classmates, eventually also to me, your proof. Once you know how to prove the statements, you will have a good understanding of the topic you chose. At this stage you will start writing a draft (can still be paper and pencil) organizing the problems of you topic into a well structured unit. Once you have this, you start typing (TeX) a first version.

Once you have typed substantial components of your paper (this can be just the abstract, or one or more proofs of statements, or complete sections), you can send me your work and I will look at it critically. You will then redo these components according to my observations and resubmit. This process may occur several times for the same part of your work, or for different parts of your paper as you make progress. At any time you can consult with me, in-class or during office hours if you need help clarifying your ideas. You have to be judicious about the level of detail needed; too little detail, and I will doubt your knowledge of the problem. Too much detail may mean a paper no one would like to read. (In the 4th to last paragraph of an article in The Atlantic we read
    The first draft is for the writer. The second draft is for the editor. The last draft is for the reader.
This is very good advice.).

Topics Covered: Miscellaneous mathematical problems from multiple areas in mathematics, or in areas involving mathematics for their resolution. Instruction on TeX and good mathematical writing skills.

Course Grading: Based on multiple papers (about one per week or week-and-a-half) and presentations in class. Clarity of exposition, both oral and written, and correctness of the mathematical content and from are fundamental.

Exam Dates: No exams. Individual grades will be based on papers and presentations. I expect your first complete draft within two weeks of starting to work on the topic, and partial drafts or preliminary versions twice per week while you are working on it (a good working discipline would be to send me your work the day after a class, i.e., W or F).

Attendance Policy: Attendance is required. An excessive number of unjustified absences will result in a failing grade.

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.

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).

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.