Math 239 03 — Introduction to Mathematical Proof

Time and Place: MWF 12:30 - 1:20, Welles 140

Instructor: Doug Baldwin
Office: South 307
Phone: 245-5659
Email: baldwin@geneseo.edu
Office Hours: Any time Monday through Friday, 8:00 AM to 5:00 PM, when I’m not committed to something else. See my Calendar for details and to make appointments electronically. You don’t need to make appointments to see me, but I recommend it in order to be sure I’ll be available. Also note that “office” hours for this course will be via video chat. We can chat at Google meeting https://meet.google.com/boo-wyaj-hcr, or you can set up another method (Zoom, Skype, telephone call, etc.) when you make an appointment.

Online Course Materials: https://www.geneseo.edu/~baldwin/math239/spring2021/course.php

Teaching Mode

This course is designated as “hybrid.” I interpret that to mean face-to-face when possible, but with online supplements, and able to be fully online if necessary. For each topic we study, I plan to follow a pattern that begins with you reading (or maybe watching a video, etc.) about the basic ideas of that topic, then having an online and/or face-to-face discussion intended to solicit (and answer) questions about that topic and to let you practice working with it. After the discussion(s), I will produce a summary of the key ideas, and answers to key questions, and post it to Canvas. For some topics, this process will involve only one class meeting; for many it will extend over two or even three. In all cases, the schedule of face-to-face class meetings sets the pace for everything else, so you will probably find yourself working at a faster pace in this course than you would in a fully online one.

In the event that we switch to fully online instruction, we will continue the online discussions, possibly supplemented by class video meetings for people who want real-time conversation, without face-to-face meetings. All other components of the course (e.g., readings, summary notes, etc.) will continue unchanged. Note that there will not be class meetings via video when face-to-face meetings are allowed.

This design means that the course can switch from hybrid to fully online (and back) on a moment’s notice. This may be necessary if, for example, the College has to switch to online instruction for part of the semester, if I have to quarantine, etc. The course design also means that, apart from it maybe being easier to engage with learning when you do it in-person with an instructor and classmates, there is no real cost to you if you switch back and forth between taking the course as a hybrid versus taking it as purely online.

Books and Other Resources

Textbook

The (required) textbook for this course is

Ted Sundstrom, Mathematical Reasoning: Writing and Proof (Version 3)

Videos

A collection of short videos by the author of our textbook, and designed to support a course he teaches from it, are available at https://www.youtube.com/playlist?list=PL2419488168AE7001

Another set of videos developed at Geneseo and intended to support a generic section of this course are available at https://www.geneseo.edu/proofspace

Other Resources

Course Schedule

Note that the following dates are best estimates. They may change as our actual needs become apparent. Refer to the Web version of this syllabus for the most current information; I will keep it as up-to-date as possible.

Grades and Such

Grading in this course will be very different from what you are used to. The main reason for the unusual grading is that I am trying to consciously undo some of the small ways in which conventional grading unconsciously disadvantages certain students. But beyond removing disadvantages for some, I believe that what I am doing also offers significant advantages to everyone.

Key Ingredients

There are 3 main ways in which grading in this course will probably differ from what you have seen before.

• Mastery Grading. “Mastery grading” is a grading system that, as far as possible, bases your grade for the course solely on whether you achieve the learning outcomes listed earlier in this syllabus. You won’t be graded on whether you participate in class, meet deadlines, etc., only on whether you achieve the course outcomes by the end of the semester.
• Distributed Oral Exams. There are no standard paper exams or quizzes in this course. Instead, I will gauge your mastery of outcomes by discussing exercise solutions or other course work with you. Although the phrase “distributed oral exam” may sound scary, what it means is that the function of traditional exams is distributed over the entire semester instead of being concentrated in a few high-stakes tests, and that it is accomplished mainly through oral discussion instead of in writing.
• Weekly Meetings. I want you to meet individually with me for a 30-minute meeting each week. Most of these meetings will be used to talk about exercises, but I also hope to use some of the time to answer questions you have, find out how the course is going for you, etc. You will set these meetings up as office hours visits, which I described above.

The Details

“Achieving” an outcome has two components: content, i.e., what ideas you know, and depth of understanding, i.e., how thoroughly you understand those ideas. This course’s learning outcomes define both components. Generally speaking, the nouns in the outcomes correspond to content, i.e., things you will learn about. Verbs in the outcomes indicate depth of understanding, i.e., things you will understand the content well enough to do.

I will give you a numeric grade for each outcome in an exercise, based mainly on the discussion of solutions and similar problems — in other words, getting the right answers matters, but is not the only, or even the main, determiner of your grade. Grades range from 0 to 4, as follows:

Although I will grade each exercise, mastery grading isn’t about how you do on any specific one. It’s about how well you’ve achieved outcomes by the end of the course. To that end, there are two other important points about exercises and their grades:

• You can redo grades. If you don’t reach the mastery you want on some outcome on some exercise, I will give you an additional related exercise to do. When you show me your solution to that exercise, I will grade it as, effectively, an additional exercise for that outcome. You can have up to one redo per outcome per exercise (unless the nature of the exercise makes redoing it infeasible, e.g., a major project).
• Only the best and most recent grades count. Your official grade for an outcome, i.e., the one I will use when assigning a grade for the course as a whole, will be the average of your most recent grade on that outcome and the highest two previous ones (or all previous ones if there are fewer than two). “Redo” grades count as separate grades in this average. For example, if you do a total of 4 exercises and redoes related to some outcome, with grades of 4, 2, 5, and 3, your most recent grade is 3, and the highest two previous grades are 4 and 5, so the official grade for that outcome is the average of 3, 4, and 5, or 4.

You will “turn in” each exercise by sharing your solution with me during one of your individual meetings. During that meeting, we’ll go over your solutions and answer any questions you have about them, and we’ll also discuss how you came up with those solutions and how you would approach similar problems.

Finally, when this course ends I will give you a letter grade for it based on the numeric grades. My approach to this is that B grades (including B- and B+) indicate that you generally met the expectations of the course, A grades that you distinctly exceeded them, and grades below B- that you fell short to varying degrees. However, I won’t decide the exact cut-offs between grades until the end of the semester, when I see how grades actually worked in practice. During the semester, you can use the mastery rubric as a qualitative guideline to how you’re doing — for example, it says that 3 out of 4 points, or 75%, is “approaching the required mastery,” so an overall average of 75% should indicate that you’re doing OK but maybe not quite as well as desired. I will be happy to discuss your grades with you at any time during the semester and give you my sense of what letter grade, or range of letter grades, I think you are heading for.

Attendance

In the context of the COVID-19 pandemic, it is vital that we all do what we can to protect the health and safety of each other. If you are feeling unwell on a day that class meets, do not attend. It is better to stay home if you are not feeling well than to attend class and risk spreading illness to others. I have designed this course so that you can progress through it without some or even all of the in-person class meetings, so not coming to class won’t affect your success in it. However, please do communicate with me about absences, and contact the Dean of Students if you expect to be out for an extended period of time.

Face masks are required in all instructional spaces (including classrooms, lecture halls, and laboratories) and all common areas including residence halls and academic buildings. If you forget your mask, please pick up a disposable one before entering the classroom. Masks must be worn for the duration of class. If you do not have a mask or are unwilling to wear one, do not come to class — I cannot safely hold class unless all students are wearing face masks.

Similarly, seating in the classroom has been arranged to preserve social distancing. Please respect it, and do not rearrange classroom furniture. Try to maintain a safe distance between yourself and others at all times, including when entering and exiting classrooms.

This policy applies to me as well as to you. If there is a day when I am feeling ill, I will switch the class to online activities instead of holding an in-person class. Similarly, I will wear a mask throughout class and other meetings, and try to always keep an appropriate distance between myself and others.

Cohorts

To support social distancing during the pandemic, Geneseo is limiting classrooms to about one third of their normal occupancies. Fitting classes into the reduced-capacity classrooms often requires splitting classes into “cohorts” of students, with each cohort attending some classes and not attending others.

I have split this class into 2 cohorts, which will meet on alternating class days.

I will send a separate announcement telling you which cohort you are in. Note that to respect occupancy limits, you may only attend classes on your cohort’s day(s). On other days, you will use the online components of the course to keep up.

Working Together

Assignments in this course are fundamentally learning exercises. You are therefore welcome to help each other with them, unless specifically told otherwise in the assignment handout. However, solutions that you turn in must represent your own understanding of the solution and must be written in your own words, even if you got or gave help on the assignment.

If you use sources other than this class’s textbook or notes in order to do an assignment, you must include a comment or footnote citing those sources in your solution. Similarly, if you get help from anyone other than me you must acknowledge the helper(s) somewhere in your solution. (But note that I generally think learning from outside sources and people is a good thing, not a bad one.)

I will penalize violations of this policy. The severity of the penalty will depend on the severity of the violation.

Academic Support Services

The college provides a range of support services to help students thrive in their classes. Of these services, the one best suited to this course is the Math Learning Center. For more information, including hours and procedures for scheduling a visit, see the MLC website at https://www.geneseo.edu/math/mlc.

Other on-campus tutoring services include the Writing Learning Center (https://www.geneseo.edu/english/writing_center) and a range of department-based tutoring centers.

The SUNY-wide STAR-NY system (www.starny.org/tutoring_schedule) provides online tutoring in a wide variety of subjects.

For more information on these and other academic support services, see the Academic Support services website at https://www.geneseo.edu/academic-support-services.

Disability Accommodations

SUNY Geneseo is dedicated to providing an equitable and inclusive educational experience for all students. The Office of Accessibility will coordinate reasonable accommodations for persons with physical, emotional, or cognitive disabilities to ensure equal access to academic programs, activities, and services at Geneseo. Students with letters of accommodation should submit a letter to each faculty member and discuss their needs at the beginning of each semester. Please contact the Office of Accessibility Services for questions related to access and accommodations.

Office of Accessibility Services
Erwin Hall 22
(585) 245-5112
access@geneseo.edu
https://www.geneseo.edu/accessibility-office

In addition, if there is anything I can do to make this class or its materials easier for you to access or use, please let me know.

Geneseo offers many other services to help students succeed. For a list of some, see https://wiki.geneseo.edu/display/PROVOST/Syllabus+Resources+Related+to+Student+Success.