Math 239 01 — Introduction to Mathematical Proof

Time and Place: MWF 11:30 - 12:20, South 328

Final Meeting: Thursday, May 3, 12:00 Noon

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 may if you want to be sure I’ll be available.

Outline of Course Materials: http://www.geneseo.edu/~baldwin/math239/spring2018/course.php

Books and Other Resources

Textbook

The (required) textbook for this course is

Ted Sundstrom, Mathematical Reasoning: Writing and Proof (Version 2.1)

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

The following dates are best estimates. They may well change as students’ 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

Your grade for this course will be calculated from your grades on exercises, exams, etc. as follows:

In determining numeric grades for individual assignments, questions, etc., I start with the idea that meeting my expectations for a solution is worth 80% of the grade. I award the other 20% for exceeding my expectations in various ways (e.g., having an unusually elegant or insightful solution, or expressing it particularly clearly, or doing unrequested out-of-class research to develop it, etc.); I usually award 10 percentage points for almost anything that somehow exceeds expectations, and the last 10 for having a solution that is truly perfect. I deliberately make the last 10 percentage points extremely hard to get, on the grounds that in any course there will be some students who routinely earn 90% on everything, and I want even them to have something to strive for. I grade work that falls below my expectations as either meeting about half of them, three quarters, one quarter, or none, and assign numeric grades accordingly: 60% for work that meets three quarters of my expectations, 40% for work that meets half of my expectations, etc. This relatively coarse grading scheme is fairer, more consistent, and easier to implement than one that tries to make finer distinctions.

This grading scheme produces numeric grades noticeably lower than traditional grading does. I take this into account when I convert numeric grades to letter grades. The general guideline I use for letter grades is that meeting my expectations throughout a course earns a B or B+. Noticeably exceeding my expectations earns some sort of A (i.e., A- or A), meeting most but clearly not all some sort of C, trying but failing to meet most expectations some sort of D, and apparently not even trying earns an E. I set the exact numeric cut-offs for letter grades at the end of the course, when I have an overall sense of how realistic my expectations were for a class as a whole. This syllabus thus cannot tell you exactly what percentage grade will count as an A, a B, etc. However, in my past courses the B+ to A- cutoff has typically fallen somewhere in the mid to upper 80s, the C+ to B- cutoff somewhere around 60, and the D to C- cutoff in the mid-40s to mid-50s. I will be delighted to talk with you at any time during the semester about your individual grades and give you my estimate of how they will eventually translate into a letter grade.

Real-World Conjectures

Mathematicians don’t discover theorems by having them spring into their minds in perfect textbook form. Rather, theorems begin life as suspicions about patterns or relationships that might exist, and proofs go through many revisions before they settle into their standard form. Sometimes the suspected relationship turns out not to hold at all, and the proto-theorem has to be modified or discarded.

In order to give you a taste of this process, I invite you to look for mathematical patterns in your daily life. When you find one, try to phrase it as a conjecture, and see if you can either prove it or disprove it. Each time you bring me such a conjecture and its proof or disproof I will give you up to 2 points worth of homework extra credit, for a maximum of 5 conjectures per student.

The exact rules for what counts as a real-world conjecture will no doubt evolve as we gain experience with them. However, here are some initial ones: Conjectures have to be things you really discover for yourself, not ones you looked up somewhere. This doesn’t mean that they have to be things no-one else has ever thought of, just that you thought of them independently of other people. They should be superficially plausible, but they don’t have to be profound, let alone true.

A Note on Notation

Mathematical notation and terminology matter. Even though they may seem arcane, each symbol and technical term has a specific meaning, and misusing symbols or terms (including not using them when you should) confuses people reading or listening to your work. Therefore, correct use of mathematical terms and notations will be a factor in grading assignments and tests in this course.

(The same applies to me, by the way: if you think I’m not using terms or notations correctly, or you just aren’t sure why I’m using them the way I do, please question me on it.)

Policy on Late and Missed Work

I will accept exercise solutions that are turned in late, but with a 10% per day compound late penalty. For example, homework turned in 1 day late gets 10% taken off its grade; homework turned in 2 days late gets 10% taken off for the first day, then 10% of what’s left gets taken off for the second day. Similarly for 3 days, 4 days, and so forth. I round grades to the nearest whole number, so it is possible for something to be so late that its grade rounds to 0.

I do not normally give make-up exams.

I may allow make-up exams or extensions on exercises if (1) the make-up or extension is necessitated by circumstances truly beyond your control, and (2) you ask for it as early as possible. At my discretion, I may require proof of the “circumstances beyond your control” before granting a make-up exam or extension.

Policy on Collaboration

Assignments in this course are learning exercises, not tests of what you know. 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.)

Tests are tests of what you know, and working together on them is explicitly forbidden. This means that if you get help from other people or sources without understanding what they tell you, you will probably discover too late that you haven’t learned enough to do very well on the tests.

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

Accommodations

SUNY Geneseo will make reasonable accommodations for persons with documented physical, emotional, or cognitive disabilities. Accommodations will be made for medical conditions related to pregnancy or parenting. Students should contact Dean Buggie-Hunt in the Office of Disability Services (tbuggieh@geneseo.edu or 585-245-5112) and their faculty to discuss needed accommodations as early as possible in the semester.