Math 311 - Introduction to Proof and Abstract Mathematics - Spring 2016 | Instructor: Professor Ellen Fagerstrom | |
Bridges 268 | Mathematics | |
Monday, Tuesday, Wednesday, Thursday, Friday: 11:00-11:50 | Office: Maclean 375 J | |
2 credits | Office phone: 477-4023 | |
Textbook: Discrete Mathematics and Its Applications, 7th edition, Kenneth H. Rosen | fagerstrom@mnstate.edu | |
web.mnstate.edu/fagerstrom | Office Hours: MTF 10:00-10:50, M 12:00-1:00, TH 12:00-1:30, M 3:00-4:00, F 12:00-2:00 |
Course Description and Outline: Methods of proof, include direct and indirect methods, mathematical relations and properties of relations, and an axiomatic treatment of Boolean Algebras.
1. Defining properties of Boolean algebra
2. Equivalence relations
3. Partial orderings
4. Proof methods and strategies
5. Proofs of properties of Boolean algebras
6. Relations and the properties of relations
7. Representations of relations
8. Rules of inference and an introduction to proofs
Course Objectives and Student Learning Outcomes:
1. Understand basic notions of relations, equivalence relations, partial orderings, and partitions.
2. Understand the axiomatic nature of mathematics.
3. Prove formal results in Boolean algebras.
4. Prove a variety of results using direct and indirect proofs.
Comments: MSUM's standard is that one semester credit hour for undergraduates is meant to represent three hours of academic work per week for the average student who has the expected preparation for the courses that he or she is enrolled in over the course of a fifteen-week semester. Therefore, for a typical course, this means that for every hour that class meets, you should expect to work for two hours outside of class reading the textbook, doing homework, or otherwise studying the material. Since this course meets in a condensed period, it will mean that you should expect to be in class five hours a week, and be working an additional ten hours a week outside of class on just this class. This does assume that you are at the level that the Mathematics Department expects for students in this course. If your background is a little weaker than that, you should expect to spend more time studying and doing homework outside of class than this, and if your background is a little stronger than that, you may be able to work less outside of class.
Attendance: I do not take attendance. However, I would strongly discourage you from missing any classes. I rarely have students even pass the course who do not come to class nearly every day. Even those that do manage to pass do not receive the best grade that they are capable of earning. Think of someone who works as a consultant. They don't have to go to work every day because there is no boss keeping track of them. But they won't get paid unless they complete all the work by the time scheduled in their contract. They are most likely to succeed when they do go to work every day. When I was a freshman, I quickly discovered that if I missed a one-hour class where I knew what was going on, it took me 1.5 hours to make up the material. The ratio was much worse if I didn't know what was going on. I suspect similar ratios are true for most people. It is simply more efficient to just go to class and participate in class and talk to classmates (who are often just as confused as you) than to skip class and try to learn it all on your own.
I give makeup exams rarely and only with valid, documented reasons that are given as soon as reasonably possible. In particular, this means before the exam. This also means that I assume that if you are sick enough to miss the exam, I assume that you are sick enough to go to the student health center. The health center can provide you with a signed and dated note saying that you were seen by a doctor (I do not need to know what you were seen for). The documentation should be consistent with the excuse (health center note for an illness, police report for a minor car accident the morning of the exam, funeral program or obituary for a funeral, etc.). Makeup exams will not be graded until the documentation has been submitted. In addition, all makeup exams are given on Study Day, which is Wednesday May 4. Vacations and other family or personal reasons will not be considered a valid excuse for missing a regular exam unless you inform me of the absence by Tuesday March 29. Any such events that are not yet scheduled are expected to be scheduled around the exam dates, which are given on the Test Dates page.
For a known absence due to military duty, jury duty, or other legal requirement where you will miss an exam, you must give me notice as soon as feasible and prior to the absence. Similarly for an absence due to an official university activity, if you provide me written notice at least two weeks prior to the absence, as per the Absence Policy (see the Policies webpage) I feel it is necessary to point out that sometimes faculty members or coaches do not remember to provide this notice in that time frame, but it is up to you to remind them, since insufficient notice will be your problem, not theirs.
Homework will be due nearly every day, and will generally be problems from the textbook. The homework will be announced in class, and will be due by 12:00 noon on the due date or whenever I start grading it, whichever is later. I do not accept late homework (unless the reason is a serious illness that lasts at least a week, or some similar reason). I will, however, keep only the best 80% or so of assignments. The exact number of assignments that will be kept will be announced near the end of the semester, when the total number of assignments is known. Each assignment will be scaled to ten points. To scale the assignments, I will take the points earned, divided by the points possible, and multiply by ten. If the decimal portion starts with a two or larger, then I will round up. If it starts with a zero or a one, I will round down. Therefore, in order to get the full ten points on the assignment, you only need to get 92% on it. Homework is to be submitted on paper.
Homework assignments may be submitted early if you know you will be gone on the due date. They may also be submitted by a friend/spouse/roommate/etc., who may slide them under my office door (MA 375J). Do not submit homework to the mailbox in the main Math office - if it is not submitted in class, bring it to my office.
Academic Honesty: You are expected to do your own work. You may certainly work with others and get help on homework assignments, but the work you submit should be your own work. Note that during exams you will not be allowed to get help from others. Make sure that you learn the material while you do the homework - that is the purpose of the assignments. Then during the exam you can demonstrate your knowledge - that is the purpose of the exams. Cheating and plagiarism will not be tolerated in any college course (or any course at any level). See the Academic Honesty Policy (available on the policy webpage) for more information and possible consequences of cheating.
Special Accommodations:
Minnesota State University Moorhead is
committed to providing equitable access to learning opportunities for all
students. The Disability Resource
Center (DRC) is the campus office that collaborates with students who have
disabilities to provide and/or arrange reasonable accommodations.
Course Requirements: You are expected to complete the daily homework, take and pass all the exams on the scheduled dates, and do all of the required portfolio proofs.
Evaluations Standards: Your course grade will include homework, portfolio proofs, and exam grades. For more details, see the grade page.
Course Outline: See the course schedule for a week-by-week outline.
Calculators: The material for this course is largely non-numeric, so a calculator is not useful for the majority of this course.
General Comments: For all graded work in this class, you must show work for credit and give exact answers. In general, if you have to write it down, you have to show it to me. My rule of thumb when grading is either whether I could do a similar calculation in my head and not make a mistake or if the point of the problem is being met (in particular, if the point of the problem is to show a known result, you will have to show it in some detail). If I feel that you needed to show more work, I will indicate it. My criteria is the same for both homework and exams.
I do not curve. I grade each student individually against a standard of whether or not you personally have mastered the material, not by comparison to other people. I also very rarely give extra credit, and when I do it is to the entire class. If you come to my office at the end of the term and ask if you can do extra credit to improve your grade, my answer will be no. The grading scale and weights for the homework and exams are given here.
I will in general return any work the next class day. If you are not there, I will not give it to friends/roommates/siblings/spouses, nor will I give out grade information on the phone or via email. (These restrictions are not arbitrary - they are based on federal law regarding student privacy.) Normally, I include any old assignments with any current ones, but I do not try to pass them back a second time unless you have turned in the most recent assignment. I will bring the old assignments with me every day, so if you ask at the end of class you can get them then.
I expect you to be responsible for yourself as far as getting notes from a classmate if you miss class. (My notes rarely have answers, just problems, so are not very useful to students.) I also expect you to turn in any homework early if you know that you will miss class. This includes those instances when the absence is due to an official university activity.
Cell Phones: Turn off your cell phones when you go to class (this class or any other class). Cellular phones and other distracting devices generally have no place in a formal or semi-formal setting, such as a classroom. Having your phone on, even in vibrate mode, is disrespectful to both your instructor and your classmates. If your cell phone rings, beeps, or has an audible vibrate during an exam I will reserve the right to require that you turn in what you have at that point, without finishing the exam, or to reduce your exam grade by 25%. The point is that such an interruption can hurt your classmates' exam grades. In mathematics in particular, regaining a train of thought that was interrupted by a classmate's phone can be very difficult for some students to return to, and their exam grades correspondingly suffer. I strongly suggest that you always remember to turn off your phone. This policy applies to any other distracting device, such as a pager or alarm clock, as well.
Similarly, I expect you to respect the learning environment by being in class on time and ready to do mathematics the entire period, and to remain in class until the end of the class. On those rare occasions where you must be late, take off your coat and get out your notebook in the hallway before entering the room, and sit down in the first available seat by the door - even if it is not where you prefer to sit. That way you minimize the interruption to your classmates.
In addition, during exams, your cell phone (or any other electronic device) may not be visible at all - put it in your closed bookbag or something similar. If you use it for your watch, you will have to bring a different clock to exams or use the classroom clock.