General Information
- Title: MTH3100, Introduction to Mathematical Proof
- Time: MW 5-6:15pm
Instructor Information
- Instructor: John Carter
- Office: Science 3034
- Office Phone: 303-556-2902
- Email: jcarte11@mscd.edu
- Office Hours: MWF at 1:00-2:00pm (or by appointment)
- Webpage: http://www.wamap.org
Course Information and Policies
Prerequisites
A satisfactory grade Calculus 2
Goals
(Adopted from Chapter Zero Instructor Resource Manual by Carol Schumacher with a nod to Dr. Dana C. Ernst) Aside from the obvious goal of wanting you to learn how to write rigorous mathematical proofs, one of my principal ambitions is to make you the student independent of me. Nothing else that I teach you will be half so valuable or powerful as the ability to reach conclusions by reasoning logically from first principles and being able to justify those conclusions in clear, persuasive language (either oral or written). Furthermore, I want you to experience the unmistakable feeling that comes when one really understands something thoroughly. Much "classroom knowledge" is fairly superficial, and students often find it hard to judge their own level of understanding. For many of us, the only way we know whether we are "getting it" comes from the grade we make on an exam. I want you to become less reliant on such externals. When you can distinguish between really knowing something and merely knowing about something, you will be on your way to becoming an independent learner. Lastly, it is my sincere hope that all of us (myself included) will improve our oral and written communications skills.
Expectations
This course will be different than most math classes that you have taken. You are used to being asked to do things like: "solve for ," "take the derivative of this function," "integrate that function," etc. Accomplishing tasks like these usually amounts to mimicking examples that you have seen in class or in your textbook. The steps you take to "solve" problems like these are always justified by mathematical facts (theorems), but rarely are you paying explicit attention to when you are actually using these facts. Furthermore, justifying (i.e., proving) the mathematical facts you use may have been omitted by the instructor. And, even if the instructor did prove a given theorem, you may not have taken the time or have been able to digest the content of the proof. This course is all about "proof." Mathematicians are in the business of proving theorems and this is exactly our endeavor. You will be exposed to what "doing" mathematics is really all about.
In a typical course, math or otherwise, you sit and listen to a lecture. (Hopefully) These lectures are polished and well-delivered. You may have often been lured into believing that the instructor has opened up your head and is pouring knowledge into it. I absolutely love lecturing and I do believe there is value in it, but I also believe that the reality is that most students do not learn by simply listening. You must be active in the learning you are doing. I'm sure each of you have said to yourselves, "Hmmm, I understood this concept when the professor was going over it, but now that I am alone, I am lost." In order to promote a more active participation in your learning, we will incorporate ideas from an educational philosophy called the Moore method (after R.L. Moore, a former professor of mathematics at the University of Texas, Austin). Modifications of the Moore method are also referred to as inquiry-based learning (IBL) or discovery-based learning.
Much of the course will be devoted to students proving theorems on the board and a significant portion of your grade will be determined by how much mathematics you produce. I use the work "produce" because I believe that the best way to learn mathematics is by doing mathematics. I learned to ride a bike by getting on and then falling off, and in a similar fashion, you will learn mathematics in this course by attempting it and sometimes falling off.
In this course, everyone will be required to
- read and interact with course notes on your own;
- write up quality proofs to assigned problems;
- present proofs on the board to the rest of the class;
- participate in discussions centered around a student's presented proof;
- call upon your own prodigious mental faculties to respond in flexible, thoughtful, and creative ways to problems that may seem unfamiliar on first glance.
As the semester progresses, it should become clear to you what the expectations are.
Course Notes
We will not be using a textbook this semester, but rather we will be using a theorem-sequence adopted for inquiry-based learning and the Moore method for teaching mathematics. The theorem-sequence that we are using is an adaptation of the notes by Ron Taylor by The Journal of Inquiry Based Learning in Mathematics. The published original version of the notes can be found here http://www.jiblm.org/downloads/dlitem.aspx?id=56&category=jiblmjournal
Attendance
Regular attendance is expected and is vital to success in this course. If you miss more than 6 classes you cannot pass this class.
Proofs
More or less all of the work you will be assessed on in this course involves writing or presenting proofs. You will be assigned proofs for practice, proofs to read, proofs to present, and the exams will involve doing proofs. It will be a semester long exercise in learning proofs by doing proofs. Traditionally in a course like this students are discouraged from working togather but, unlike a traditional Moore method course, you are allowed and encouraged to work together. You can use the online forum at or you can meet up and work togather. You should however be careful that you aknowledge any help you recieve.
I have written some Proof guidelines to give you a sense of what I will look for when grading your proofs.
Class Presentations
Most days there will be proofs presented by students. These will be written up in sets (several at a time). Then each proof will be presented by its author. To steamline this process I will ask that you claim proofs in advance (in the online forum) to present. This way you can see what proofs are still open for presentation.
You will notice that the grade calculation includes a class participation component. This gives you incentive to pay attention to the presentations. You will get graded on how you interact with the people presenting. Also, you should keep a notebook with all of the proofs presented in class. To make this easier I will ask that each proof presented be written up in the online forum. You will recieve some participation credit for this.
Exams
There will be a midterm exam and a cumulative final exam. All exams will may consist of an in-class part and a take-home part. Each exam will be worth roughly 25 percent of your overall grade. Make-up exams will only be given under extreme circumstances, as judged by me. In general, it will be best to communicate conflicts ahead of time.
Rules of the Game
You should not look to resources outside the context of this course for help. That is, you should not be consulting the web, other texts, other faculty, or students outside of our course. On the other hand, you may use each other, the course notes, me, and your own intuition.
Basis for Evaluation
Your final grade will be determined by the scores of your presentations, class participation, and exams. grade calculation
Additional Information
Getting Help
There are many resources available to get help. First, I recommend that you work on homework in groups as much as possible. You should come see me whenever you can. Also, you are strongly encouraged to ask questions in the course forum, as I will post comments there for all to benefit from.
Closing Remarks
(Adopted from pages 202-203 of The Moore Method: A Pathway to Learner-Centered Instruction by C.A Coppin, W.T. Mahavier, E.L. May, and G.E. Parker) There are two ways to approach this class. The first is to jump right in and start wrestling with the material. The second is to say, "I'll wait and see how this works and then see if I like it and put some problems on the board later in the semester after I catch on." The second approach isn't such a good idea. If you try every night to do the problems, then either you will get a problem (Shazaam!) and be able to put it on the board with pride or you will struggle with the problem, learn a lot in your struggle, and then watch someone else put it on the board. When this person puts it up you will be able to ask questions that help you and the others understand it, as you say to yourself, "Ahhh, now I see where I went wrong and now I can do this one and a few more for the next class." If you do not try problems each night, then you will watch the student put the problem on the board, but perhaps will not quite catch all the details and then when you study for the exams or try the next problems you will have only a loose idea of how to tackle such problems. And then the anxiety will build and build and build. So, take a guess what I recommend that you do.
If you are struggling too much, then there are resources available for you. Work together and help each other learn. Use the course forum! I am always happy to help you. If my office hours don't work for you, then we can probably find another time to meet. It is your responsibility to be aware of how well you understand the material. Don't wait until it is too late if you need help. Ask questions!
NC Policy
The NC policy has changed beginning with this semester. For a 100% refund the date is August 23 and for a 50% refund the date is September 1. The last day to obtain an NC is Friday Oct. 23. This is a hard deadline and will be enforced as such. The department will not approve any late NC requests. Students must request an NC through MetroConnect; faculty approval is no longer required. Holidays: Observance of religious holidays follows College policy, which is posted on the web at http://handbook.mscd.edu in the Academic and Campus Policies for Students section. Each student is responsible for understanding and abiding by the policy.
Accommodations for Students with Disabilities
The Metropolitan State College of Denver is committed to making reasonable accommodations to assist individuals with disabilities in reaching their academic potential. If you have a disability that may impact your performance, attendance, or grades in this class and are requesting accommodations, then you must first register with the Access Center, located in the Auraria Library, Suite 116, 303-556-8387. The Access Center is the designated department responsible for coordinating accommodations and services for students with disabilities. Accommodations will not be granted prior to my receipt of your faculty notification letter from the Access Center. Please note that accommodations are never provided retroactively (i.e., prior to the receipt of your faculty notification letter.) Once I am in receipt of your official Access Center Faculty Notification Letter, I would be happy to meet with you to discuss your accommodations. All discussions will remain confidential. Further information is available by visiting the Access Center website