|Course Overview. The central purpose of this course is to introduce you to careful use of language in the context of mathematical reasoning and proof. The course is meant to make you think about mathematics in a completely new way, in a more mature way. It should set you on the path to becoming a mathematical producer rather than mathematical consumer. As part of this venture, we will discuss the basic principles of logic and various proof techniques, applying them in the context of the essential building blocks of mathematical structures: sets, relations (including orderings and equivalence relations), functions, etc. While the class will introduce you to some new mathematics, the emphasis of the course is on process rather than content. You and your fellow students will be proving theorems yourselves and presenting them to each other in a seminar setting. Thus I hope that the most important lines of communication will be between students rather than instructor to student as is the case in many classes.|
|The Text. Of course, we will be using Carol Schumacher's text Chapter Zero (2nd ed, published by Addison Wesley).|
Grades. Your grade will be based on your performance on homework, participation (broadly defined, see below), two midterms, and the final exam. Each of the midterms will have two components: an in-class component and a take-home component. The final exam will be entirely take-home. Each will be weighted as follows.
Class Work. Foundations will
be different from other math courses you have had. Because the purpose
of the class is to change the way that you think and reason about mathematics,
it is essential that you become immersed in the work of the course. It
is not enough to respond to what an instructor does or tells you. You
and your fellow students are the ones that make things happen in class.
Without your active participation, nothing will happen. Perhaps more than
in any class you take, you will get benefit out of the course in direct
proportion to how much effort you put in. Thus class work is the most
substantial portion of the grade. It has several components: written assignments,
class presentations and class participation generally. (This last includes
contributing to class discussions, asking good questions, and active participation
when another student is presenting work at the board.) And, I should add,
attendance. If you donít attend you canít participate. You are expected
to be in class on time, if you arenít your grade will be adversely affected.
More about class participation: The person who is presenting his or her work at the board is not the only person with responsibilities in a presentation. The students sitting at their desks have a central role to play, as well. Students presenting their work are not meant to replace a seasoned polished lecture that would be given by an experienced instructor. Nor should they be made to. They are counting on their fellow students to help them by making clarifying suggestions and asking questions. I will feel free to ask questions of persons who are sitting down. Also, it is imperative that everyone is respectful. It can be scary for some students (even the very brightest, I will add) to get up to the board to present a proof to a class of twenty people. If you catch a mistake, say so, but do so with respect and encouragement. If you see the correct argument faster than a classmate, then please be patient and avoid making disparaging comments that might make others feel as though they are slow to catch on. The success of Foundations rests on a supportive and encouraging learning environment, and our goal is to get the class to a point where people are competent in (and confident when) presenting mathematical arguments both orally and in writing.
Both midterm examinations will have a take-home component
and an in-class component. The two components are designed to address
Take-home Component. You will be required to construct proofs for theorems that you have not seen before. You are on your honor not to discuss take-home exams with anyone but Prof. Holdener until all exams have been turned in. You may not consult any books except the textbook, but you are free to use any class notes, any previously proved theorems, and anything that is distributed in class. All guidelines for written assignments also apply to take-home exams.
In-class Component. The purpose of these exams will be to encourage everyone to gain a command of the basic mathematical facts that are discussed in class. The questions will be straightforward for anyone who has been digesting the material along the way. Typical questions will ask you to define important terms, answer true/false and short answer questions on the basic material and perhaps state an important theorem or two. You may be asked to give a simple proof of a fact that has already been presented and discussed in the class.
|Academic Honesty. In general, the rules set forth in the 2011-2012 Course of Study apply. Presenting the work of others as your own is strictly prohibited. In the case of homework, you may collaborate with others in discussing how a problem may be solved, but your write-up must be your own. If you submit work that contains the words of someone else, then you must provide proper citation. Assistance can not be given nor received (other than by the instructor) on any quiz or exam associated with this course. For further information, consult Prof. Holdener.|
|Learning Disabilities. If you have a physical, psychological, medical or learning disability that may impact your ability to carry out assigned course work, feel free to discuss your concerns in private with me, but you should also consult the Office of Disability Services at 5453. The Coordinator of Disability Services, Erin Salva (firstname.lastname@example.org), will review your concerns and determine, with you, what accommodations are appropriate. (All information and documentation of disability is confidential.) It is Ms. Salva that has the authority and the expertise to decide on the accommodations that are proper for your disability. Though I am happy to help you in any way I can, I cannot make any special accommodations without proper authorization from Ms. Salva.|
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