General Information
and Course Policies

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.

Component of total grade

% of Total



Participation - includes quizzes, in-class presentations, and class participation
(which means, of course, that excessive absences or tardiness will lower your grade; see Class Presentations and More about class participation below )


Exam 1


Exam 2


Final Exam




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.

Written Assignments: Since Math 222 is primarily a language course, you will be expected to learn clearly and precisely to express mathematical ideas in writing. Several times during the semester you will be asked to write up and turn in the proof of some theorem. My evaluation of your proofs will depend on both the mathematical content of your argument as well as the form of your argument. When grading for content I will be looking to see if you understood the mathematical ideas required for the proof. When grading for form, I will consider your clarity of expression, the completeness of your argument, your proper usage of both English and mathematical grammar and notation, and whether you really said what you meant to say.

Of course, form and content cannot be entirely divorced. If your writing is sufficiently muddled that the reader cannot tell what you meant to say, both grades will suffer. Likewise, if you really donít understand what it is you are trying to say, the writing will be fuzzy and unclear. However, it is not impossible to distinguish the factors; the grades will be separated so you can see where improvement is needed.

When you write up an assignment, you are expected to include sufficiently many details to enlighten someone who does not already know what you are trying to say. This may require that you restate a definition or previous theorem and say how it is used in your proof. Do not be afraid to include too many details. If you are in doubt about whether or not to say something that you feel is pertinent, always do so!

Class Presentations:
I have said that most of the class will consist of students presenting work to each other. You will be expected to do your share in this. To ensure that everybody comes to class prepared on a regular basis, I will often choose who presents at the board with the help of a die. I've found that by introducing an element of randomness, we avoid the problem arising when students expect a bye on one lesson because they presented during the previous lesson. Some times I will rely on volunteers to make presentations. This makes it possible for students to present the work about which they feel most confident. But the fact that so much of the grade depends on this participation means that all students must volunteer on something like a regular basis. Donít assume that because others volunteer, you (or your grade) are off the hook.

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.

Examinations. Both midterm examinations will have a take-home component and an in-class component. The two components are designed to address different issues:

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.

Exam Dates:

Exam 1 (in-class) Friday, February 24
Exam 1 (take-home) You may take it during any 72 hour period between the end of class on Friday, February 24 and the beginning of class on Wednesday, February 29.
Exam 2 (in-class) Wednesday, April 18
Exam 2 (take-home) You may take it during any 72 hour period between the end of class on Friday, April 13 and the beginning of class on Wednesday, April 18.
Final Exam: The final exam will be distributed on the last day of class and is due by 4:30pm on Tuesday, May 8. (This is the time regularly scheduled for the Period 2 final exam.)

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 (, 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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