Text: Calculus, an integrated approach to functions and their rates of change, Preliminary Edition by Robin J. Gottlieb, Addison-Wesley, 2002.
Grading: The grade will be calculated based on 5 components:
| Daily homework assignments | 10% of the final grade |
| Projects and papers | 10% of the final grade |
| Gateway exam | 10% of the final grade |
| Five tests | Each worth 10% of the final grade |
| Final examination | 20% of the final grade |
Homework Assignments: Practice is a primary component of the mathematical learning process; thus homework problems will be assigned on a daily basis. But beyond just providing practice, the problems I assign are meant to be extend and deepen the understanding you have gained from the reading and the class period. The problems are not always easy, but the thought that goes into them always pays off in the long run.
All of this means that much of the learning you do will be done outside of the classroom, but it doesn't mean that when class is dismissed you are on your own. I strongly recommend that you start on the homework as soon after class is over as possible. That way, if (when?) you get stuck on an assignment you can come to see me and get help before it is due.
No late assignments will be accepted. The four lowest homework grades will be dropped before the calculation of the final homework average. In addition, assignments that are not turned in due to illness or other unexpected absences will be dropped if the absence is excused. If you have advance notice that you will be absent (whether or not the absence is excused) I expect you to make arrangements to turn in the assignment early or to have someone turn it in for you. (For example, sporting events, your sister's wedding, religious holidays, etc.)
Projects and Papers: Extended reasoning and the ability to express yourself in writing are both very important in mathematics, as they are in any other field of endeavor. During the course you will be asked to write some short papers on topics relevant to the class. For each of these papers you will be working on an extended project with one or two partners. Your group will turn in a single paper and, except in extraordinary circumstances, each member of the group will receive the same grade.
The process of working on a project has two major components, each of which should constitute about half the work on the paper. The first is to work out the mathematical details of the topic that you have been assigned. The second is to make sense of those mathematical details and to organize them into a coherent narrative. The paper may very well include symbols, computations, and graphs; however, these will need to be accompanied by generous verbal explanations that explain the mathematical ideas.
Writing math papers: Write as if your intended audience were a fellow student in the course who has not considered the question you have been asked to write on. In other words, the instructor is not your intended reader; you are writing to a first-time student of calculus who knows only what you knew when you began to work out the details of the topic on which you are writing. The essay must not assume your reader has access to a statement that defines the problem. You thus need to provide introductory material and diagrams that set up the problem as well as explaining the solution to it. Turn in a single paper for your group.
Differentiation "Gateway" Exam. In a nutshell, the calculus is a coherent set of ideas that describe change using mathematics. Whereas symbolic manipulation is not the central idea of the course, it is the language in which we describe the mathematical ideas of the calculus and a powerful set of tools that help us use those ideas to answer questions that interest us---essentially, the grammar rules that we add to English grammar to help us speak the language of calculus. It is imperative that you obtain sufficient facility with symbolic manipulation that the manipulations themselves do not form a barrier between you and the ideas that they represent. They have to become part of the background.
On the exam you will be tested on your ability to differentiate a wide range of elementary functions using the various differentiation rules that will be discussed in the class (the sum and difference rules, the factoring-out-the-constant rule, the product rule, the quotient rule, and the chain rule---and possible combinations of these). You will also be asked to find the equation of the tangent line to a given function at a given point. The gateway exam will consist of seven problems. You will need to get all of them correct in order to pass.
| There are no errors that "don't count." Leaving out a parenthesis, or putting equal signs between things that are not equal are errors, and will be treated as such. Our ability to use the grammar correctly affects out ability to think about and express mathematical ideas. I expect you to use all aspects of symbolic grammar correctly; nevertheless, I recognize that sometimes one makes a the written equivalent of a typo. So you will be allowed up to one minor notational error on the gateway exam. |
The gateway exam will be given in class after all the differentiation rules are covered. If you pass the gateway exam the first time you take it, you will receive the entire 10% plus a 2% bonus for getting it right the first time. (That is, a total of 12% out of 10% possible!) If you do not pass the exam the first time, you will need to take the exam outside of class hours by arrangement with Prof. Schumacher. You will be allowed to take at most two retakes per week and at most one per day. You will not be allowed to take a gateway exam after 4 p.m. on Friday, May 1, 2009 (the last day of classes in the spring semester). If you pass the gateway within two weeks after it is first offered in class, you will receive the full 10% credit. If you pass it after this time you will receive 5% (half of the total possible). If you do not pass the exam, of course, you will receive no credit for this aspect of the course.
Tests: You will have five major tests over the course of the year. The second will cover mostly the material which has been covered since the first test; likewise, the third will cover mostly what has been covered since the second, and so forth. However, you will be responsible for all the material covered in the course in as much as it relates to the topics being tested.
| Test # 1 | Friday, September 26, 2008 | |
| Test # 2 | Wednesday, November 5, 2008 | |
| Test # 3 | Friday, December 12, 2008 | Note: Violates Grace Period |
| Test # 4 | Monday, February 9 |
|
| Test # 5 | Friday, March 27 | |
| Gateway Exam | Wednesday, April 15 | |
| Final Examination | Friday, May 8, 2009 |
From 6:30-9:30 p.m. |
Final Examination: Because this is a year-long course, there will (of course) be no final exam at the end of the fall semester. The final examination will be a cumulative, three hour final given at the end of the spring semester. If you cannot attend the final exam due to illness or another unforseen emergency, permission to take the final at another time must be granted by the dean's office. See the student handbook for details.
Academic honesty: Though you are encouraged to work with other students on outside
assignments, it is understood that every piece of written or computer-generated work that you submit must finally
be your own. In any case, if you work with a fellow student or students, you should make a note of this on your
paper. (There is no penalty for this! It is merely a matter of academic honesty.) If the assignment is a
group assignment, the members of the group should contribute equally to writing the final product---in other words,
don't put your name on a paper written by others. Moreover, make sure that you are willing to stand behind everything that is written in a paper which carries your name. For further information, consult the student handbook or ask
your instructor.
Resources for help: Prof. Schumacher is the primary source for help with the course. Do not hesitate to ask questions in or out of class.
And please don't consider office hours to be a resource of last resort. I consider them to be a part of the course like any other, and many of my very best students have been 'regulars' in office hours. There is much that I can do for you in a one-to-one situation that I simply cannot do in a group setting. You should take advantage of the fact that I am easily available to help you outside of class.
Other students in your class can also be a source of help. Having a classmate with whom
to work and talk regularly about classwork is a well-known factor in improving performance in calculus. You need
not look for a student who "knows more" than you do. This arrangement works best for both partners
if the students who are working together are well matched in ability and background. In addition, upper-class student
assistants will conduct evening help sessions for calculus students. Details about these problem sessions will
be announced as soon as I know them.
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 (salvae@kenyon.edu), 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.