Math 110A
Precalculus Mathematics
Fall, 2004

## Course Topics

In this course we learn foundational material for practically all successive mathematics courses. This semester we will study functions including those most commonly found in applications (polynomial, rational, exponential, logarithmic and trigonometric), graphs of functions, transformations and combinations of functions, function inverses, arc length and area for circles, trigonometric identities, methods for “solving” right triangles, and methods for solving conditional equations and inequalities. As time permits, we may cover other topics as well. Our textbook, of which we will cover the majority of the first seven chapters, is Precalculus: A Study of Functions and Their Applications, by Swanson, T., Andersen, J. and Keeley, R. (Harcourt, 2001).

## Course Objectives

The main objective of precalculus is suggested by its name: to get ready for calculus. So most of the time in this course the answer to the question, “Why should we know this?” is “Because there are occasions in the calculus sequence where this knowledge is crucial or serves as a means to a greater end.” (If you do not intend to go on and take calculus, see me immediately about a better course for you!) At the most basic level, then, you should strive to learn well the material of the course. At a broader level, here is a list of questions, not tied to any specific precalculus topic, that point to ways I hope you will be affected by the course.
• Am I able to speak about the individual concepts and how they fit together in terms similar to those used in the textbook and/or by the professor? Am I using the language of mathematics properly, expressing my problem solutions in a clear flow from start to finish?
• Is my general trend away from a “give me the map” frame of mind (i.e., “Just tell me how to do the problem”) and towards an “explorer's” mindset (i.e., “I want to be able navigate my way through unfamiliar situations”)?
• For those concepts that were already familiar to me, am I shedding ideas I thought I knew to be true but could not say why, and replacing them with ones that I can support?
• Am I learning to see the little differences that matter — the ones that make one problem far different from another — as well as the (seemingly) big differences that do not?
• Am I learning to recognize those spots during an in-class example where detailed notes are most important?
• Am I getting better at reading the textbook? Am I beginning to anticipate questions that seem important to the author and/or professor? Can I work through book ”Examples” without actually reading their “Solutions”?
While the specific day-to-day skills of the course are to be mastered, your current/future enjoyment and success in mathematics courses is equally dependent upon growth in the areas listed above. Do not expect this growth to occur just by doing what is required of you in the course. It is likely possible to earn good marks in the course and still answer “No” to the above questions at semester's end. If you really wish to become mathematically adept, however, you should begin immediately to think creatively about how you can structure your study habits so that your answers are increasingly “Yes”. Here are
some ideas the professor has which may be helpful.

## Contacting the Professor

My office is NH 281. The hours I am intentionally in my office for student questions are posted on my homepage, and are subject to change during the semester. If we cannot hook up at one of these times, feel free to talk with me about an appointed time to meet, or swing by my office in the hopes that I am available to help. If you feel yourself falling behind in the class, it is very important not to put things off, but to seek help right away. Do not wait until a time close to an exam before speaking with me.

I may be reached by phone at x66856, but a better way to reach me is by email. If you require my approval for something, do not consider having left a message for me as equivalent to having obtained that approval.

## Use of Technology

A good deal of computer use will be expected of you in this course. Generally speaking, daily homework assignments and other course information are available on the the web, and it is your responsibility to access this information online. (I strongly urge you to download and use Mozilla's Firefox web browser for this purpose instead of Microsoft Internet Explorer, as the latter will frequently look in the wrong place for files and then say they cannot be found.) While many announcements, hints, etc. may be given in class, things that cannot wait until the next class period will be sent to you as email messages. Thus, it is important that you be checking your email daily, preferably later in the day. I have requested a class email list to which you can send messages at

math110a@calvin.edu

Any mail sent to this address will be received by all members of the class (including me). You may use it as a forum for discussing assigned problems, topics that came up in class, etc.

In addition, a number of assigned problems will require the use of a graphing calculator, or the like (Click here for a java applet that emulates one).

Whatever technology you use, beware of becoming too reliant upon it. For skills which you ought to be able to do by hand, you will generally be required to demonstrate your work on exams as if you had no helpful technology at your disposal (despite the capabilities of your graphing calculator).

Concerning written homework, you may borrow someone's idea for solving a problem, but cite your source (a classmate, peer, book—provide the usual bibliographic information, website—provide the url, etc.). All written assignments (except in the event a group project is assigned) are to be written up separately on your own, using your own words. Give as much attention to presenting your solutions in a coherent manner (using mathematical symbols as part of your sentence structure) as you give to actually solving problems, as it is the explanation of each problem that is graded (not simply the answer itself). Handing in (uncited) another's writeup of any part of an assignment will be considered an instance of academic dishonesty (See Section 4.2.8 of the Faculty Handbook), resulting in a zero for the entire assignment.

If any part of an exam write-up is not your own, or is the result of unauthorized access to information stored anywhere in any form, the result on the first instance will be a score of zero. A second occurrence will result in automatic failure of the course.

## Evaluations

Each of the following will be components of your overall grade: assignments (graded for correctness), exams (there will be four — see the course calendar for their dates), quizzes (some as-yet-undetermined quantity of them), participation and a cumulative final.

Homework will be assigned on a daily basis and usually collected two times per week. We will try to get it marked in a timely fashion, at which time I will place it in a folder marked “graded homework” in the box outside my office where you may pick it up at your convenience. There is a corresponding “new homework” folder, in which you may place homework that is to be collected that day. I consider it late if it has already been collected by the grader by the time you place it in the folder, so the safest thing is to hand it in at the end of class. Homework that is late may receive only 75% of the score it would have received otherwise, and that only if it is handed in before the others of the set have been returned.

At semester's end, I will compare your grade on the final exam with what you have received on the four in-class exams. If the final is better, then I will replace the worst of these with the final exam grade. For students who have been present for all exams, this generally means that you may miss on a set of topics once without penalty, so long as you understand those topics thoroughly for the final exam. If you must miss an exam for reasons other than serious illness (about which you must contact your professor in advance) or another college-related involvement for which an excused absence is granted, there will be no opportunity for a make-up. In this case, the final will automatically count in place of one missed exam. Cheap airfares, early departures for vacations and the like are not valid excuses for missing an exam.

## Accomodations

Reasonable academic accomodations will be made for individuals with documented disabilities. Any student who this concerns should notify one of the coordinators for services for students with disabilities in the Center for Student Success, Spoelhof College Center 360. That student should also meet with me during the first two weeks of the semester to discuss academic accomodations.

## Citizenship

The type of concentration required for mathematics/statistics calls for a distraction-free environment. Please do your part to make the classroom one conducive for learning by arriving on time, not working on homework assignments during class, refraining from frivolous talk, and actively participating in in-class discussions/activities.

Please speak with me about problems or issues as they arise during the semester. I am still growing as a teacher, and if you have concerns, it is simply a matter of “building one another up” that you should raise them in an appropriate moment, preferably while adjustments may still be made that affect your class.