Fall 1999 Syllabus

PRECALCULUS WITH MODELING EMPHASIS. This course is designed for students wishing to study mathematical ideas frequently applied in management, social, and life sciences. Topics will include linear, quadratic, exponential, and logarithmic functions; curve fitting; systems of linear equations; and linear programming. Applications to various disciplines will be investigated through the construction and analysis of mathematical models. Microcomputer graphics and computational packages will be introduced and used in the analysis of selected models. This course and a knowledge of trigonometry provides adequate preparation for MAT 220, Calculus I. This course is non-credit for anyone with credit in MAT 110, Precalculus With Trigonometry.

Prerequisite: MAT 012 or waiver. This course may be used to fulfill the Quantitative Reasoning requirement.

• To become familiar with the major concepts and techniques of precalculus, including linear, quadratic, exponential, and logarithmic functions.
• To develop skills in formulating, solving, and interpreting mathematical problems.
• To gain experience with real world applications of precalculus concepts and with curve-fitting.
• To use a scientific calculator to explore concepts of precalculus.
• To practice communicating mathematical ideas to others.
• To become a more independent learner and logical thinker.

The main text Algebra and Trigonometry is by Paul A. Foerster. We will cover chapters 2-6:

Chapter 2, Functions and Relations

Functions are a mathematical way of understanding and formalizing relationships and trends in commonly occurring types of data. We will consider the concept of a function algebraically as well as graphically since we will find both very useful.

Chapter 3, Linear Functions

A linear function is a function which forms a line when graphed and has a constant rate of increase (or decrease). Many, many relationships can be graphed as lines, so this is a very, very important function. An example is the amount you pay for photocopies; each copy is $0.07, so the per copy increase in cost to you is constant.

Chapter 4, Systems of Linear Equations and Inequalities

In this section we will explore situations in which we have more than one linear function to consider in solving a problem. This will help us answer real world questions such as arise in such various disciplines as business, medicine, and agriculture.

Chapter 5, Quadratic Functions

Quadratic functions are "bowl-shaped" like the inside of a satellite dish. When you throw a ball into the air and graph its height as a function of time, you get a graph of a quadratic function. We will consider these functions and develop the tools needed to solve real world questions involving them.

Chapter 6, Exponential and Logarithmic Functions

Exponential functions have a graph shaped like a "boomerang" lying on one of its sides. Our planet's human population continues to grow exponentially causing many people to worry about running out of certain resources on the planet. Logarithms will help us to understand and answer questions which involve exponential functions.

Our course home page is located at http://www.berea.edu/Math/Faculty/Jan/MAT112/.
Use this page as a resource to find this syllabus and other course-related information.

For the benefit of the students in the class, all course grade computations are continually updated by the instructor, so students may check frequently on their in-progress course grade during the term.

Tests and frequent short quizzes will be given in this course. Approximately one announced quiz will be given each week in which there is no test. In general, the announced quizzes will consist of questions on the assigned text readings or homework-like problems.

The three test dates are not pre-scheduled as the instructor believes it is very important that students have input into when the tests are held. However, the tests will fall approximately in the following weeks:

• Week of October 4
• Week of November 1 or 8
• Week of December 6

The comprehensive final exam will be during the regularly scheduled final exam period, Tuesday, December 14, from 10:00 to 11:50 A.M., on the second day of Fall Term finals. By Berea College policy, no instructor can reschedule a final exam on his or her own, so please plan now to take it then.

All written work should be neat, organized, and should show sufficiently many steps to demonstrate a clear understanding of the techniques used. Homework is due at the beginning of class on the announced date due. If a student must miss class due to either a sickness or a planned absence, homework is still expected to be submitted on time. Assignments may be requested in advance.

Late assignments will be accepted for reduced credit up until the homework is returned, and late work must be labeled as late. Written or printed homework assignments may be turned in before class or at the instructor's office, but should NOT be sent through the CPO, attached in ccMail, or given to a student assistant. A selection of the assigned homework problems will be graded for credit, and assignments not meeting the above standards may receive reduced credit.

Learning to work in teams effectively is strongly encouraged. Some homework assignments will be specifically designed for teamwork, others for individual work, but on most homework you can choose to work alone or in a team. All homework assignments must clearly include all of the authors' names at the top of each page. On any assignment in which half or more of the work was completed in a team, a single copy of the assignment should be handed in with all of the team's participants listed as authors. Teams can generally consist of one, two, or three members due to the nature of the work in this course. Unless otherwise stated, teams shall not consist of more than three members for most work. On any assignment where less than half of the work was completed in a team, individual assignments should be handed in with the author acknowledging all of the help received for each problem. This includes significant help received from the instructor or in the Math Lab Consultants. Note that the instructor or a Math Lab Consultant may help with homework, and while this help should not be acknowledged as co-authorship, it should still be mentioned. This is meant to be a sharing process; do not "give credit" to other students who have not attempted to contribute to the work or to the team's work, because it is ultimately not a help for the student who did not contribute to the work. Thoughtful practice, not (even mindful) copying, is ultimately the best way to learn. Note that on all team-completed assignments, students must describe the roles played by each author on the assignment.
Warning: Please be careful to conform to these standards for teamwork, since they are designed to encourage good learning practices. (Furthermore, copying another's work or otherwise failing to adhere to these standards may even result in a charge of academic dishonesty.)

Class lectures, discussions, and in-class calculator work are considered to be a vital key to success in this course. It is the hope of the instructor that class sessions are both informative and useful, therefore attendance is expected at each class session unless a specific exception is made. This policy will be enforced in several ways. Quizzes may be announced or occasionally "popped," and because the lowest quiz grade will be dropped, under nearly all circumstances, make-up quizzes will not be given. Likewise, make-up tests will under almost no circumstances be given, so missed tests will therefore count as the student's dropped 100 points. Absences from class are noted, and repeated absences will adversely affect the student's grade. The final grade may be lowered by one third of a letter grade for each absence after the fourth. Thus, it is the responsibility of the student to speak to the instructor about each absence from class. This should be done as soon as possible, and if at all possible before the absence occurs. Students who miss class are held responsible for all of the material covered, assigned, and collected during their absence.

The members of this class constitute a learning community. Learning in such a community best takes place in an atmosphere in which instructor and the students treat everyone with mutual respect. Students need not always raise their hands in order to ask questions or to make comments, but they should not interrupt the instructor or fellow students in doing so. Students typically find the atmosphere set by the instructor to be a sometimes playful and nearly always relaxed one, but students will still need to work hard and consistently both in and out of class in order to do well. If at anytime you have thoughts, comments, or suggestions about how the class atmosphere could be improved or made into one which is more supportive of your learning, please come by or drop me a note about it. I welcome such suggestions.

The teaching assistant for this course will be assigned later. She or he and most of the other Math Lab Consultants will also be able to answer questions about the mathematical content in the course during consultations in the Math Lab. The Math Lab is open each Sunday from 6:00 to 7:45 PM and each Monday through Thursday 7:00 to 9:15 PM (except on evenings of convocations when it closes early). Students are strongly encouraged to make use of the help available in the Math Lab, as well as in the instructor's office hours. Best results are obtained trying to solve problems alone or in a group before asking for help, so in either place, students should be prepared to show what they have already tried. Topics in this course build throughout the course, so students should be sure to do their best to keep up with the class, so as to not get behind and possibly forever lost. Remember, no question to which one does not know the answer is ever "dumb" unless it goes unanswered because it remained unasked.