You may wish to bookmark the
course website: http://math.hws.edu/~mitchell/Math100S06/index.html where
I will post most of the course documents.
About Math 100
Historically, mathematics
has been recognized as one of the most important disciplines.
This is especially true today
for true anyone contemplating a career in the natural sciences, most of the social sciences, especially
economics, and also architecture.
Although students are repeatedly told that mathematics is important,
sadly, most mathematics instruction fails to communicate exactly why this
is the case.
Calculus is the study of functions, their rates of change and their rates of accumulation.
"Precalculus" refers to a body of mathematics that must be mastered in order for you to be
prepared for calculus. The content of the course can vary but the goal is always the same:
Obtain a familiarity with the language of functions. Beyond being familiar with what a function is,
there are a number of basic types of functions that are most often encountered.
So a thorough understanding of functions includes being familiar with particular
types of functions such as: linear functions, polynomials, rational, exponential,
logarithmic, and trigonometric functions. In short, you should leave this course with a basic toolkit
of functions. One of the most powerful methods for understanding functions is to examine
their graphs. This is a theme that continues through differential calculus.
The study of functions is important for two reasons.
First, functions, together with sets, form the basic core
of all mathematics. Second and perhaps more important, functions
constitute the basic mathematical building blocks
for describing quantifiable relations
in the world (both real and "virtual"). Functions provide the basic language for
expressing connections between quantities, deducing consequences,
and making predictions. As such, they are
an indispensable tool in the
investigation of all kinds of scientific questions.
Our text provides an introduction to this
real-world context for the study of functions.
Over the course of the term I hope you begin to
appreciate the power and applicability of functions.
Goals and Outcomes
For several majors in the natural and social sciences one or two terms of calculus are
required.
In order to be successful in calculus, one needs to be proficient with the basic language and grammar of a certain
portion of mathematics. In particular, a calculus student needs to be familiar with the
algebra and geometry of functions.
The objective of this course is for you to gain familiarity
with and display the algebraic and analytic mathematical
skills required for success in calculus. The content of this course is
highly specific and the course is intended only for those who intend to continue on to calculus.
There are several goals for the Math 100 including
- displaying a facility with algebraic manipulation of elementary functions and equations;
- gaining an ability to translate an equation of an elementary function into a graph;
- displaying an ability to translate a verbal description into one or more mathematical models (or equation);
- displaying a facility with the relation between trigonometric functions and circles;
- understanding the relation between a function and its inverse (including when such inverses exist);
- developing a "toolkit" of functions including linear, polynomial, rational, trig, inverse trig, logarithmic,
and exponential functions.
Prerequisites and a Caution
This course is intended only for students preparing for calculus.
If you are looking to satisfy the Colleges' quantitative reasoning goal,
or you simply wish to do another mathematics course, this course is inappropriate.
There are better alternatives that I will gladly discuss with you.
We will briefly review material on fractions, exponents, and factoring, but I
assume that this material is truly a review. If you do not have these basic algebra
skills (as indicated by a score of at least 10 on the Mathematics Placement Test),
then this course is likely to be very difficult for you. Again, you can discuss alternatives with me, but do so immediately.
In short, my assumption is that you will all be taking calculus next term. If you do not intend to take calculus,
this course is inappropriate for you and you should see me immediately.
Thus, I assume that you are motivated to work hard to gain the skills that will make you successful in
calculus. In other words, I expect that you will be willing to do a lot of practice.
Text and Other Materials
Our text will be
Precalculus: Sixth Edition by Larson and Hostetler. You may wish to purchase a scientific calculator for
use in this class. Graphing calculators will not be allowed for tests. In addition, I encourage you to purchase a three-ring binder
as I will be passing out material nearly every class. A binder will help you keep your work organized. I also encourage you
to do all your work in
pencil.
Every Tuesday our section will meet for a problem-solving laboratory.
Attendance
is required. These labs are an excellent time for you to ask questions about the
course material. Bring your text, notes, and calculators.
Some of the questions will require written answers that go
beyond simply solving equations and doing routine problems.
Most students find lab sessions very helpful.
Homework
Becoming proficient in mathematics is like becoming proficient in playing a sport
or an instrument: (1) lots of practice is necessary and (2) it helps if you have a
positive attitude. To help you practice, each day I will assign reading and homework
problems.
Written assignments are due at the beginning of
the next class; no late homework will be accepted. Because I will want to give you relatively
immediate feedback, I may sometimes grade only a randomly chosen subset of the assigned problems. I will post the
answers to all questions by my office door once the problems have been collected. You are encouraged to stop by and
review these answers and come in for help as needed.
If some extraordinary circumstance
arises and you cannot make it to class, it is still your responsibility to make sure
that your homework does get to class. See the section on
Academic Integrity below regarding
assistance on homework.
There will be an exam every Friday on all the material that we have covered up to the preceding class on Wednesday.
Note the word "all;" the tests will be cumulative. The tests will be rather short at the beginning of the term but
will get longer as the term progresses and we have covered more material. All exams are closed-book, closed-notes. For some
exams I may permit you to use a scientific calculator but not a graphing calculator.
Graded homework (see above) will count for 20% of your final grade.
The final exam also counts for 20%.
The remaining 60% will come from weekly exams. Note: I will drop your lowest weekly exam grade.
It is impossible to construct fair makeup exams
in mathematics. For your own protection, my policy is that there are
no makeup examinations.
If for some extraordinary reason you find you are unable to take an exam,
let me know as soon as possible, certainly well before the exam is administered.
I also reserve the right to take class participation and attendance (see below) into
account in determining final grades.
Academic Integrity
I encourage you to
discuss course material with your classmates or consult with the Math Intern, Derrick
Moore (in Lansing 310), or me. However,
graded homework assignments must be your own work. While you may not copy work from a classmate,
do feel free to get help on homework from the intern or me.
Verbalizing your questions, explaining your mathematical
ideas to me or the intern will increase your understanding. Remember, to take advantage of this extra help, especially
from the Math Intern who is available many evenings. However, the work you hand in must be your own;
copying from a classmate, a solutions manual, or any other source is a violation of academic integrity.
Because of the nature of this course, its assignments,
and its assessment, your
attendance and participation is crucial.
Mathematics is learned by regular, sustained, attentive effort over an extended period.
Only when such effort has been invested will the concentrated study for an exam have
any benefit. Therefore,
attendance at class is required. Unexcused absences may adversely affect
your grade; certainly
more than three absences will lower your grade.
| Classes or Labs Missed |
Effect on Grade |
| None |
+1.5 |
| 1 |
+1.0 |
| 2 |
+0.5 |
| 3 |
0.0 |
| 4 |
-3 |
| 5 |
-7 |
| 6 |
-12 |
| 7 or more |
Automatic Failure |
If you must miss a class for some reason beyond your control,
talk to me about it in advance.
Please help me out the first week or two of class by reminding me of
your name when you ask a question in class or lab. It will help me (and
your classmates) to learn your names more quickly.
Finally, common courtesy demands that you be on time for class and that
you do not leave the room during class (unless you are ill). This will help you, your
classmates, and me to give our full attention to the course.
Math Intern
Remember that the Math Intern, Derrick Moore, is available in Lansing 310 for extra
help during the day and the evenings. His office hours
are listed at the beginning of this document. Please utilize this extra resource.
Here are a few simple things that you can do to be more successful in the course.
- Come to all classes.
- Take good notes. If I write something on the board, you should be writing it in your notes.
- Do the readings and practice problems carefully.
- Keep the answers to problems and notes on the readings in a journal.
- Review the notes from the last class before coming to class again. In fact,
I suggest recopying the notes! This makes studying for a test easy.
- Come in for help whenever you need it, preferably before you get too far behind.
- Visit the Math Intern for help in the evenings.
- Review some of the previous lab questions once a week.
- Ask questions in class. Ask questions about the homework and readings.
This assumes a fairly rapid pace through the listed materials. We may need
to adjust this schedule based on our actual work in class.
- January 16-27: Brief Algebra Review: Exponents, Radicals, Factoring, Absolute Value, Solving Equations.
Appendices A.1-A.6.
- January 30-February 3: Graphs of Equations, Lines, and Functions.
Chapter 1.1-1.3.
- February 6-10: Analyzing Graphs, a Toolkit of Functions. Chapter 1.4-1.6
- February 6-10: Creating New Functions: Chapter 1.6-1.7.
- February 13-17: Inverse Functions, Quadratic Functions. Chapter 1.8-2.1.
- February 20-24: Polynomials. Chapter 2.2-2.3.
- February 27-March 3: Rational Functions and Partial Fractions. Chapter 2.6-2.7.
- March 6-8: Exponential Functions: Chapter 3.1.
- Wednesday, March 8: Test Today?
- March 20-24: Exponential and Logarithmic Functions. Chapter 3.1-3.2.
- March 27-31: Solving Equations with Logs and Exponentials. Chapter 3.3-3.4.
- April 3-7: Radian Measure, Trig Functions using the Unit Circle. Chapter 4.1-4.2.
- April 10-14: Graphs of Trig Functions. Chapter 4.5-4.6
- April 17-21: Inverse Trig Functions, Trig Identities. Chapter 4.7, 5.1.
- April 24-28: More Work with Trig Identities: Chapter 5.1-5.3.
- May 1-2: Review.
- Final Exam Sunday May 7, 2006 at 11:00 AM.