GRADE COMPUTATION Go to Grading.
QUIZZES
Homework is not collected, but a QUIZ is scheduled at the very beginning of nearly every class, and the problem(s) will come from the topic most recently introduced. The date given is the date the topic was introduced, NOT the date of the quiz. Plan time to ask me questions between classes.
Ask me for help before it's too late. Free tutoring may be available, starting about two weeks into a fall or spring semester, and ending before final exams. If you study with someone else, be sure both of you are learning. You are expected neither to give nor to receive help (except from me) on a paper submitted for a grade.
ATTENDANCE POLICY
Missing class will usually make it harder for you to learn the subject, and you will usually miss a quiz in the process. The only makeup quizzes will be those already scheduled during class periods. You are responsible for information missed because of absence. But absence will not necessarily have a direct effect on your grade. You are expected to arrange your other classes, studying for tests, employment, and appointments with physicians or advisors at times which do NOT conflict with meetings of this class.
Makeup quizzes are not given outside class, nor on the specific
topic you miss when you are absent. But only your best quiz scores count,
so you have some extra grades to replace missing quizzes. Please do not
ask for additional makeup quizzes! Remember: if you miss class,
you will find it harder to keep up.
Schedule conflict is not an excuse: arrange your appointments so as
not to conflict with class! Other instructors are not permitted to
schedule tests or final exams that conflict with this scheduled class.
If this happens to you, I will gladly discuss the matter with the other
instructor.
Special arrangements can sometimes be made for the final exam
if you talk to me early enough.
Illness the day of a test is an excuse for missing a test (not
a quiz); talk to me about arranging a makeup test (not quiz). Once
you have seen the test, I will not allow you to take a makeup.
Makeup tests may be arranged in case of an emergency, but you
must convince me that the cause of your missing the scheduled time was
a serious matter. If you know of a problem beforehand, please discuss
it with me then. If you miss a test shortly before or shortly after a scheduled
vacation, you must document your activities by letters from physicians
or court officials. If you just extend your vacation, you will not be permitted
to make up the test.
COURSE OBJECTIVES
This is a basic course for mathematics majors, and students are expected
to learn:
(1) what a mathematical proof is
(2) how to do a mathematical proof
(3) how definitions are used in proof
(4) how to find a counterexample
(5) how to do a proof by induction
(6) how to read and learn from a textbook
For your future success in mathematics, these six points are more important
to learn than the subject matter of discrete mathematics, which includes
sets, relations, functions, and methods of counting.
I will spend some time in class introducing new ideas. But I expect
you to read portions of the book to learn new material. Prepare for
class. If you can't understand something, take the following steps:
(a) Make sure you understand the statement or question that gives trouble.
Check the definitions of words. (Sometimes the index of a textbook
will help you find the definitions.)
(b) If you still can't understand, ask me. You may visit me in
office hours or take a chance that I'll be there some other time.
Consider calling my office telephone, either to make sure I'm there, or
to ask me a question over the telephone.
(c) It's also good to ask questions in class, but that might not be
soon enough to complete your homework or prepare for a class activity.
PROOF
The most important thing you can learn is how to write a mathematical proof. A single example is not a proof. The example must be so general that it includes all possible cases. Or perhaps the possible cases can be grouped in two or three categories; then if you can prove the theorem for each category, you have a proof. However, a single counterexample is enough to DISprove a statement. Pay close attention to the discussion of proof in the following pages.
WRITING A SOLUTION
Even the solution to a problem which does not require proof will be judged by its logic, clarity, and completeness, as well as the correctness of its conclusion. Please follow these directions.
Summarize the relevant information in the problem using conventional
symbols; explain unconventional symbols. Draw a table, sketch, or
graph if appropriate, placing relevant symbols in their proper places.
Place the steps on the paper in a reasonable order. State the final
result or conclusion, using words and previously defined symbols in appropriate
combination.
-----------------------
Writing the solution to a problem in mathematics is a valuable skill which must be learned. Your solutions to graded problems will be judged by their logic, clarity, and completeness, as well as the correctness of their conclusion. Please follow these directions.
Summarize the relevant information in the problem using conventional symbols; explain any unconventional symbols. Draw a table, sketch, or graph if appropriate, placing relevant symbols in their proper places. Place the steps on the paper in a reasonable order. State the final result or conclusion, using words and previously defined symbols in appropriate combinations. Use at least three significant figures in calculation, provided the data are accurate enough.
FORBIDDEN FORMS
Even if a solution is otherwise correct, the following mistakes may
result in a partial loss of credit:
= Using an "equals" sign between expressions that are not equal, such
as 2.5 = .4938 or x = 2x
= Confusing variables with functions: y=y(x)
CALCULATORS / COMPUTERS
You may use a scientific calculator whenever you wish, for homework, tests/final, and class discussions. the yx key may be useful, but we will not use trigonometric functions. Computer programming is encouraged in homework, but not on tests/final.
Don't get too many special features, because you won't use them in this course and they may confuse you. The following features cause trouble, but it is very hard to avoid all of them:
(1) MODE. This allows changing the display, but if you operate it accidentally,
you may be unable to read the display.
To reset the
calculator for normal operation, try pressing these keys: MODE, 9
To reset the
calculator for 3 decimal places, try pressing these keys: MODE, 7, 3
(2) SCIENTIFIC NOTATION. If you square 0.03, the answer 0.0009 may
be written 9.00x10-4, meaning 9.00 with
the decimal point moved 4 places to the left. But your calculator may express
it as 1.00 - 4, which may at first appear to be a mistake. A proper
use of the MODE feature can prevent this accident, but some calculators
are not so quick to switch to scientific notation.
SKILLS NECESSARY TO BEGIN DISCRETE MATHEMATICS
Students in MATH 210 are expected to be proficient in proving trigonometric identities.
But even if you are well prepared to begin, you will have to prepare each new assignment faithfully, if you want to succeed in calculus. Every time you get behind, it is hard to catch up.
CLASSROOM PHILOSOPHY AND DECORUM
I would like this class to discuss mathematics informally. Try to get to know other students, and look for ways to contribute to the discussion of problems. But when the class meets together, please avoid private discussions; they interfere with the class discussion.
Class discussion is comfortable only if participants show respect for each other. This means speaking kindly, taking others' ideas seriously, and assuming they speak with good will. We are evaluating other people's solutions, but we are not evaluating the people.
TEST REVIEW AND EXTRA CREDIT Go to Test Topics
There will be review classes partly devoted to extra credit presentations by students. In some of these reviews, you may receive extra credit for discussing a problem as described BELOW. Each time, you can earn extra points to be added to your total grade. You are limited to one extra cedit per review, and there may not be time enough for all interested students on the later tests, so consider doing some extra credit for the first or second test.
The first step is to CHOOSE A TOPIC from the review list. You may make up your own problem or choose one from the list provided, but let me approve your choice, so that two people don't do the same problem. Use problems like homework problems (on the topics of the test), but not homework problems already assigned. It is your responsibility to avoid homework problems, or you will lose all credit. I will suggest some problems.
Put your sorting number at the upper right corner of the solution you give me, and put your name at the top center. It is not necessary to state the problem on your solution sheet, but do indicate the section, page, and problem number. When you have worked out your problem on an ordinary sheet of paper, make (and pay for) enough "Xerox" copies for the class, and bring them to me at the review class.
To receive credit, you must be present at the review session to discuss
your problem. Don't read the solution to the class, but point out
the salient features of the problem. What was hard for you about
the problem? What approaches helped you solve it? What principles
and techniques does it use?