Math 3200 Fall 2008
(Scroll down for occasional supplementary notes)
General course description:
Syllabus for Math 3200:
Introduction to higher mathematics, fall 2008.
Instructor: Professor Roy Smith; office 448 Boyd. phone 706-542-2595,
office hours MWF: 11:10am -
12:10pm or appt.
email: roy@math.uga.edu, and rcsmith97@comcast.net
Prerequisites: a passing grade in an integral calculus course, eg. 2260.
The general objectives of the course are to learn to read and understand mathematical statements and proofs, and to discover and write up correct, clear mathematical statements and proofs. Topics include logic, integers, polynomials, induction, sets, relations, functions, congruences.
Text: An Introduction to mathematical thinking, by William J. Gilbert and Scott A. Vanstone. There is graded homework, 3 or 4 tests and one final exam, all required.
Tests: #1: 9/15/2008; #2: 10/13/2008; #3: 11/21/2008. dates subject to change.
Final exam: 8am -11am, wed., dec 17. (please check this on the web.)
The final will not be moved, so be sure you have no conflicts with our final.
Attendance is required; repeated absences may result in being withdrawn. Problems will be explained at the board by all class members. There are no make-up tests. You are expected to do your own work on all homework, tests and exams. Working together or ÒbrainstormingÓ with others on homework problems is good up to a point, but you must write up your own work independently. Be sure you work out and write up on your own everything you hand in, since on tests and at the board you are always on your own.
Advice: do not seek help or hints on homework until you have thought hard by yourself first, to gain practice in finding solutions. Notes, books, and calculators are not allowed on tests. Read the University policy on academic honesty [available on the web].
GRADING FORMULA: Your grade will not be lower than that given by the formula: 15% HW & quizzes + 60% Test Average + 25% FINAL EXAM.
Letter grades:
0-59F, 60-69D, 70-72C-, 73-76C, 77-79C+, 80-82B-, 83-86B, 87-89B+, 90-92A-, 93-100A.
NOTE: This syllabus provides a general plan for the course; deviations may be necessary.
GENERAL
EXPECTATIONS AND ADVICE for MATH 3200:
1) LEARN THE BASIC
INFORMATION THOROUGHLY.
Study book and
lectures until you know and understand all definitions, theorems, formulas and
procedures. This involves
memorizing and understanding. Know
the definition of prime integer; greatest (or universal) common divisor;
relatively prime integers; negation, converse and contrapositive of a
statement; statement of well ordering principle, prime and relatively prime
divisibility properties; existence and uniqueness of prime factorization for
integers; rational root theorem; division algorithm; etc... with perfect accuracy. Then explain what each of these things
means. Read the book, attend all
classes, and review lecture notes daily.
2) PRACTICE LOGICAL
REASONING.
One benefit of a
mathematics course is learning to make convincing arguments. Know and be able to explain why the
procedures work, and to use ideas from the course to solve problems we have not
treated in the lectures. Learn to
make a clear statement and to prove or disprove it. Practice understanding my proofs and the bookÕs, and attempt
as many proof problems as possible.
Practice using the methods we have emphasized in new situations.
3) DEVELOP
COMPUTATIONAL POWER.
Learn to solve
problems and to make detailed and accurate calculations. This can only be done by working large
numbers of problems, not just the few that are assigned. I will frequently choose problems from
the book, or similar ones, to put on tests. Study the worked out examples, attempting them yourself
first. Know how to carry out the
Euclidean algorithm to find gcd's, and be able to solve linear equations in
integers.
4) ASK QUESTIONS. Get
troublesome points explained well before the test. (I am not available for help on the day of a test.) If you
cannot meet office hours, email me at both addresses. I will test
understanding, not just your ability to repeat things from the board. You must be able to state general
principles correctly, apply them to old and new situations, and write up your
solutions in understandable, complete form. Keep up, and study for the final, since people who do not do
well earlier, or who do not restudy for the final, do not do well on the
final.
Remember: Practice working problems, reading and writing proofs, attend class & review notes, ask questions.
Supplementary notes:
notes on induction and binomial theorem:
notes on greatest common divisors: