MATH 135 – DISCRETE MATHEMATICS
Spring 2006
Instructor: Dr. George Bradley
Office: 420 College Hall
Phone: 396-5115 (office) 396-6467 (department office)
Office Hours: Monday and Wednesday, 1:00-2:30
Tuesday and Thursday, 1:30-2:30
Appoints may also be available before noon or after 4:20 Mon-Thurs, and sometimes on Fridays.
Email: ,
Text: Rosen, Discrete Mathematics and its Applications, (5th edition).
Major Topics: Logic, sets and set operations, functions, algorithms and their complexity, matrices, methods of proof, mathematical induction, counting arguments, permutations and combinations, probability, relations, graphs.
Goals of the Course:
· To know what a proposition is and the rearrangements and truth values of them.
· To understand the connectives of propositions and construction of truth tables.
· To be able to work with quanitifiers
· To understand the basics of logic.
· To be able to make truth tables.
· To be able to do direct proofs, indirect proofs, and proofs by contradiction.
· To be able to do induction proofs.
· To understand basic set theory concepts such as union, intersection, complement, and Cartesian product.
· To be able to determine if a given relation is a function, and if so, find the domain, range, and determine if the function is one-to-one, onto, or neither.
· To find algorithms and determine their complexity.
· To be able to use the division algorithm, find lcm and gcd of two numbers, and use the Euclidean algorithm.
· To do calculations involving matrices of real numbers and also Boolean matrices.
· Be able to count the number of elements in a set using the Multiplication Principle, permutations, and combinations.
· To understand the Pigeonhole Principle.
· To find the probabilities of discrete events.
· To understand the differences between a function and a relation.
· To be understand the properties of relations, especially equivalence relations.
How you will be evaluated: There will be three hourly in-class exams and a comprehensive final exam. Each hourly exam will be worth 100 points and the final exam will be worth 160 points. In addition, you will have nine 20-point quizzes. Quizzes may be in class, take home or a combination thereof. Only the top seven quizzes will be counted, so the total number of points you can earn from quizzes is 140. Since the total number of possible points for the semester is 600, I will divide the total number of points you earn by 6. Grades will be assigned according to the following scale:
90-100 A
80- 89 B
70- 79 C
60- 69 D
0- 59 F
Plus/minus grades will be used only in borderline cases (89-91, etc.).
Tentative exam dates are February 8, March 15, and April 12. Make-up tests will not generally be given. Anyone missing a test and not having a legitimate, verifiable excuse will be given a zero for that test. Please notify me in advance if you know you will have to miss a test.
The final exam will be given on Tuesday, May 2, at 11 AM. Everyone must take the exam at this time.
In class quizzes will generally be given on Wednesdays. No make-up in class quizzes will be given, and no late quizzes will be accepted.
Cheating on an exam or quiz will not be tolerated and could result in failing the class.
Attendance: I will not take attendance, but you will find it much easier to learn the material from class lectures and discussion than by simply reading the textbook.
Homework: Homework problems will be assigned every class period. These assignments will not be collected, but I will spend time at the beginning of each class answering questions you have. If all of your questions are not answered in class, please come and see me during office hours or make an appointment.
Try not to get behind-it's difficult to catch up and you won't know what's going on in class.
I hope the semester goes well for all of you in this class and your other classes. Please see me if you have any problems, because I am here to help.