CSIT 241 Discrete Math I Spring 2007
Tentative Syllabus and Course Policies
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Instructor: Dr. Iyad Abu-Jeib
Office: 109 Fenton Hall
Office Phone: 673-4757
Office Hours: MWF 4:00-5:00 PM, R 12:00-1:00 pm, F 5:00-6:00 PM or by appointment.
E-mail: abu-jeib@cs.fredonia.edu
Website: http://www.cs.fredonia.edu/abu-jeib
Meeting Times:
MWF 11:00 - 11:50 Fenton 175.
R 11:00 - 11:50 Fenton 174.
Textbook:
Discrete Mathematics with Graph Theory", 3rd edition, by Edgar G. Goodaire and Michael M. Parmenter, 2006, Prentice Hall. ISBN: 0-13-167995-3In addition to the material in the textbook, there will be material covered from other sources. References:1) Discrete Mathematics for Computer Science, by H. Joseph Straight, available through the campus bookstore on an installment basis.
2) Discrete Math Workbook by James Bush (will be on reserve in the library).
Prerequisites: MATH 121/123 and CSIT 121.
Note: Credit will not be given for both CSIT 241 and MATH 210.
Grading:
1. Two hour exams and a comprehensive final. Each hour exam will consist 15% of your course grade. The final will consist 25% of the course grade.
2. Assignments. The assignments will consist 15% of your course grade.
3. Quizzes. The quizzes will consist 20% of the course grade.
4. Attendance and participation. Attendance and participation will consist 10% of the course grade. Here is the attendance policy:
a) You'll be allowed to miss at most 3 classes with no documented acceptable excuse (email is not considered as such).
b) Any class you miss after the first 3 classes described above will result in deducting 2% of your course grade. This applies until the 10% portion of the course grade assigned for attendance is consumed. Attendance may be taken randomly (may be 8 random classes).
c) If the student does not have satisfactory attendance, the student may not be notified, but I'll take a note of that and keep it in my records until I assign the course grades at the end of the semester.
d) You must be on time. You must not leave before the class ends. Repeated late arrival or early departure may be considered as absence.
e) Excusable absence must be documented and must be inline with the college's policy about that. You must inform me in advance if you intend to miss class for a legitimate reason. Legitimate reasons are reasons such as death in the family (with a proof) and illness (with a doctor's report). Absences for family gatherings or family problems or to catch a flight or because of another course, etc, are not considered excusable absences.
Remark: There is a possibility that I may not include attendance in the course grade for those who don’t want to count attendance. If that is the case, the 10% portion of the course grade that is assigned for attendance and participation will go for the final exam.
Attendance: Attendance is required (see above). You are responsible for material presented in class and for announcements announced in class. If you miss a class, it’s your responsibility to ask about the material covered in the class you missed and about the announcements announced that day. Make ups of exams/quizzes/worksheets are allowed only if you have a documented hardship. Late assignments won’t be accepted. Any measure to improve your grades (like extra-credit, extra points, and dropping a quiz/assignment (if happened)) may apply only to students who have satisfactory attendance.
Note: What’s stated above does not mean that I’ll give you extra-credit work or extra points or drop a quiz/assignment. I may do one of them or more of them or none.
Incomplete: Incomplete grade will be given only if you meet the university guidelines for incomplete.
Grading Scale: 92-100: A, 90-91: A-, 88-89: B+, 82-87: B, 80-81: B-, 78-79: C+, 72-77: C, 70-71: C-, 68-69: D+, 62-67: D, 60-61: D-, < 60: F.
Behavior: Inappropriate behavior will not be tolerated and severe consequences may follow. Any behavior that may result in disturbing the class, students, or the professor, is considered inappropriate behavior.
Academic Integrity (Fraud, Plagiarism, Cheating, Collusion): The consequences of any violation of academic integrity may include (but not limited to): a formal warning, a grade of zero assigned to that particular work (quiz, assignment, exam, project, etc), a failing grade in the course.
Final Exam: The final exam is accumulative. It will be Thursday, May 10, 1:30 PM – 3:30 PM.
Remarks:
1) This course is not CCC, but it’s required for CS majors.
2) I may assign extra work to do for bonus points or do something else to improve your grades. Such work (if assigned) will be optional.
3) If you need help, please do not hesitate to ask for it. My job is to help you understand the material and succeed. I’ll be extremely happy to answer your questions and to assist you.
4) If you have a hardship, please let me know in advance.
5) I’ll be extremely happy to get a feedback from you about my teaching style and the level of difficulty of the exams and the assignments. We have to work together to make improvements if such improvements are needed. You can provide me with feedback directly or indirectly (by leaving a note underneath my office door or using the teaching feedback form on my website).
6) You must do your assignments by yourself. Do NOT work in pairs or in groups unless I ask you to.
7) I may cover material not available in the textbook. You are responsible for such material and for everything I mention in class.
8) I may not grade all the assignments and I may not grade all the questions/parts in the assignment I decide to grade.
9) Check your Fredonia email daily. I may contact you any day by email.
10) The syllabus is subject to change.
11) Bring your Fredonia ID to the exams and the quizzes.
12) The grading scale is subject to be made more flexible if that’s needed to improve the grades.
13) Keep all of your graded assignments, quizzes, exams, and all other graded stuff.
14) At some point of time, I’ll give you usernames and passwords to access your grades and other stuff. You’ll be able to change the password, but if you're taking two classes with me, make sure that each class has a different password.
15) Sometimes I repeat questions. Repeated mistakes result in harsher grading.
16) Here's how (unless I tell you something else) my makeup work is done (of course provided there is an acceptable documented excuse): If a student misses a quiz, the next quiz will be doubled (counted twice) and if a student misses a test, the next one will be doubled (i.e. counted twice). That does not apply, of course, to the final.
17) Always use only the notation used in class. Using a different notation may result in no credit or partial credit.
18) Always spread out when a quiz/test is given.
19) Never give two answers for the same question. If you do that, you'll get no credit.
20) On tests, quizzes, homework, always cross out unwanted writing.
21) An extra credit quiz may be given (may be without advanced notice) within a week of a quiz/test/homework. There will be no make up for such a quiz. Such quizzes will be given only when necessary.
22) I may make random photocopies of some random graded quizzes/homework/exams.
23) For “identify the error” questions, identifying non-errors as errors would result in deduction of points.
24) Suppose that I asked you to find all solutions of an equation and suppose the equation has two solutions. If you write down three solutions and two of them are the correct ones, you will not get a full credit and if you write down more than 3 solutions and two of them are the correct ones, you may get no points at all. A similar thing can be said about "find the error" questions.
25) One of the goals of discrete math (this is in addition to the fact that it's needed for other courses) is to offer students experience in mathematical thinking, problem solving, logic and reasoning.
26) If you make a mistake in "determine whether the following is true or false" in the truth value of one of the statements but that has no effect on the truth value of the whole compound statement, I may not deduct points. But, if you make a mistake in the truth value of a statement that changes the truth value of the whole compound statement, I may give you no points at all even if your answer is correct. For example, suppose the compound statement is true and it's of the form (F -> F) but someone ended up having (T -> F) and said the compound statement is true, then I give no points, because (T -> F) is a false statement.
27) I may ask each student to answer a question or more every class.
28) If a class was cancelled for an unexpected reason and a test/quiz/assignment/homework was scheduled or due that day, it will be held/due next meeting time.
Objectives:
The material covered in this course is needed for other computer science classes (e.g. data structures, algorithms, etc). The course offers a mathematical background needed for computer science.
Topics (not necessarily in order and not necessarily from the textbook):
Logic, sets, proof techniques, matrices, basic number theory, modular arithmetic, functions, linear transformations, relations, basic combinatorics, and possibly other topics (not necessarily from the textbook). In detail, the topics are:
1. Logical connectives (operators) and logical equivalence.
2. Existential quantifiers, universal quantifiers, and negation.
3. Proof techniques including direct proof, proof by cases, proof by contrapositive, proof by contradiction, proof of "if and only if", proof of "the following are equivalent", proof of statements of the form "there exist(s) ... ", proof by induction (weak form and strong form), etc.
4. Resolution proofs.
5. Sets and their theorems; mutually (pairwise) disjoint sets, partitions.
6. Operations on sets including power set, Cartesian product, difference, symmetric difference, intersection, and union; notation used for a finite union of sets and for a finite product of sets; product of sets in the plane R2 and the space R3.
7. Venn Diagrams.
8. The Principle of Well-Ordering.
9. Composite and prime numbers.
10. Factoring a number as a product of primes.
11. Canonical form.
12. Fundamental Theorem of Arithmetic.
13. Quotients, remainders, and their theorems.
16. The greatest common divisor.
17. The least common multiple.
18. Writing the greatest common divisor as a linear combination of the two numbers.
19. Integers modulo n; Zn; addition and multiplication in Zn; exponents in Zn.
20. Finding the additive and multiplicative (reciprocal) inverse in Zn.
21. Solving congruence equations.
22. Congruence linear systems (if time permits).
23. Binary relations; reflexive, symmetric, anstisymmetric, transitive, equivalence, and partial orders.
24. Equivalence classes, representation of binary relations as digraphs.
25. Composition of binary relations, inverse of a binary relation.
26. Total orders, minimum, minimal, maximum, maximal, Hasse diagrams. (Asymmetric and circular binary relations are not covered.)
27. Relations and Functions, cardinality, countable and uncountable sets.
28. Matrices and vectors: special types of matrices such as the zero matrix, the identity matrix, diagonal matrices, lower-triangular matrices, upper-triangular matrices.
29. Operations on matrices: addition, subtraction, and scalar multiplication.
30. Operations on vectors: addition, subtraction, scalar multiplication, and dot (inner) product.
31. Multiplication of matrices; properties of addition and multiplication of matrices; definition of inverse and inverse of 2 x 2 matrices.
32. Transpose, powers of matrices, properties of powers and transpose, symmetric matrices, skew-symmetric matrices, orthogonal matrices.
33. Elementary row operations, row-equivalent matrices, elementary matrices, row-echelon form, reduced row echelon form, Gaussian elimination, Gauss-Jordan elimination, finding the determinant by using Gaussian elimination or Gauss-Jordan elimination, finding the inverse by using Gauss-Jordan elimination, homogeneous systems and non-homogeneous systems.
34. Linear transformations, kernel, range, the matrix of a linear transformation, etc.
35. Combinatorics, multiplication principle, addition principle, permutations, combinations, r-permutations, r-combinations, generalized combinations and permutations.
36. The pigeonhole principle (all forms).
37. Derangements (exactly/at least/at most k in their original positions, recursive formulas for Dn).
38. The binomial theorem.
39. Other topics if time permits.