CSCI 1323 - Discrete Structures

Spring 2008

MWF 10:30-11:20am , 227 HAS

Professor: Yu Zhang office: 201H HAS phone: 999-7399 email: yzhang@cs.trinity.edu Office hours: MWF 11:30am-1:30pm or by appointment
Help session hours: W 4:30-6:30pm, 228 HAS
TA: Phillip Coleman Phillip.Coleman@Trinity.edu

Course Pre-requisites

None.

Textbook

Judith L. Gersting, Mathematical Structures for Computer Science. Freeman Publishing, sixth edition, 2006.

Course URL

http://www.cs.trinity.edu/~yzhang/teaching/spring2008/CSCI1323.

Goals of This Course

  1. Formal Logic—Propositional and Predicate Formulas and Logic
  2. Proofs—Formal Reasoning, Proof Methods, Induction, Recursion and Recurrences
  3. Sets and Combinatorics—Set Theory, Counting, Inclusion/Exclusion,
  4. Permutations, Combinations, Binomial Theorem
  5. Relations and Functions—Terminology, Properties, Examples, Cardinality
  6. Graphs and Trees—Terminology and Applications

At the end of this course you should

  1. Be able to learn basic mathematical concepts such as sets, relations, functions, and graphs, relationships between them, and their properties,
  2. Be able to learn to reason correctly,
  3. Be able to learn techniques for solving problems,
  4. Be able to become proficient in using mathematical notations (both in reading and writing).

Email and WWW

We will be using an email list this semester to communicate pertinent messages to everyone in the class. I will put together the list of email addresses in the first two weeks of class. It is the student's responsbility to ensure that they watch for and read any messages throughout the semester. In addition, this web page will continually be updated with the class schedule, resources, and other information.

Late Turn-in Policy

The penalty for late assignments will be -10% per day (determined on a 24-hour basis relative the due-time, which is the start of class ), down to a minimum of 50% (you can still get 1/2 credit if you turn it in by the end of the semester).

Exams and Grading

There will be about 7 homeowrk assignments, and several quizzes which will be given randomly in class.
There will be one mid-term exam (approximately in the middle week of March) plus a comprehensive final.

Grades will be determined by the percentage of total points earned during the course of the semester. The total points will be computed according to the following approximate weighting scheme, though it is subject to slight adjustment as appropriate:

Homework Assignments 30%
Midterm exam 20%
Final exam 30%
Quiz 20%

Grade Curving

The top 30% of students will get an A.
The next 15% will get a A- or B+.
The next 35% will get a B or B-.
The next 15% will get a C+ or C.
If you are in the lowest 5%, you will probably end up with a D+,D or F.

Attendance Policy

Lecture attendance is encouraged, but will not be used for grades. Unavoidable absences are understood, but each student is responsible for any missed material. For excused absences, an opportunity will be provided to make up any graded work that was missed. For unexcused absences, a grade of zero will be assigned for in-class assignment. Missed exams will be rescheduled without penalty for an excused absence, or with a 25% penalty if the absence is not excused. If you are going to be absent when an assignment is due you should try to turn in the assignment early. If that is not possible, be sure to include a request for an extended turn-in time in your e-mail.

To request approval of an absence or late turn-in, send me an e-mail explaining the reason prior to the class or due date. Tell me if you believe it is a university excused absence. If advance notification is not possible (e.g. unexpected illness) send the e-mail within 48 hours of the absence and be sure to explain why you were not able to notify me in advance. For illness, follow-up the e-mail by submitting a note from a doctor or clinic to my office.

Miscellaneous Notes

All students are covered by Academic Honor Code. Do not copy anybody else's homework assignments or source code, or even give the appearance of having shared work. You are welcome to talk with each other about problems and solutions unless otherwise specified, but do not turn in syntactically similar work. Cheating will be dealt with according to the university's policies on academic integrity.

If you have a documented disability and will need accomodations in this class, please speak with me privately early in the semester so I may be prepared to meet your needs. If you have not already registered with Disability Services for Students, contact the office at 999-7411. You must be registered with DSS before I can provide accommodations.


Tentative Schedule

The following is a planning schedule. It may be modified as necessary during the course. Students will be expected to have some familiarity with the material in the schedule at the beginning of the lecture.

week of topic Gersting
1/13 Introduction to Problem Solving MethodsCh 2.1
1/20 LogicsCh 1
1/27 Logics Ch 1
2/3 Mathmatical Induction Ch 2.2
2/10 Counting Ch 3.2
2/17 Permutations and Combinations Ch 3.4
2/24 Binomial Theorem. Ch 3.6
3/2 Probability Ch 3.5
3/9 Sets Ch 3.1
3/16 Review and Midterm .
3/23 Relations Ch 4.1, 4.2
3/30 Relations Ch 4.1, 4.2
4/7 Functions Ch 4.4
4/14 Functions Ch 4.4
4/21 Review for Final Exam .
4/28 Final exam .


Calendar

Details about lectures, homework assignments, exams etc. are added here.

Monday Tuesday Wednesday Thursday Friday




1/16
Go over syllabus.
Read Appendixes A and B.
Motivation.
1/17
1/18
Introduction to Problem Solving Methods (Ch. 2.1).
1/21
Martin Luther King, Jr. Day (no class).
1/22

1/23
Fundamentals of Logic. (Ch. 1)
1/24
Last day for Add/Drop.
1/25
Basic Connectives and Truth Tables.
Interpreting English by Logic Statements.
1/28
Valid Argument.
Logic Equivalence.
The Laws of Logic.
Substitution Rule.
Applications of the Laws of Logic:
1. Simplification of Compound Statement.
2. Negate Component Statement.
3. Compare the Efficiency of Two Program Segments.
4. Simplify Switching Networks.
HW1 Assignment.
1/29
1/30
Logic Implication.
The Rules of Inference.
Modus Ponens.
Modus Tollens.
Law of the Syllogism.
Rule of Conjunction.
Rule of Disjunctive Syllogism.
1/31
2/1
Rule of Contradiction.
2/4
Quiz 1.
Quiz 1 Key.
2/5
2/6
HW1 is due.
Quantifers.
Logic Equivalences and Implications for Quantified Statements.
HW2 Assignment.
2/7
2/8
Mathmatical Induction (Ch 2.2).

Monday Tuesday Wednesday Thursday Friday
2/11
Mathmatical Induction.
2/12
2/13
Mathmatical Induction (cont.).
2/14
2/15
HW2 is due.
Quiz 2 Key.
The Harmonic Numbers.
2/18
An altrnative form.
HW3 Assignment.
2/19
2/20
Recursive definition.
The Fibonacci Numbers.
The Lucas Numbers.
2/21
2/22
Quiz 3 Key.
2/25
Counting (ch 3.2, 3.4, 3.6).
The Rules of Sum and Product.
Permutations.
2/26
2/27
HW3 is due.
HW4 Assignment.
Combinations.
2/28
2/29
No class.

Monday Tuesday Wednesday Thursday Friday
3/3
Quiz 4 Key.
The Binomial Theorem.
3/4
3/5
Set Theory.
Set and Subset.
The Pascal's Triangle.
3/6
3/7
Set Theory (cont.).
Set operations.
Negate A delta B.
The Laws of Set Theory.
Counting and Venn Diagram.
An example of Counting and Venn Diagram.
3/10
No class.
3/11
3/12
No class.
3/13
3/14
HW4 is due.
HW5 Assignment.
Midterm Exam Review.
HW1 Solution.
HW2 Solution.
HW3 Solution.
3/17
Spring Break (no class).
3/18
3/19
Spring Break (no class).
3/20
3/21
Spring Break (no class).
3/24
Relations (Ch 4.1, 4.2).
Reflexive.
3/25
3/26
Q&A session (no class).
Midterm Exam Key.
3/27
3/28
Symmetric.
Transitive.
Last day for Withdraw.
3/31
HW5 is due.
Antisymmetric.
Partial order.
Quivalence.
In-class Exercise of Relations - Key.
HW6 Assignment.
4/1
4/2
Quiz 5.
Zero-One Matrices.
4/3
4/4
Zero-One Matrices.

Monday Tuesday Wednesday Thursday Friday
4/7
Directed Graphs.
4/8
4/9
Partial Orders.
Partitions.
4/10
4/11
HW6 is due.
Functions (Ch 4.4).
One-to-One Functions.
Onto Functions.
HW7 assignment.
4/14
No class.
4/15
4/16
No class.
4/17
4/18
No class.
4/21
Special Functions.
4/22
4/23
Quiz 6 Key.
Function Composition and Inverse Functions.
The Pigeonhole Principle.
4/24
4/25
Final exam review.
HW7 is due.
4/28
Q&A session (no class).
Final due day for all assignments by 5pm.
Final Exam 6-8pm.
4/29
4/30
5/1
5/2
5/3
5/4
5/5
5/6
5/7


Last updated: Monday, Jan. 8, 2007 by Yu Zhang.