SHAW UNIVERSITY

College of Arts and Sciences

Department of Natural Sciences and Mathematics

MAT 212 - 1 (3 credit hours)  Spring 2009

Discrete Mathematics

Prerequisite:  MAT 115 or Higher

Instructor: Do Yeong Shin                                                                                                      Office Location: TUP 103

Email:  dyshin@shawu.edu                                                                                                      Telephone:  919-546-8232

Class Time: MWF  14:00 – 14:50                                                                                  Class Room: TUP 204                        

Office Hours: MW 08:30 – 08:50, 11:00 – 11: 50                                                       

                        TTh  09:30 – 11:50

                        Other Times by Apointment

Important Dates: (The following dates could be flexible.)

Last Day to Drop a Course:  January 26, 2009

Last Day to Withdraw From University:   February 4, 2009

Last Day of Classes:   April 30, 2009

                                Final Exams:   May 4 – 7, 2009

Program Mission

The mission of the Mathematics Program is to prepare students with the knowledge, skills, and competencies, for employment in fields of work requiring quantitative and problem solving skills, and also to pursue graduate studies in Pure and Applied Mathematics. The mission is also to produce graduates who are equipped with analytical and critical thinking skills to enable them to formulate problems, solve them, and interpret their solutions, and communicate the solution.

Program Goals 

The primary goals of the Mathematics unit for this period are as follows:

1.        Produce graduates with the mathematical knowledge and competence with computational and quantitative skills to succeed in the field of work requiring quantitative and problem solving skills

2.        Produce graduates with the knowledge and competencies to be prepared for graduate studies in Pure and Applied Mathematics and further research

3.        To improve the academic performance of students and increase student retention.

Program Learning Outcomes (PLO’s) 

1.1   Students will be able to think analytically and logically. They will be able to apply the subjects such as Euler circle, syllogism, etc., to their daily lives. 

1.2   Students will be able to develop simple algorithms, to determine the order of operations, and to solve linear homogeneous recurrence relations.  They will learn Boolean algebras and their applications, and automata, grammars, and languages

1.3     Students will be able to use graph theory in the fields of transportation, networking and circuit diagram.

2.1   Students will be able to understand the various techniques of proving theorems and will be able to state and prove theorems using definitions and properties.

3.1     Periodic meetings of all the major students with all the math faculty will be arranged to give an opportunity to students and faculty to communicate and exchange ideas to provide the students with what their academic needs are and make their learning experience more enjoyable.

3.2     The advisors will meet with their advisees at least two times a semester to make sure the students are taking the right courses and are in the right track for timely graduation. Also they will address any academic needs the advisees have and make them more comfortable to stay and complete the major program.

3.3     Inform the students of opportunities on Summer Internships and summer Institutes and encourage them to get these experiences and also take them to undergraduate conferences where they can meet other undergraduate math students and exchange ideas and learn about graduate school and research opportunities. Make arrangements for organizing tutoring sessions for students who need help in their class work.

Course Description:

This is a discrete mathematics course intended for students who have knowledge of MAT 115 or higher. 

This is  a recommended course for  students majoring in Mathematics and Mathematics Education and Sciences, and also a core requirement for students majoring in Computer Science and Computer Information Systems. This course is a study of logic and proof, relations, various algorithms, counting methods, graph theory, network models, and Boolean Algebras and combinatorial circuits, automata.  Students will be exposed to symbolic manipulations, critical thinking and problem solving techniques by applying the concepts to solve application problems.

Conceptual Framework Theme:

To produce graduates who are critical-thinking problem solvers with the knowledge, pedagogical and technological skills, and professional dispositions needed to function as effective teachers in a diverse world.

Student Learning Outcomes:  

After completing this course successfully, the students will be able to do the following:

Required Textbook & Resources:

Discrete Mathematics, 7^th Edition, Richard Johnsonbaugh, Prentice Hall

1)   Understanding Finite Mathematics by James Radlow, Prindle, Weber & Schmidt    Publishing Co.

2)  Mathematical Structures for Computer Science by Judith L. Gersting, W.H. Freeman & Co.                                                                                             3)   First Course in Discrete Mathematics by John C. Molluzzo, Wadsworth Publishing Company.                                                                                      4)  Introduction to Computer Science by Neil Graham, West Publishing

Tentative Topics:

    Logic and Proof

       a.  Quantifiers

          b.  Proofs  

          c.  Mathematical Induction

   The Language of Mathematics

          a.  Number Systems

          b.  Relations

          c.  Equivalent Relations

          d.  Matrices of Relations

          (e.  Relational Databases)

          f.  Hash Functions

    Algorithms

          a.  The Euclidean Algorithm

          b.  Recursive Algorithms

          (c.  Compexity of Algorithms)

     Counting Methods

           a.  Permutations and Combinations

           b.  The Pigeonhole Principle

Graph Theory

          a.  Paths and Cycles

          b.  Hamiltonian Cycles and the Traveling Salesperson Problem

          c.  Spanning Trees

          d.  Binary Trees

 Network Models

          a.  A Maximal Flow Algorithm

          b.  Matching

 Boolean Algebras and Combinatorial Circuits

          a.  Combinatorial Circuits

          b.  Boolean Algebras

          c.  Boolean functions and Synthesis of Circuits

 Automata, Grammars, and Languages

          a.  Sequential Circuits and Finite-State Machines

          b.  Finite-State Automata

          c.  Languages and Grammars

 (Computational Geometry)

          a.  The Closest-Pair Problem

Tentative Test Schedule

                             Test #1                                           Wednesday, February 11, 2009

                             Test #2                                           Wednesday, March 11, 2009

                             Test#3                                            Wednesday, April 8, 2009

                             Final Exam                                    The University Schedule     

Course Evaluation:

Quiz/Homework                                                                                             30% of final grade

It is student's responsibility to turn in the assigned homework on due date.  Late homework will be lowered 10 points per day.  No homework will be accepted after the solutions are given.  If you fail to turn in the assigned homework on due date because of your obligation to the university, your personal illness and your immediate family member's illness, you should attach the university excuse to your homework to avoid the penalty described above.

Tests                                                                                                                                                     30% of final grade

Class Participation  (Instructor's Decision)                                                                                10% of final grade

Comprehensive final                                                                                                                         30% of final grade

It is student's responsibility to take each test on the announced date.  If you cannot take the scheduled test on the announced date because of your own reasons, use my e-mail (dyshin@shawu.edu) to leave your name, course name, acceptable reason(s) by the instructor and the time you can makeup the test.  Makeup test must be arranged in no more than 5 working days from the date the test is given, and the time must not hinder with the instructor’s daily schedule. Otherwise makeup test will not be given.  When you miss the final exam, there will be NO makeup.

Attendance Policy:

 Students who miss classes are responsible for subject matter covered, any announcements made regarding quiz, test or any other relevant matter, during their absence.

More than 3 (if class meets 3 times a week ) or 2 (if class meets 2 times a week ) unexcused absences may result in failure in the course.  You are responsible to find out or know about any announcements or the subject matter covered, during your absence.

Student Classroom Decorum Expectations:

To enhance the learning atmosphere of the classroom, students are expected to dress and behave in a fashion conducive to learning in the classroom. More specifically, students will refrain from disruptive classroom behavior (i. e., talking to classmates, disrespectful responses to teacher instructions; swearing; wearing clothes that impede academic learning such as but not limited to, wearing body-revealing clothing and excessively baggy pants; hats/caps, and/or headdress). Students will turn off telephones prior to entering the classroom. Students who exhibit the behaviors described above, or similar behaviors will be immediately dismissed from class at the third documented offense. The student will be readmitted to class only following a decision by the department chair. The student may appeal the decision of the department chair to the Dean of the College offering the course, and, subsequently, to the Office of the Vice President for Academic Affairs, and then to the President of Shaw University. The decision of the President will be final. Failure to follow the procedures herein outlined will result in termination of the appeal, and revert to the decision of the department chair.

 Each behavior construed by the teacher/professor as non-contributive to learning will be recorded, properly documented, and appropriately reported to the student and to the chair of the academic department offering the course. The report will be in written form with a copy provided to both the student and the department chair. The faculty member should retain a copy for his/her own records. Additional student behavior codes may be found in Student Affairs.