CSCI13680-01 Course Syllabus

Discrete Structures

Fall 2019


Name:              Dr. Yao
Office:             Atkinson Hall 317

Telephone:      (478) 445-5483
URL:       or

Office Hours:  8:20 AM-9:20 AM, 10:50 AM-12:20 PM

on Tu. and Th. and by appointments

·         Emails that are not urgent only will be answered during the office hours

Classrooms: Atk 104 (12:30-1:45PM on Tu., Th.) and A&S143 (4:00-4:50PM on Tu)


“Mathematical Structures for Computer Science –Discrete Mathematics and Its Applications”, seventh Edition, 2014, by Judith Gersting.   

PREREQUISITE: C or better in CSCI 1302 and Math 1113 (or approval of professor).


This course serves the objective of learning an intensive introduction to discrete mathematics as it is used in computer science.

This course offers an intensive introduction to discrete mathematics as it is used in computer science. Topics include functions, relations, sets, propositional and predicate logic, simple circuit logic, proof techniques, cryptography, discrete probability, graphs and trees, and understand basic Finite-State Machines, Turing Machines, and Formal Languages.




Students will be able to:

  • Explain with examples the basic terminology of functions, relations, and sets.
  • Perform the operations associated with sets, functions, and relations.
  • Relate practical examples to the appropriate set, function, or relation model, and interpret the associated operations and terminology in context.
  • Demonstrate basic counting principles, including uses of diagonalization and the pigeonhole principle.
  • Apply formal methods of symbolic propositional and predicate logic.
  • Describe how formal tools of symbolic logic are used to model algorithms and real-life situations.
  • Use formal logic proofs and logical reasoning to solve problems such as puzzles.
  • Describe the importance and limitations of predicate logic.
  • Outline the basic structure of and give examples of each proof technique described in this unit.
  • Discuss which type of proof is best for a given problem.
  • Relate the ideas of mathematical induction to recursion and recursively defined structures.
  • Identify the difference between mathematical and strong induction and give examples of the appropriate use of each.
  • Apply the tools of probability to solve problems such as the Monte Carlo method, the average case analysis of algorithms, and hashing.
  • Understand cryptography
  • Understand basic graph and Trees
  • Understand basic Finite-State Machines, Turing Machines, and Formal Languages



·         Outcome 1: An ability to apply mathematical foundations, algorithmic principles, and computer science theory in the modeling and design of computer-based systems

·         Outcome 4: An understanding of security issues



·         Outcome (a) An ability to apply knowledge of computing and mathematics appropriate to the discipline

·         Outcome (b): An ability to analyze a problem, and identify and define the computing requirements appropriate to its solution

·         Outcome (e): An understanding of security issues

·         Outcome (j): An ability to apply mathematical foundations, algorithmic principles, and computer science theory in the modeling and design of computer-based systems in a way that comprehension of the tradeoffs involved in design choices.  



·         Formal Logic: Statements, Symbolic Representation, and Tautologies

·         Formal Logic: Propositional Logic, Quantifiers, Predicates, and Validity

·         Formal Logic: Predicate Logic, Logic Programming

·         Proof Techniques

·         Induction Recursion and Recurrence Relations

·         Analysis of Algorithms

·         Sets

·         Counting

·         Principle of Inclusion and Exclusion

·         Pigeonhole Principle

·         Relations

·         Topological Sorting

·         Relations and Databases

·         Functions

·         Matrices

·         Graphs and Their Representations

·         Trees and Their Representations

·         Cryptography

·         Decision Trees

·         Huffman Codes

·         Boolean Algebra and Computer Logic

·         Modeling Arithmetic

·         Computation and Languages

·         Finite-State Machines

·         Turing Machines

·         Formal Languages


                                             Percentage           Date
         Weekly Quiz               25%                    Every Tuesday (in A&S143)

         Mid-term exam           35%                    Oct. 10, 2019 (in Atk104)
         Final Exam                  40%                   Thursday, Dec 12, 2019 10:30 AM-12:45 PM

                                                                        (in Atk104)

         Total                               100%

      Grade              Percentage
        A                90% and up
        B                80% - 89.99%
        C                70% - 79.99%
        D                60% - 69.99%
        F                59.999% or less  


·         You are expected to read the textbook prior to and after class.

·         Class participation is essential in learning computer technology.  It is your responsibility to attend the class in order to achieve good learning, therefore obtain a good grade. 

·         You must NOT miss a test unless you have a verifiable excuse.  An unexcused absence from a test will result in a numerical grade of zero for that test.

·         All quizzes are teamwork.  You must form a 3-people team for the weekly quizzes.  The mid-term and final exam are individual work.

·         Prior to mid-semester, you will receive feedback on your academic performance in this course.  Your overall grades are updated on a regular basis on the Web throughout the semester.    


The integrity of students is a critical component of the academic process.  All written work submitted in this course must be individual work unless the instructor assigns a team of students to work on an assignment. Students must properly document all outside sources used for projects, programs, and homework. The submission of another’s work as one’s own is plagiarism, and will be dealt with using the procedures outlined on the Undergraduate Catalog.



Week One            Formal Logic: Statements, Symbolic Representation, and Tautologies

Week Two           Formal Logic: Propositional Logic, Quantifiers, Predicates, and Validity

Week Three         Formal Logic: Predicate Logic, Logic Programming, Proof of Correctness

Week Four           Proof Techniques

Week Five           Induction Recursion and Recurrence Relations, Analysis of Algorithms

Week Six             Sets, Counting, Principle of Inclusion and Exclusion, Pigeonhole Principle

Week Seven         Relations, Topological Sorting, Relations and Databases

Week Eight          Relations, Topological Sorting, Relations and Databases

Week Nine           Functions, Matrices

Week Ten            Graphs and Their Representations, Trees and Their Representations

Week Eleven       Graphs and Their Representations, Trees and Their Representations

Week Twelve       Decision Trees, Huffman Codes

Week Thirteen     Modeling Arithmetic, Computation, and Languages

Week Fourteen    Finite-State Machines

Week Fifteen       Turing Machines

Week Sixteen      Formal Languages 


·         Fall Break: Oct. 14-15, 2019

·         Oct. 17, 2019 (5 PM) is the last day to drop without academic penalty (Unless if maximum number of dropped courses has been exceeded)

·         Thanksgiving Holidays (Nov. 27-29, 2019)

·         Last Day of Classes: Dec. 9, 2019


The intellectual property of class assignments and other materials developed using university resources that are commercialized are reviewed under the USG and GC policies to determine ownership and/or payment rights. USG policies can be found at and GC policies can be found at


Electronic video and/or audio recording is not permitted during any class unless the student obtains permission from the instructor and every student present. If permission is granted, any distribution of the recording is prohibited. Violation of this policy is grounds for removal from the class and referral for disciplinary action. Students granted specific electronic recording accommodations from Disability Services do not require special permission; however, the instructor must be notified. Any distribution is prohibited.


If you have a disability as described by the Americans with Disabilities Act (ADA) and the Rehabilitation Act of 1973, Section 504, you may be eligible to receive accommodations to assist in programmatic and physical accessibility. Disability Services, a unit of the GCSU Office of Institutional Equity and Diversity, can assist you in formulating a reasonable accommodation plan and in providing support in developing appropriate accommodations to ensure equal access to all GCSU programs and facilities. Course requirements will not be waived, but accommodations may assist you in meeting the requirements. For documentation requirements and for additional information, we recommend that you contact Disability Services located in Maxwell Student Union at 478-445-5931 or 478-445-4233.


Given the technological sophistication of Georgia College students, the student opinion survey is being delivered through an online process. Your constructive feedback plays an indispensable role in shaping quality education at Georgia College. All responses are completely confidential and your name is not stored with your responses in any way. In addition, instructors will not see any results of the opinion survey until after final grades are submitted to the University. An invitation to complete the online opinion survey is distributed to students near the end of the semester. Your participation in this very important process is greatly appreciated.


Fire drills will be conducted annually. In the event of a fire alarm, students will exit the building in a quick and orderly manner through the nearest hallway exit. Learn the floor plan and exits of the building. Do not use elevators. If you encounter heavy smoke, crawl on the floor so as to gain fresh air. Assist disabled persons and others if possible without endangering your own life. Assemble for a head count on the front lawn of main campus or other designated assembly area.


Students are permitted to miss class in observance of religious holidays and other activities observed by a religious group of which the student is a member without academic penalty. Exercising of one’s rights under this policy is subject to the GC Honor Code. Students who miss class in observance of a religious holiday or event are required to make up the coursework missed as a result from the absence. The nature of the make-up assignments and the deadline for completion of such assignments are at the sole discretion of the instructor. Providing verifiable proof of the religious affiliation and activities are at the sole discretion of the instructor as well.  Failure to follow the prescribed procedures voids all student rights under this policy.


An academic grievance or appeal is an allegation by a student of substantial and/or unjustified deviation, to the student’s detriment, from policies, procedures and/or requirements regarding admission, grading policies, special agreements, instructor’s requirements and academic requirements of the University. Students shall have the right to file academic grievances or appeals according to the procedures approved by the University and outlined in the University Catalog.  This information is also available on the Georgia College Intranet.