MATH 280
Discrete Mathematical Structures Fall 2017

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Instructor

Rick Halterman

School of Computing
1117E Hickman Hall
Southern Adventist University
Collegedale, TN 37315-0370
423-236-2871

halterman@southern.edu
http://computing.southern.edu/halterman

Office Hours: http://computing.southern.edu/halterman/General/OfficeHours


Course Venue

HSC 1307    MWF 10:00–10:50 am


Textbook

Applied Discrete Structures. Doerr, Alan and Levasseur, Kenneth. 2017.

This textbook is Creative Commons Licensed and available online for free at http://faculty.uml.edu/klevasseur/ADS2/


Prerequisite

Math 120 Precalculus Algebra; familiarity with a programming language.


Purpose

Catalog description:

MATH 280. Discrete Mathematical Structures 3 hours
Prerequisite: MATH 120 recommended; Familiarity with a programming language.
An examination of many of the mathematical concepts of particular use to computer scientists. The topics include set theory, relations, graph theory, combinatorics, Boolean algebra, proof techniques, and finite state automata.

This course has several objectives:

  1. to acquaint the student with the precise vocabulary and powerful notation used in formal computer science study
  2. to introduce useful abstractions in problem solutions and representations that have application in many areas of computer science
  3. to foster rigorous thinking skills that can enhance the quality of work of computing professionals


Class Requirements and Grading

Grade Distribution. Final grades are determined according to the following table:

Overall Average
(a)
Letter
Grade
92 ≤ a A
90 ≤ a < 92   A–
88 ≤ a < 90   B+
82 ≤ a < 88 B
80 ≤ a < 82   B–
78 ≤ a < 80   C+
70 ≤ a < 78 C
60 ≤ a < 70   C–
58 ≤ a < 60   D+
52 ≤ a < 58 D
50 ≤ a < 52  D–
a < 50 F

Class Work. The average used to determine the final grade is computed from the following class activities and is weighted as indicated.

Activity Weight
Participation 10%
Quizzes 10%
Assignments 20%
Test 1 20%
Test 2 20%
Final Examination 20%

Remarks

All homework assignments are due at the beginning of class on the day designated. Since solutions may be discussed during that class period, late submissions are not accepted. If a class must be missed, assignments can be submitted early. Generally, one week is allotted to complete each assignment. The time is meant to permit ample opportunity to think the problems through carefully and produce good solutions. It is usually a mistake to postpone doing the homework until a few days before it is due. It is expected that each student work individually on each homework assignment. Tests will be given based largely on the experience gained by doing the problems, so it is important to spend adequate time doing the homework.

All assignments should legible! Ideally you should typeset your assignment with LaTeX or Microsoft Word. Any time you spend with LaTeX will pay off in later computer science courses, especially CPTR 486 Senior Seminar. LaTeX is a markup language, and its tools are available for free for Windows, Mac OS X, and Linux (see http://latex-project.org/ftp.html).

Appropriate study for the course includes reading the textbook (at least as far as last class's lecture material) and staying current in the assignments.

Weekly quizzes encourage students to remain current in their class preparation. Quiz contents may be based on material covered since the previous quiz. Usually quizzes will be distributed at the beginning of the class period. Missed quizzes may not be made up; however, the lowest quiz score will be dropped during the last week of the semester.

Class periods that do not offer a quiz may include a worksheet to be completed during the class period by the student. Careful attention in class facilitates the completion of the worksheet. Worksheets contribute to the participation grade and may not be made up.

Each test contributes significantly to the overall grade so studying for tests should be taken seriously. In certain situations, due to unavoidable circumstances, a missed test may be made up. Arrangements for the retake should be made before the time of the originally scheduled test. The make-up test may vary greatly in form from the original test, but its content (topics addressed) will be the same.

Since the assigned material and activities are sufficient for most students, no extra credit will be available. However, well-prepared students wishing to enhance their learning experience beyond the class activities will be directed, upon request, to additional resources. Any such additional work will not influence the grade for this class.

All students must have an active email account to receive electronic mailings concerning this class. Each student should check her mail daily to see if any important announcements have been posted. (Such announcements include corrections, hints, assignment updates, etc.) Also, I'm often easier to reach via email if you have specific questions about class.

Ethics. It is expected that each student work individually on individual assignments.  For team assignments, collaboration is limited to teammates. Problems on tests will be based largely on the experience gained by doing past assignments, so it is important that each student do his/her own work for adequate preparation for the examinations. Except among teammates, portions of assignments never should be shared. Those involved in allowing their work, or parts of their work, to be copied, or copying from other students' programs risk receiving a grade of F in the course.

Incidents of academic dishonesty will be reported to the Associate Vice-president of Academic Affairs.

Class study. Appropriate study for the course includes reading the textbook (at least as far as last class's lecture material) and working through the exercises at the end of each chapter.

Class decorum. Please comply with the standards of classroom attire as specified in the Student Handbook.  Notebook computers are welcome, and the classroom and lab (generally) have an excellent wireless signal.  Those with computers should mute the volume and sit in the rear of the class so as not to distract students behind them.  Electronic devices must be turned off during quizzes and tests.  You are expected to remain in the classroom during quizzes and tests, so be sure to take care of affairs (such as bathroom visits and tissue acquisition) before you sit for the quiz or test.

Examinations The dates for each test is listed in this syllabus. In certain situations, due to unavoidable circumstances, a missed test may be made up. Arrangements for the retake should be made before the time of the originally scheduled test. The make-up test may vary greatly in form from the original test, but its content (topics addressed) will be the same. Because of this difference, any points added (the so called "curve") to tests taken during the regularly scheduled time may not apply to retakes.

Please note the date and time for our final exam on the tentative class schedule. You need to plan to take your final exam at the scheduled time. Please make your work and vacation plans accordingly. Academic Administration will grant approval for variance from the published exam schedule only in cases of verified, serious, illness or a death in the immediate family. Academic Administration may, in case of exceptional and unavoidable circumstances, approve a variance, in consultation with the professor of this course. A $65 processing fee may be assessed.

Extra credit. Since the assigned material and activities are sufficient for most students, no extra credit will be available for additional work. However, well-prepared students wishing to enhance their learning experience beyond the class activities will be directed, upon request, to additional resources. Any such additional work will not influence the grade for this class.  

SAU account.  All students must have an active Southern Adventist University email account. This account is necessary to receive class messages and to be able to use the computers in the programming lab. If you normally use a different email address, please set up your SAU account to forward your email to your preferred address; instructions about how to do this are available upon request.

Disability Support Services. In keeping with the University’s policy, if you are a student who believes you may need an accommodation based on the impact of a disability or learning challenge, (i.e. physical, learning, psychological, ADHD or other type), you are strongly encouraged to contact Disability Support Services (DSS) at 423-236-2544 or stop by Lynn Wood Hall, Room 1082. Please note that accommodations are not retroactive and cannot be implemented until faculty or staff members have received the official Letter of Accommodation from DSS. Specific details of disabilities remain confidential between students and DSS unless a student chooses to disclose or there is legitimate academic need for disclosure, which is on a case-by-case basis. For further details, visit the Disability Support Services website at http://www.southern.edu/disabilitysupport.


Topics and Schedule

Week Beginning Text Chapter Topics
Aug 21 1 Elementary set theory: sets, notation, operations, Cartesian product and power sets, summation notation
Aug 28 2 Combinatorics: basic counting techniques, multiplication principle, addition principle, permutations, combinations
Sep  4 3 Mathematical logic: propositions, logical operators, truth tables, laws of logic, quantifiers
Sep 11 3 Methods of proof: direct proofs, contraposition, contradiction, mathematical induction
Sep 18 4, 5 Methods of proof for sets, laws, of set theory, duality; matrix algebra: matrix addition, scalar multiplication, matrix multiplication, laws of matrix algebra
Test 1 on Wednesday, September 20
Sep 25 6 Relations and graphs: basic definitions, graphs of relations, properties of relations, closure operations
Oct  2 7 Functions: basic definitions, injective, surjective, and bijective functions, function composition, identity and inverse, closure operations
Oct  9 8 Recursion and recurrence relations: recursion, sequences, recurrence relations
Midterm Break on Friday, October 13
Oct 16 9 Elementary graph theory: basic definitions, computer representation, connectivity, graph traversals
Oct 23 10 Trees: basic definitions, spanning trees, rooted trees, binary trees, Huffman trees
Test 2 on Monday, October 23
Last day to withdraw and receive a W on Thursday, October 26
Oct 30 11 Algebraic systems: operations, algebraic systems, properties of groups, integers modulo n
Nov  6 14 Monoids and automata: monoids, finite automata, regular expressions
Nov 13 Formal languages: context-free grammars, parse trees, Turing machines
Nov 20 Thanksgiving Break
Nov 27 15 Introduction to group theory: cyclic groups, permutation groups, subgroups
Dec  4 Error correcting codes: error detection, error correction, Hamming distance, group codes
Dec 12 Final Examination on Tuesday, December 12 at 10:00 am
Note day and time!