Course Syllabus

Class Hours: Friday 9:00 – 13:00, Class 3D.

Office Hours: Wednesday 15-16, Office 3rd Floor.

Phone: +355 4 44512345 Ext. 348

E-mail: ngjini@unyt.edu.al

 

A systematic study of the mathematics that forms the basis of theoretical work in computer science. This semester course is an introduction to number theory, discrete probability theory, graph theory and Boolean algebras. It focuses on elementary logic as a working tool; it brings together the basic tools of discrete mathematics: relations, graphs and digraphs, and matrices, giving several views of the same set of ideas. Equivalence relations get a careful treatment and are applied to modular arithmetic on Z. It includes basic counting techniques and elementary probability, too.

Prerequisite:  College Algebra

 

Course Purpose

It emphasizes the conceptual understanding, quantitative reasoning, and contemporary applications by maintaining a dynamic balance among theory, applications, modeling, and drill. Students work to develop a deeper understanding of a range of mathematical topics using interactive math tutorials that allow the student to solve math problems interactively.

 

Required Readings:

 

Main textbook: Discrete Mathematics, Kenneth A. Ross and Charles R. B. Wright, Prentice-Hall International Editions.

 

Additional textbooks:

  • Discrete mathematics for Computer Science, Haggard G., Schlipf J., Whitesides S., Thompson Brooks/Cole.
  • Epp, S., Discrete Mathematics with Applications, 3rd edition, PWS Publishing Company.

 

Course Objectives

Upon completion of this course, students should be able to:

  1. Have a complete knowledge on various discrete structures available in literature.
  2. Have gained some confidence on how to deal with problems which may arrive in computer science in near future.
  3. Set Theory: Demonstrate a working knowledge of set notation and set theory, recognize the connection between set operations and logic, and prove results involving sets.
  4. Fundamentals and application of Logic: Formulate and interpret statements presented in disjunctive normal form and determine their validity by applying the rules and methods of propositional calculus. Reformulate statements from common language to formal logic using the rules of propositional and predicate calculus, and assess the validity of arguments.
  5. Methods of Proof: Formulate short proofs using the following methods: direct proof, indirect proof, proof by contradiction, and case analysis.
  6. Proof by Induction: Construct elementary proofs using ordinary and strong induction in the context of studying the properties of recursion, relations, and graph theory, and identify fallacious inductive arguments.
  7. Combinatorics and probability: Apply basic counting principles including the pigeonhole principle and rules for counting permutations and combinations. Apply discrete probability’s axioms and laws for calculating different probability distributions and the respective expectation, variance and standard deviation.
  8. Relations: Determine when a relation is reflexive, symmetric, antisymmetric, or transitive, apply the properties of equivalence relations and partial orderings, and explain the connection between equivalence relations and partitioning a set.
  9. Graph theory: Explain basic definitions and properties associated with simple planar graphs and trees, including isomorphism, connectivity, and Euler’s formula, and describe the difference between Eulerian and Hamiltonian graphs.
  10.  Boolean Algebras: variables and operations, logic networks, Karnaugh maps and their applications in computer sciences, digital logic, and statistics.

 

Content of the Course

Some Special Sets.

Set Operations.

 

  1. Counting and Probability.

Basic Counting Techniques.

Basic rules of Probability, Venn Diagram.

Conditional Probability, Tree diagram, Baye’s Rule.

Discrete Probability Distributions, mean, variance and standard deviation.

 

  1. Elementary Logic.

Relations.

Propositional Calculus.

Methods of Proof.

More Propositional Calculus.

 

Relations.

Matrices.

Multiplication of Matrices.

Equivalence Relations and Partitions.

The Division Algorithm and Z(p).

 

  1. Introduction to graphs and trees.

Graphs and Digraphs.

Edge traversal problems.

Trees.

Vertex traversal problems.

Minimum spanning.

 

  1. Boolean Algebra.

Boolean algebras.

Boolean expressions.

Logic networks.

Karnaugh maps.

Course Requirements

 

Participation: Participation extends beyond mere attendance. Active participation is meant as the effort and the interest that a student shows in the class, including homework. After each session students are expected to study all the relevant material, read all the associated exercises, identify the difficult points and pose their questions in the next session either directly to me or in the class. You may miss up to three classes without penalty – your first two absences count whether you have a good excuse or not. Each absence beyond the first three will cost you points off of your participation grade. The only exceptions to this rule are severe illness (doctor’s note required) and UNYT approved trips/activities. Appropriate documentation for absences beyond the first three is necessary the class day directly before or after the one you miss. You are expected to attend class and I do keep attendance records. In general: this class is intensive and interactive. Missing class could seriously affect your grade! Students who are absent more than 20% of the total hours of the semester (i.e. 12 hours) may be required to withdraw from the course.

Class conduct: Exams are closed books. Also, you use your own calculator and nothing else will be allowed. Mobile phones are strictly not tolerated in the class for any use (including computations). Cheating and plagiarism in any form will result immediately in the grade F.

Students are responsible for everything that is announced, presented or discussed in class. The way to avoid any misunderstanding associated with this course is to attend class. Please, be courteous during class; both to me and your colleagues. I find late arrivals distracting, which cause a decline in the quality of my lecture. Importantly, it is also disruptive to your colleagues. Please, refrain from talking during class; it is disruptive to your colleagues and the lecture. I expect the best behavior from all of you. This is what education is all about. Please, consider that the language of instruction is English, so all our conversation into the class must be in this language.

 

Exams: Two examinations will be taken, a midterm exam during week seven of the course and a final exam covering all course content during the final examination period. Exam format may combine a mixture of short answer, true/false, matching, sort answer, and reasoning problems covering all readings, lecture, hand-out and class discussion content. Another test will be included in the period between the midterm and final exam.

 

Final Examination: Friday, February 5, 2016, Time: 9:00 -13:00.  

 

General Requirements

Deadlines in submitting the homework are critical. Therefore, late assignments and absence from tests will not be tolerated.   In the event of illness or emergency, contact your instructor IN ADVANCE to determine whether special arrangements are possible. The University’s rules on academic dishonesty (e.g. cheating, plagiarism, submitting false information) will be strictly enforced. Please familiarize yourself with the STUDENT HONOUR CODE, or ask your instructor for clarification.

 

Criteria for Determination of Grade

 

  UNYT
Active Participation & Homework 10%
Midterm exam  30%
Test 20%
Final exam 40%

 

 

Grading scale follows the official UNYT as below:

 

Letter Grade Percent (%) Quality Points Generally Accepted Meaning
           A 96-100 4.00 Outstanding work
           A- 90-95 3.67
           B+ 87-89 3.33 Good work, distinctly above average
           B 83-86 3.00
           B- 80-82 2.67
           C+ 77-79 2.33 Acceptable work
           C 73-76 2.00
           C- 70-72 1.67
           D+ 67-69 1.33 Work that is significantly below average
           D 63-66 1.00
           D- 60-62 0.67
           F 0-59 0.00 Work that does not meet minimum standards for passing the course

 

 

Technology Expectations: usage of power-point, excel, word.  Students must keep copies of all assignments and projects sent by e-mail.

Assignments are to be word-processed and converted into pdf files. Continuing and regular use of e-mail is expected.

 

STUDENTS: If you feel that you have encountered special learning difficulties or serious problems that interfere with your studies, please make an appointment with UNYT Counseling Center, Dr. E Cenko (enilacenko@unyt.edu.al) and/or the Academic Support Center, Dr. A Canollari (albanacanollari@unyt.edu.al). They are trained to help students with learning difficulties and have offered to provide this service to our students, just as it is offered in all American universities; you can also discus with your academic advisor.

If you need help with course content, please refer to the Math Center. Please feel free to talk to me for additional information.

 

 

GOOD LUCK!

Date Prepared: October 6 / 2015

Prepared by Prof. Dr. Nertila Gjini

 

 

Faculty: Business &Economics.

Department: Maths & N.Sciences.

Grade: Undergraduate.

Majors: Computer Sciences.

Study Fileds: Computer Science and Management of Information Systems.

Course Year: 2.

Course Program: UNYT.

Scheduele: FRI 09-13:00

Instructor: Prof. Dr. Nertila Gjini

Credits: 4

Prerequisite: College Algebra