 Course Title : Discrete Mathematics
Code Course
Type
Regular
Semester
Lecture
(hours/week)
Seminar
(hours/week)
Lab
(hours/week)
Credits ECTS
CMP 130-1 A -1 3 1 0 3.50 5
Lecturer and Office Hours
Teaching Assistant and Office Hours
Language
Course Level
Description This is an introductory course in discrete mathematics. The aim of this course is to introduce students to ideas and techniques from discrete mathematics that are widely used in science and engineering. This course teaches students how to think logically and mathematically and apply these techniques in problem solving. To achieve this goal, students will learn logic and mathematical reasoning, communities, induction and recursion, relations, functions. Counting techniques, permutations, combinations, recurrences, algorithms for their generation.
Objectives At the end of the course, the student will be able to understand and apply the elementary logic and algebra of the sets, in the construction of inductive reasoning, in combinatorics, in solving recursive relations.
Course Outline
WeekTopics
1Elements of mathematical logic: statements and logical connections. Propositional Equivalences. Applications propositional logic. (Adapted lectures in Albanian: Discrete Mathematics-Anjeza Pasku, Pages 1-21)
2Predicates and quantifiers. Rules of logical deduction, methods of proofs. (Adapted lectures in Albanian: Discrete Mathematics-Anjeza Pasku, Pages 22-35)
3Sets, sets operations. Functions. Sequences and rrecurence relations. (Adapted lectures in Albanian: Discrete Mathematics-Anjeza Pasku, Pages 36-57)
4Sums, zero-one matrices. Algorithms and the growth of functions. Complexity of algorithms (Lectures adapted in Albanian: Discrete Mathematics-Anjeza Pasku, Pages 57-88)
5Number Theory: Divisibility and Modular Arithmetic. Primes, lcm and gcd of numbers (Adapted lectures in Albanian: Discrete Mathematics-Anjeza Pasku, Pages 89-111)
6Solving congruences. Applications of congruences (Adapted lectures in Albanian: Discrete Mathematics-Anjeza Pasku, Pages 111-125)
7Mathematical induction. Strong induction and well ordering (Adapted lectures in Albanian: Discrete Mathematics-Anjeza Pasku, Pages 125-138)
8Midterm
9Recursive definitions and structural induction. Recursive Algorithms (Adapted Lectures in Albanian: Discrete Mathematics-Anjeza Pasku, Pages 138-149)
10Relations and their properties. Representation of relations. Equivalence relations. (Adapted lectures in Albanian: Discrete Mathematics-Anjeza Pasku, Pages 150-178)
11Partial orderings. Hasse diagrams. Lexicographical order and topological classification (Adapted lectures in Albanian: Discrete Mathematics-Anjeza Pasku, Pp 178-194)
12The Basics of counting. The Pingeonhole principle. Permutations and combinations. (Adapted lectures in Albanian: Discrete Mathematics-Anjeza Pasku, Pp 195-214)
13Binomial coefficients and identities. Generalized permutations and combinations. (Adapted lectures in Albanian: Discrete Mathematics-Anjeza Pasku, Pages 214-228)
14Advanced counting techniques. Applications of recurrence relations in problem modeling. Solving linear recurrent relations (Adapted lectures in Albanian: Discrete Mathematics-Anjeza Pasku, Pages 228-243)
15Divide and Conquer algorithms and recurrence relations. Repetition. (Adapted lectures in Albanian: Discrete Mathematics-Anjeza Pasku, Pages 243-250)
16Final Exam
Prerequisites
Textbook
Other References
Laboratory Work
Computer Usage
Other
Learning Outcomes and Competences
1In terms of knowledge and understanding, at the end of the course, the student is expected to be able to: • Explain basic models of discrete mathematics and technology. • Explain how these models can be applied to the respective problems.
2In terms of competencies and skills at the end of the course, the student is expected to be able to: • Analyze the given problems logically. • To express problems in formal language • Solve problems using recursive methods • Solve combinatorial problems
Course Evaluation Methods
In-term studies Quantity Percentage
Midterms135
Quizzes230
Projects00
Term Projects00
Laboratory00
Attendance00
Contribution of in-term studies to overall grade65
Contribution of final examination to overall grade35
Total100
ECTS (Allocated Based on Student) Workload
Activities Quantity Duration
(hours)
(hours)
Course Duration (Including the exam week : 16 x Total course hours) 16464
Hours for off-the-classroom study (Pre-study, practice) 14456
Assignments 000
Midterms 122
Final examination 122
Other 000