CEN130 Discrete Mathematics

5 ECTS - 3-0 Duration (T+A)- 2. Semester- 3 National Credit

Information

Code CEN130
Name Discrete Mathematics
Term 2024-2025 Academic Year
Semester 2. Semester
Duration (T+A) 3-0 (T-A) (17 Week)
ECTS 5 ECTS
National Credit 3 National Credit
Teaching Language İngilizce
Level Lisans Dersi
Type Normal
Mode of study Yüz Yüze Öğretim
Catalog Information Coordinator Prof. Dr. UMUT ORHAN
Course Instructor
1 2
Prof. Dr. UMUT ORHAN (A Group) (Ins. in Charge)


Course Goal / Objective

In this course, the mathematical foundations related to computer sciences like formal logic, set theory, mathematical induction, methods of counting, discrete probability, elementary graph theory are discussed.

Course Content

Logic, Sets, Function, Algorithm Complexity, Modular Arithmetic, Sequences and Strings, Recurrence Relations, Combinatorics, Probability and Bayes Theorem, Graph Theory, Trees, Finite-State Machine and Automata, Context Free Language and Grammar

Course Precondition

none

Resources

Notes on Discrete Mathematics, M. A. Lerma, Northwestern University

Notes

Discrete Mathematical Structures: Theory and Applications, D.S. Malik and M.K. Sen, Thomson.


Course Learning Outcomes

Order Course Learning Outcomes
LO01 Solves a problem using rules of logical inference
LO02 Interprets partially ordered sets using Hasse diagram
LO03 Encrypts a message with RSA method
LO04 Interprets problems with the pigeonhole principle
LO05 Interprets simple classification problems using probability and Bayes' Theorem
LO06 Represents problems with graphs
LO07 Solves problems with graph algorithms
LO08 Represents problems with trees
LO09 Solves problems with tree algorithms
LO10 Interprets language problems with Finite State Machines
LO11 Interprets language problems with Context Free Grammar


Relation with Program Learning Outcome

Order Type Program Learning Outcomes Level
PLO01 Bilgi - Kuramsal, Olgusal Adequate knowledge of mathematics, science and related engineering disciplines; ability to use theoretical and applied knowledge in these fields in solving complex engineering problems. 5
PLO02 Bilgi - Kuramsal, Olgusal Ability to identify, formulate and solve complex engineering problems; ability to select and apply appropriate analysis and modeling methods for this purpose. 3
PLO03 Bilgi - Kuramsal, Olgusal Ability to design a complex system, process, device or product to meet specific requirements under realistic constraints and conditions; ability to apply modern design methods for this purpose. 2
PLO04 Bilgi - Kuramsal, Olgusal Ability to select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in engineering practice; ability to use information technologies effectively. 3
PLO05 Bilgi - Kuramsal, Olgusal Ability to design and conduct experiments, collect data, analyze and interpret results to investigate complex engineering problems or discipline-specific research topics. 3
PLO06 Bilgi - Kuramsal, Olgusal Ability to work effectively in interdisciplinary and multidisciplinary teams; individual working skills. 1
PLO07 Bilgi - Kuramsal, Olgusal Ability to communicate effectively verbally and in writing; knowledge of at least one foreign language; ability to write effective reports and understand written reports, prepare design and production reports, make effective presentations, and give and receive clear and understandable instructions. 1
PLO08 Bilgi - Kuramsal, Olgusal Awareness of the necessity of lifelong learning; ability to access information, follow developments in science and technology, and constantly renew oneself. 1
PLO09 Bilgi - Kuramsal, Olgusal Knowledge of ethical principles, professional and ethical responsibility, and standards used in engineering practice.
PLO10 Bilgi - Kuramsal, Olgusal Knowledge of business practices such as project management, risk management and change management; awareness of entrepreneurship and innovation; knowledge of sustainable development.
PLO11 Bilgi - Kuramsal, Olgusal Knowledge of the effects of engineering practices on health, environment and safety in universal and social dimensions and the problems of the age reflected in the field of engineering; awareness of the legal consequences of engineering solutions.


Week Plan

Week Topic Preparation Methods
1 Logic and Proofs, Propositions Reading related chapter in lecture notes Öğretim Yöntemleri:
Anlatım
2 Sets, Function-Relation Reading related chapter in lecture notes Öğretim Yöntemleri:
Anlatım
3 Algorithm Complexity, Modular Arithmetic, RSA Reading related chapter in lecture notes Öğretim Yöntemleri:
Anlatım
4 Sequences, Strings, Induction, Recurrence Relations Reading related chapter in lecture notes Öğretim Yöntemleri:
Anlatım
5 Combinatorics, The Pigeonhole Principle, Probability and Bayes Theorem Reading related chapter in lecture notes Öğretim Yöntemleri:
Anlatım
6 Introduction to Graph Theory, Representations of Graphs Reading related chapter in lecture notes Öğretim Yöntemleri:
Anlatım
7 Paths and Circuits in Graphs Reading related chapter in lecture notes Öğretim Yöntemleri:
Anlatım
8 Midterm exam Study to lecture notes and apllications Ölçme Yöntemleri:
Yazılı Sınav
9 Graph Algorithms Reading related chapter in lecture notes Öğretim Yöntemleri:
Anlatım
10 Trees, Binary Trees Reading related chapter in lecture notes Öğretim Yöntemleri:
Anlatım
11 Decision Trees, Game Trees Reading related chapter in lecture notes Öğretim Yöntemleri:
Anlatım
12 Spanning Tree Algorithms Reading related chapter in lecture notes Öğretim Yöntemleri:
Anlatım
13 Finite-State Machine and Automata Reading related chapter in lecture notes Öğretim Yöntemleri:
Anlatım
14 Context Free Language an Grammar Reading related chapter in lecture notes Öğretim Yöntemleri:
Anlatım
15 Review for Final exam Reading related chapter in lecture notes Öğretim Yöntemleri:
Anlatım
16 Final Exam Study to lecture notes and apllications Ölçme Yöntemleri:
Yazılı Sınav
17 Final Exam Study to lecture notes and apllications Ölçme Yöntemleri:
Yazılı Sınav


Student Workload - ECTS

Works Number Time (Hour) Workload (Hour)
Course Related Works
Class Time (Exam weeks are excluded) 14 3 42
Out of Class Study (Preliminary Work, Practice) 14 3 42
Assesment Related Works
Homeworks, Projects, Others 0 0 0
Mid-term Exams (Written, Oral, etc.) 1 12 12
Final Exam 1 18 18
Total Workload (Hour) 114
Total Workload / 25 (h) 4,56
ECTS 5 ECTS

Update Time: 23.06.2024 05:08