# Basic Logic and Algebra (MATH111) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Basic Logic and Algebra MATH111 3 0 0 3 6
Pre-requisite Course(s)
None
Course Language English N/A Bachelor’s Degree (First Cycle) Face To Face Lecture, Question and Answer. To provide an introduction to logic, number theory and groups, rings and fields through examples. Moreover to encourage the students to investigate proofs of some algebraic expressions and theorems. The students who succeeded in this course; write a statement using logical expressions, evaluate logical expressions and perform the basic operations on sets, prove some mathematical statements and theorems, determine whether a relation is an equivalence relation or not, understand and use divisibility and the Euclidean Algorithm, know elementary definitions and examples in groups, rings, and fields. Logic, sets, induction, relations, functions, elementary number theory, elementary examples of groups, rings and fields, the real numbers.

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Logical Form and Logical Equivalence, Truth Tables, Conditional Statements, pp. 1-17
2 Valid and Invalid Arguments, Rules of Inferences, pp. 17-43
3 Introduction to Predicates and Quantified Statements pp. 75-97
4 Methods of Proofs (Direct Proof and Counter Example I/II/III: Introduction/ Rational Numbers/Divisibility) pp. 133,145,151, pp. 175-177,181
5 Elemantary Number Theory: Unique Factorization Theorem, Division into Cases s. 153,157
6 Elemantary Number Theory: The Quotient-Remainder Theorem,The Euclidean Algorithm pp. 162,192
7 Mathematical Induction pp. 217,220,229
8 Sets, Subsets, Set Operations, Power sets pp. 255 ,265, pp. 272,273,277
9 Relations on sets pp. 571-578,584, 585
10 Equivalence Classes p. 597,599
11 Functions Defined on a General Set pp. 389-402
12 One-to-One, Onto and Inverse Functions, Compositions of Functions pp. 403,408,407, pp. 415,432
13 Real Numbers, Binary Operations
14 Definitions and Elementary Examples of Groups, Rings and Fields
15 Review
16 Final Exam

### Sources

Course Book 1. Epp, Susanna S., Discrete Mathematics with Applications, 2nd Edition, Pacific Grove, CA, Brooks/Cole, 1995 2. Chapter Zero, Schumacher,C., Fundamental Notions of Abstract Mathematics, 2nd Edition, Addison-Wesley, 2001

### Evaluation System

Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics 5 6
Homework Assignments 7 7
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 2 52
Final Exam/Final Jury 1 35
Toplam 15 100
 Percentage of Semester Work 65 35 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area X
2 Can apply gained knowledge and problem solving abilities in inter-disciplinary research X
3 Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary X
4 Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study X
5 Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework X
6 Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility X
7 Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation X
8 To have an oral and written communication ability in at least one of the common foreign languages ("European Language Portfolio Global Scale", Level B2) X
9 Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge X
10 Follows scientific, cultural, and ethical criteria in collecting, interpreting and announcing data in the research area and has the ability to teach. X
11 Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. X

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 14 4 56
Presentation/Seminar Prepration
Project
Report
Homework Assignments 5 4 20
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 2 8 16
Prepration of Final Exams/Final Jury 1 10 10