ECTS - Basic Logic and Algebra
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 | 1. Semester | 3 | 0 | 0 | 3 | 6 |
| Pre-requisite Course(s) |
|---|
| N/A |
| Course Language | English |
|---|---|
| Course Type | Compulsory Departmental Courses |
| Course Level | Bachelor’s Degree (First Cycle) |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Question and Answer. |
| Course Lecturer(s) |
|
| Course Objectives | 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. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | 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 |
|---|---|
| Other Sources | 2. Chapter Zero, Schumacher,C., Fundamental Notions of Abstract Mathematics, 2nd Edition, Addison-Wesley, 2001 |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| 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 |
|---|---|
| Percentage of Final Work | 35 |
| Total | 100 |
Course Category
| Core Courses | |
|---|---|
| Major Area Courses | |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
| # | Program Qualifications / Competencies | Level of Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Acquires skills to use the advanced theoretical and applied knowledge obtained at the mathematics bachelors program to do further academic and scientific research in both mathematics-based graduate programs and public or private sectors. | X | ||||
| 2 | Transplants and applies the theoretical and applicable knowledge gained in their field to the secondary education by using suitable tools and devices. | X | ||||
| 3 | Acquires the skill of choosing, using and improving problem solving techniques which are needed for modeling and solving current problems in mathematics or related fields by using the obtained knowledge and skills. | X | ||||
| 4 | Acquires analytical thinking and uses time effectively in the process of deduction | X | ||||
| 5 | Acquires basic software knowledge necessary to work in the computer science related fields and together with the skills to use information technologies effectively. | X | ||||
| 6 | Obtains the ability to collect data, to analyze, interpret and use statistical methods necessary in decision making processes. | X | ||||
| 7 | Acquires the level of knowledge to be able to work in the mathematics and related fields and keeps professional knowledge and skills up-to-date with awareness in the importance of lifelong learning. | X | ||||
| 8 | Takes responsibility in mathematics related areas and has the ability to work affectively either individually or as a member of a team. | X | ||||
| 9 | Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields. | X | ||||
| 10 | Has the ability to communicate ideas with peers supported by qualitative and quantitative data. | X | ||||
| 11 | Has professional and 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 | ||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | 16 | 3 | 48 |
| 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 |
| Total Workload | 150 | ||