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 | 3 | 0 | 0 | 3 | 6 |
| Pre-requisite Course(s) |
|---|
| None |
| Course Language | English |
|---|---|
| Course Type | N/A |
| 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 | X |
|---|---|
| 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 | 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 | ||||
ECTS/Workload Table
| 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 |
| Total Workload | 102 | ||