| MATHEMATICS (TURKISH, PHD) | |||||
| PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT1003 | Abstract Mathematics I | Fall | 3 | 2 | 4 | 6 |
| The course opens with the approval of the Department at the beginning of each semester |
| Language of instruction: | En |
| Type of course: | Departmental Elective |
| Course Level: | |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Instructor MAHMOUD JAFARI SHAH BELAGHI |
| Course Objectives: | To enable the student to obtain skills and logical perspectives that prepare them for subsequent courses inside the department,to understand and use the language and notation of mathematics, to communicate using mathematical language, to comprehend and construct mathematical arguments,to introduce fundamental concepts of mathematics which are essential for mathematical thinking and.to provide most common methods of mathematical proofs , to develop the mathematical maturity of the student,for further studies in mathematics. |
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The students who have succeeded in this course; The students who succeeded in this course; o will be able to describe prof methods. o will be able to conclude validity of propositions. o will be able to apply concepts of logic to proof methods. o will be able to formulate and develop mathematical statements. o will be able to distinguish mathematical implications. o will be able to adopt proof techniques to fundamental topics:set theory, graphs, correspondences, functions, relations, construct sets and relations of given property. o will be able to compare sets (with respect to cardinality etc. ),compare functions (with respect to injectivity, surjectivity, invertibility, the properties of image and preimage under them etc.),demonstrate basic abstract structures. |
| The language of mathematics. Theorems, Theory of logics. Statements and Proofs. Quantifiers. Sets. Product of sets. Correspondances and functions. Images under graphs and functions. Composite graphs and functions. Sections, retractions, injections and surjections. Relations. Equivalence and Ordering. Ordering. Partially ordering. Total ordering. Well ordering. Directed sets. Intervals. Axiom of choice. |
| Week | Subject | Related Preparation | |
| 1) | The language of mathematics. | ||
| 2) | Theorems, Theory of logics. | ||
| 3) | Statements and Proofs. | ||
| 4) | Quantifiers. | ||
| 5) | Sets. Product of sets. Graphs. | ||
| 6) | Correspondances and functions. | ||
| 7) | Union and Intersection of a family of sets, coverings and partitions. | ||
| 8) | Inverses of Graphs ,correspondances and functions. Images of the family of sets under graphs and functions. | ||
| 9) | Composite functions, graphs and correspondences. Sections, retractions,injections and surjections. | ||
| 10) | Product of a family of sets. | ||
| 11) | Relations.Equivalence relations. | ||
| 12) | Ordering. Partially ordering. Total ordering. | ||
| 13) | Well ordering. Directed sets. Intervals. | ||
| 14) | Axiom of choice. Summary of the course topics, directions and notices for the final exams. | ||
| 15) | Final exams. | ||
| 16) | Final exams. | ||
| Course Notes: | Naive Set Theory, Halmos P R, The Theory of Sets, Bourbaki N , Schaum’s Outline , Theory and Problems of Finite Mathematics, Seymour Lipschutz. |
| References: |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | % 0 | |
| Laboratory | % 0 | |
| Application | % 0 | |
| Field Work | % 0 | |
| Special Course Internship (Work Placement) | % 0 | |
| Quizzes | % 0 | |
| Homework Assignments | % 0 | |
| Presentation | % 0 | |
| Project | % 0 | |
| Seminar | % 0 | |
| Midterms | 2 | % 45 |
| Preliminary Jury | % 0 | |
| Final | 1 | % 55 |
| Paper Submission | % 0 | |
| Jury | % 0 | |
| Bütünleme | % 0 | |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 45 | |
| PERCENTAGE OF FINAL WORK | % 55 | |
| Total | % 100 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Special Course Internship (Work Placement) | 0 | 0 | 0 |
| Field Work | 0 | 0 | 0 |
| Study Hours Out of Class | 14 | 5 | 70 |
| Presentations / Seminar | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework Assignments | 0 | 0 | 0 |
| Quizzes | 0 | 0 | 0 |
| Preliminary Jury | 0 | ||
| Midterms | 2 | 2 | 4 |
| Paper Submission | 0 | ||
| Jury | 0 | ||
| Final | 1 | 2 | 2 |
| Total Workload | 118 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |