Mathematics (English) | |||||
Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 |
Course Code: | MATH262 | ||||
Course Name: | Axiomatic Set Theory 2 | ||||
Semester: | Spring | ||||
Course Credits: |
|
||||
Language of instruction: | English | ||||
Course Condition: | |||||
Does the Course Require Work Experience?: | No | ||||
Type of course: | Compulsory Courses | ||||
Course Level: |
|
||||
Mode of Delivery: | Face to face | ||||
Course Coordinator: | Prof. Dr. SELÇUK DEMİR | ||||
Course Lecturer(s): | Prof. Dr. Selçuk Demir | ||||
Course Assistants: |
Course Objectives: | The course aims to introduce the axiom of choice, Zorn Lemma and some of their equivalents, to further develop the abılty to make and write complete proofs. |
Course Content: | The content of the course consists of well-ordered sets, axiom of choice, Zorn lemma, their applications and the abilty to organize and write complete proofs. |
The students who have succeeded in this course;
1) will understand well-odered sets and their properties. 2) will understand axiom of choice and some of its equivalents like Zorn lemma and they will be able to use them to create proofs. 3) will develop their ability to write complete proofs to a higher level. |
Week | Subject | Related Preparation |
1) | Orders | |
2) | Well-ordered sets | |
3) | Transfinite induction | |
4) | Zermelo’s Theorem | |
5) | Transfinite induction and Hamel basis | |
6) | Zorn’s Lemma and its application | |
7) | Operations on cardinals revisited | |
8) | Midterm Exam | |
9) | Ordinals | |
10) | Ordinal arithmetic | |
11) | Recursive definitions and exponentiation | |
12) | Application of ordinals | |
13) | More equivalents of axiom of choice, | |
14) | Review |
Course Notes / Textbooks: | ders notları |
References: | A. Nesin: Set Theory lecture notes |
Course Learning Outcomes | 1 |
2 |
3 |
||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Program Outcomes | |||||||||||
1) Have the knowledge of the scope, history, applications, problems, methods of mathematics and knowledge that will be beneficial to humanity as both scientific and intellectual discipline. | |||||||||||
2) Have the ability to establish a relationship between mathematics and other disciplines and develop mathematical models for interdisciplinary problems. | |||||||||||
3) Have the ability to define, formulate and analyze real life problems with statistical and mathematical techniques. | |||||||||||
4) Have the ability to think analytically and use the time effectively in the process of deduction. | |||||||||||
5) Have the ability to search the literature, understand and interpret scientific articles. | |||||||||||
6) Have the knowledge of basic software to be able to work in the related fields of computer science and have the ability to use information technologies at an advanced level of the European Computer Driving License. | |||||||||||
7) Have the ability to work efficiently in interdisciplinary teams. | |||||||||||
8) Have the ability to communicate effectively in oral and written form, write effective reports and comprehend the written reports, make effective presentations. | |||||||||||
9) Have the consciousness of professional and ethical responsibility and acting ethically; have the knowledge about academic standards. | |||||||||||
10) Have the ability to use a foreign language at least at B1 level in terms of European Language Portfolio criteria. | |||||||||||
11) Are aware of the necessity of lifelong learning; have the ability to access information, to follow developments in science and technology and to constantly renew themselves. |
No Effect | 1 Lowest | 2 Average | 3 Highest |
Program Outcomes | Level of Contribution | |
1) | Have the knowledge of the scope, history, applications, problems, methods of mathematics and knowledge that will be beneficial to humanity as both scientific and intellectual discipline. | 2 |
2) | Have the ability to establish a relationship between mathematics and other disciplines and develop mathematical models for interdisciplinary problems. | |
3) | Have the ability to define, formulate and analyze real life problems with statistical and mathematical techniques. | |
4) | Have the ability to think analytically and use the time effectively in the process of deduction. | 3 |
5) | Have the ability to search the literature, understand and interpret scientific articles. | |
6) | Have the knowledge of basic software to be able to work in the related fields of computer science and have the ability to use information technologies at an advanced level of the European Computer Driving License. | |
7) | Have the ability to work efficiently in interdisciplinary teams. | |
8) | Have the ability to communicate effectively in oral and written form, write effective reports and comprehend the written reports, make effective presentations. | |
9) | Have the consciousness of professional and ethical responsibility and acting ethically; have the knowledge about academic standards. | |
10) | Have the ability to use a foreign language at least at B1 level in terms of European Language Portfolio criteria. | 3 |
11) | Are aware of the necessity of lifelong learning; have the ability to access information, to follow developments in science and technology and to constantly renew themselves. | 3 |
Semester Requirements | Number of Activities | Level of Contribution |
Midterms | 1 | % 40 |
Final | 1 | % 60 |
total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 40 | |
PERCENTAGE OF FINAL WORK | % 60 | |
total | % 100 |
Activities | Number of Activities | Preparation for the Activity | Spent for the Activity Itself | Completing the Activity Requirements | Workload | ||
Course Hours | 13 | 0 | 4 | 52 | |||
Application | 13 | 0 | 0 | ||||
Study Hours Out of Class | 13 | 0 | 4 | 52 | |||
Midterms | 1 | 0 | 15 | 15 | |||
Final | 1 | 0 | 25 | 25 | |||
Total Workload | 144 |