| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Introductıon To Algebra | IME 309 | 5 | 3 + 1 | 4 | 7 |
| Ön Koşul Dersleri | |
| Önerilen Seçmeli Dersler | |
| Dersin Dili | Türkçe |
| Dersin Seviyesi | Lisans |
| Dersin Türü | Zorunlu |
| Dersin Koordinatörü | Doç.Dr. ERCAN MASAL |
| Dersi Verenler | Doç.Dr. ERCAN MASAL, |
| Dersin Yardımcıları | Res.Assist.Mithat TAKUNYACI |
| Dersin Kategorisi | Alanına Uygun Temel Öğretim |
| Dersin Amacı | To give detailed information to students of elementary education about binary operations which are on many fields of mathematics. To introduce algebraic structure as group, subgroup, ring, subring, ideal which set up a theoretical substructure of especially linear algebra by the help of binary operations and give main group, varieties of subgroup |
| Dersin İçeriği | Binary operations, definition of group, subgroups, permutation groups, homomorphism, cyclic groups, residue classes, normal subgroups, quotient groups, definition of ring, subrings, ideals. |
| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 1 | Explain detailed information about binary operations, show properties of a given operatione | Lecture, Drilland Practice, | Testing, Homework, |
| 2 | Define subgroup and theorems related subgroup and apply them to problems. | Lecture, Drilland Practice, | Testing, Homework, |
| 3 | Explain the definition of rank of a element and solve the problems related rank. | Lecture, Drilland Practice, | Testing, Homework, |
| 4 | Explain theorem of normal subgroup and demonstrate a subgroup is whether normal subgroup or not. | Lecture, Drilland Practice, | Testing, Homework, |
| 5 | Explain definition of group homeomorphism, express theorem of isomorphism. Demonstrate core of a homeomorphism. Solve the problems related homeomorphism | Lecture, Drilland Practice, | Testing, Homework, |
| 6 | Express the concept of ring, demonstrate that algebraic structure is whether ring or not | Lecture, Drilland Practice, | Testing, Homework, |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 1 | Binary operation and concept of group | |
| 2 | Examples of group | |
| 3 | Theorems of subgroup and their applications | |
| 4 | Cyclic groups and their applications | |
| 5 | Rank of a element and its applications, dihedral group | |
| 6 | Residue class, Lagrange Theorem and quotient group | |
| 7 | Normal subgroups and their applications | |
| 8 | Group homeomorphism and theores of isomorphism | |
| 9 | Mid – Term Exam | |
| 10 | Applications of homeomorphism | |
| 11 | Permutation groups | |
| 12 | Ring and its applications | |
| 13 | Subring and ideals | |
| 14 | Ring homeomorphism |
| Kaynaklar | |
|---|---|
| Ders Notu | |
| Ders Kaynakları | |
| Sıra | Program Çıktıları | Katkı Düzeyi | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Have general information about basic concept, theory and applicaitons on mathematics | X | |||||
| 2 | Have ability of mathematical thinking and apply to real life | X | |||||
| 3 | Classify a problem systematically also create comprehensible, understandable and objective solutions | X | |||||
| 4 | Establish relationship among events looked different | X | |||||
| 5 | Get clear and exact ideas about relationships among time, place and numbers | X | |||||
| 6 | Use principles of scientific method on problem solving | X | |||||
| 7 | Have character on explorer, impartial, disinterested, give sound decisions, open mind and believe that spreading information is needed | X | |||||
| 8 | Think creative and critical | X | |||||
| 9 | Improve methods as fast, understandable and practical to faced problems | X | |||||
| 10 | Have information about national and international modern problems | ||||||
| 11 | Get life long learning behaviour | ||||||
| 12 | Know and apply approach, aim, goal, principle and techniques of teaching program on special field with basic value and principles of Turkish National Education System | ||||||
| 13 | Evaluate development and learning of students, provide to evaluate self-assessment and other students. Use the assessment results to better instruction; share the results with student, parent, administrators and teachers. | ||||||
| 14 | Endeavor for constant development by making self-evaluation. Open the new knowledge and ideas, have a role to develop himself/herself and his/her institution. Have enough knowledge and conscious to protection subjects on society values and environment. | ||||||
| 15 | Interrogator ( get habit to find source of knowledge by asking “Why?” question instead of direct acceptance to given knowledges ) | X | |||||
| Değerlendirme Sistemi | |
|---|---|
| Yarıyıl Çalışmaları | Katkı Oranı |
| 1. Ara Sınav | 60 |
| 1. Kısa Sınav | 15 |
| 1. Ödev | 10 |
| 2. Kısa Sınav | 15 |
| Toplam | 100 |
| 1. Yıl İçinin Başarıya | 50 |
| 1. Final | 50 |
| Toplam | 100 |
| AKTS - İş Yükü Etkinlik | Sayı | Süre (Saat) | Toplam İş Yükü (Saat) |
|---|---|---|---|
| Course Duration (Including the exam week: 16x Total course hours) | 16 | 4 | 64 |
| Hours for off-the-classroom study (Pre-study, practice) | 16 | 3 | 48 |
| Mid-terms | 1 | 10 | 10 |
| Quiz | 2 | 3 | 6 |
| Assignment | 1 | 20 | 20 |
| Performance Task (Laboratory) | 1 | 30 | 30 |
| Toplam İş Yükü | 178 | ||
| Toplam İş Yükü / 25 (Saat) | 7,12 | ||
| Dersin AKTS Kredisi | 7 | ||