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Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| MATHEMATICS PR. | |
| Code | MT312 |
| Name | Algebra IV |
| Term | 2017-2018 Academic Year |
| Semester | 6. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Üniversite Dersi |
| Type | Normal |
| Label | C Compulsory |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. LEYLA BUGAY |
| Course Instructor |
Doç. Dr. LEYLA BUGAY
(Bahar)
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
The aim of this course is to teach the matrix groups with algebraic viewpoints and to teach linear transformations which is determined by matrix groups in an inner space.
Course Content
Matrix groups, Linear transformations which is determined by by matrix groups in an inner spaces
Course Precondition
Resources
Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | - | Is able to prove Mathematical facts encountered in secondary school. | |
| PLO02 | - | Recognizes the importance of basic notions in Algebra, Analysis and Topology | |
| PLO03 | - | Develops maturity of mathematical reasoning and writes and develops mathematical proofs. | |
| PLO04 | - | Is able to express basic theories of mathematics properly and correctly both written and verbally | |
| PLO05 | - | Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. | |
| PLO06 | - | Expresses clearly the relationship between objects while constructing a model | |
| PLO07 | - | Draws mathematical models such as formulas, graphs and tables and explains them | |
| PLO08 | - | Is able to mathematically reorganize, analyze and model problems encountered. | |
| PLO09 | - | Knows at least one computer programming language | |
| PLO10 | - | Uses effective scientific methods and appropriate technologies to solve problems | |
| PLO11 | - | Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians | |
| PLO12 | - | In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields | |
| PLO13 | - | Knows programming techniques and is able to write a computer program | |
| PLO14 | - | Is able to do mathematics both individually and in a group. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Field, Skew field and Quaternions | Required readings | |
| 2 | Matrices and Linear transformations | Required readings | |
| 3 | The general Linear groups | Required readings | |
| 4 | All matrix groups are real linear groups | Required readings | |
| 5 | Hermitian transformations and Hermitian matices | Required readings | |
| 6 | Symmetric transformations and Symmetric matices | Required readings | |
| 7 | Inner spaces with finite dimension over a field or skew field | Required readings | |
| 8 | Mid-term exam | Summary | |
| 9 | Uniter group and transformations | Required readings | |
| 10 | Orthogonal group and transformations | Required readings | |
| 11 | Invariant subspaces and orthogonal groups | Required readings | |
| 12 | Orthogonal matrices and isometries | Required readings | |
| 13 | Self-adjoint transformations and orthogonal groups | Required readings | |
| 14 | Orthogonal transformations on dual spces | Required readings | |
| 15 | Orthogonal transformations on dual spces | Required readings | |
| 16 | Final exam | ||
| 17 | Final exam |
Assessment (Exam) Methods and Criteria
| Assessment Type | Midterm / Year Impact | End of Term / End of Year Impact |
|---|---|---|
| 1. Midterm Exam | 100 | 40 |
| General Assessment | ||
| Midterm / Year Total | 100 | 40 |
| 1. Final Exam | - | 60 |
| Grand Total | - | 100 |