TÜRKÇE
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Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| MATHEMATICS PR. | |
| Code | MT312 |
| Name | Algebra IV |
| Term | 2018-2019 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, linear transformations which is determined by matrix groups in an inner space, certain special transformations and matrices to the students.
Course Content
In this course Matrix groups, Linear transformations which is determined by by matrix groups in an inner spaces, general linear groups and its algebraic properties, Hermitian transformations and Hermitian matices, Symmetric transformations and Symetric matices, Orthogonal matrices and Izometries are described.
Course Precondition
Resources
Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Recognizes the general linear groups and its algebraic properties. |
| LO02 | Recognizes Hermitian and symmetric linear transformations. |
| LO03 | Recognizes the unitary groups and its algebraic properties. |
| LO04 | Recognizes the unitary transformations. |
| LO05 | Recognizes the unitary groups and its algebraic properties. |
| LO06 | Recognizes the orthogonal transformations. |
| LO07 | Recognizes some relationships between orthogonal matrices and some special transformations. |
| LO08 | Recognizes the izometries. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | - | Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. | 5 |
| PLO02 | - | Understands importance of basic consepts of Algebra, Analaysis and Topology. | 5 |
| PLO03 | - | Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. | 4 |
| PLO04 | - | Demonstrate the ability to express the basic theories of mathematics both correctly. | 4 |
| PLO05 | - | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | 5 |
| PLO06 | - | Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem. | 3 |
| PLO07 | - | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | 3 |
| PLO08 | - | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | 5 |
| PLO09 | - | Comprehends at least one of the computer programming languages. | 0 |
| PLO10 | - | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | 0 |
| PLO11 | - | Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians | 0 |
| PLO12 | - | In addition to their professional development, they demonstrate their ability to continuously improve themselves by identifying their educational needs in scientific, cultural, artistic and social areas in line with their interests and abilities. | 0 |
| PLO13 | - | Understands the programming techniques and shows the ability to do programming. | 0 |
| PLO14 | - | Demonstrates the ability to study mathematics both independently and as a group. | 0 |
| PLO15 | - | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | |
| PLO16 | - | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | |
| PLO17 | - | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | |
| PLO18 | - | Gains the ability to use information technologies effectively for contemporary mathematical applications. | |
| PLO19 | - | Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields. | |
| PLO20 | - | Gains the consciousness of prefesional ethics and responsibility. |
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 | Real Linear groups | Required readings | |
| 5 | Hermitian transformations and Hermitian matrices | Required readings | |
| 6 | Symmetric transformations and symmetric matrices | Required readings | |
| 7 | Inner spaces with finite dimension over a field or skew field | Required readings | |
| 8 | Mid-Term Exam | Review of the topics discussed in the lecture notes and sources again | |
| 9 | Uniter transformations and uniter matrices | Required readings | |
| 10 | Orthogonal transformations and orthogonal matrices | Required readings | |
| 11 | Invariant subspaces | Required readings | |
| 12 | Isometries | Required readings | |
| 13 | Self-adjoint transformations | Required readings | |
| 14 | Dual spaces | Required readings | |
| 15 | Certain transformations on dual spaces | Required readings | |
| 16 | Term Exams | Review of the topics discussed in the lecture notes and sources again | |
| 17 | Term Exams | Review of the topics discussed in the lecture notes and sources again |
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 |