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Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| MATHEMATICS PR. | |
| Code | MT414 |
| Name | Advanced Linear Algebra |
| Term | 2020-2021 Academic Year |
| Semester | 8. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Label | E Elective |
| Mode of study | Uzaktan Öğretim |
| Catalog Information Coordinator | Dr. Öğr. Üyesi ELA AYDIN |
| Course Instructor |
Dr. Öğr. Üyesi ELA AYDIN
(Bahar)
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
The course covers issues related to vector spaces, linear functions , iner product spaces, dual spaces and double duals and find the diagonalizations and Jordan form of matrices.
Course Content
The concept of this course is Give elementary knowledge about vector spaces,The algebra of Linear Transformations, Inner product spaces, Isometries between vector spaces. Finding Dual vector spaces and double dual, Determine Annihilators of vector spaces, Relationship between functionals and linear systems, Representation of Linear Transformations by matrices. Invariant subspaces, To compute triangular, diagonal and Jordan canonical forms.
Course Precondition
Resources
Prof. Dr. H. Hilmi HACISALİHOĞLU," Lineer Cebir", Gazi Üniversitesi Yayın No: 152, 1985.
Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Know basics about vector spaces. |
| LO02 | Understand the independence between linear functions and matrices. |
| LO03 | Find diagonal form of linear functions and matrices. |
| LO04 | Find dual and double dual of vector spaces. |
| LO05 | Find the annihilator of subspaces and its bases. |
| LO06 | Define embedding from a space to another. |
| LO07 | Find transpoze of linear function. |
| LO08 | Find the Jordan form of linear function. |
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. | 2 |
| PLO04 | - | Demonstrate the ability to express the basic theories of mathematics both correctly. | 1 |
| PLO05 | - | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | 1 |
| 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. | 5 |
| PLO08 | - | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | 4 |
| 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 | Vector spaces and find their basis | Review of the relevant pages from sources | |
| 2 | İınner products and inner product spaces | Review of the relevant pages from sources | |
| 3 | Orthonormal basis | Review of the relevant pages from sources | |
| 4 | Linear Operations and embeddings | Review of the relevant pages from sources | |
| 5 | Linear functionals and dual basis | Review of the relevant pages from sources | |
| 6 | Double duals and annihilators | Review of the relevant pages from sources | |
| 7 | Homogen systems and linear functionals | Review of the relevant pages from sources | |
| 8 | Mid-Term Exam | Review of the topics discussed in the lecture notes and sources | |
| 9 | Transpose of Linear functions | Review of the relevant pages from sources | |
| 10 | Polynomial algebras | Review of the relevant pages from sources | |
| 11 | Representation of linear transformations by matrices and diagonalizations | Review of the relevant pages from sources | |
| 12 | Invariant subspaces | Review of the relevant pages from sources | |
| 13 | Direct sums | Review of the relevant pages from sources | |
| 14 | Jordan form and aplications | Review of the relevant pages from sources | |
| 15 | Solving Problems, final exam | Review of the relevant pages from sources | |
| 16 | Term Exams | Review of the topics discussed in the lecture notes and sources | |
| 17 | Term Exams | Review of the topics discussed in the lecture notes and sources |
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 |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 114 | ||
| Total Workload / 25 (h) | 4,56 | ||
| ECTS | 5 ECTS | ||