TÜRKÇE
ENGLISH
Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| MATHEMATICS PR. | |
| Code | MTS384 |
| Name | Lattice Theory |
| Term | 2020-2021 Academic Year |
| Semester | 6. Semester |
| Duration (T+A) | 2-0 (T-A) (17 Week) |
| ECTS | 3 ECTS |
| National Credit | 2 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Label | E Elective |
| Mode of study | Uzaktan Öğretim |
| Catalog Information Coordinator | Doç. Dr. DİLEK ERSALAN |
| Course Instructor |
Doç. Dr. DİLEK ERSALAN
(Bahar)
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
Students recognize some basic definitions,examples, theorems and problems about Lattices.
Course Content
Some basic definitions and examples about Lattices, Isomorphic Lattices and sublattices, Distributive and Modular Lattices, Comlete and Algebraic Lattices, Closure Operators.
Course Precondition
Resources
A course in universal algebra, Stanley Burris, H.P. Sankappanavar
Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Recognizes the Lattices and its examples. |
| LO02 | Recognizes the isomorphic Lattices, sublattices and their examples |
| LO03 | Recognizes the Distributive and Modular Lattices and their examples. |
| LO04 | Recognizes the Complete and Algebraic Lattices and their examples. |
| LO05 | Recognizes the Closure operators of Lattices. |
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. | 1 |
| 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. | 5 |
| PLO04 | - | Demonstrate the ability to express the basic theories of mathematics both correctly. | 5 |
| 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. | 2 |
| PLO07 | - | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | 4 |
| PLO08 | - | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | 2 |
| 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. | 4 |
| 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. | 5 |
| 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 | Definitions of lattices and examples | Required readings | |
| 2 | Definitions of lattices and examples | Required readings | |
| 3 | Isomorphic Lattices, and Sublattices | Required readings | |
| 4 | Distributive and Modular Lattices | Required readings | |
| 5 | Distributive and Modular Lattices | Required readings | |
| 6 | Complete Lattices, Equivalence Relations, and Algebraic Lattices | Required readings | |
| 7 | Closure Operators | Required readings | |
| 8 | Mid-Term Exam | Summary | |
| 9 | Closure Operators | Required readings | |
| 10 | Definitions of universal algebra and examples | Required readings | |
| 11 | Definitions of universal algebra and examples | Required readings | |
| 12 | Isomorphic Algebras, and Subalgebras | Required readings | |
| 13 | Algebraic Lattices and basis theorem | Required readings | |
| 14 | Algebraic Lattices and basis theorem | Required readings | |
| 15 | Solving problems | Required readings | |
| 16 | Term Exams | summary | |
| 17 | Term Exams | summary |
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 | 2 | 28 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 2 | 28 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 6 | 6 |
| Final Exam | 1 | 16 | 16 |
| Total Workload (Hour) | 78 | ||
| Total Workload / 25 (h) | 3,12 | ||
| ECTS | 3 ECTS | ||