| MATHEMATICS (TURKISH, PHD) | |||||
| PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| FİZ6034 | General Theory of Relativity | Spring | 3 | 0 | 3 | 8 |
| The course opens with the approval of the Department at the beginning of each semester |
| Language of instruction: | Tr |
| Type of course: | Departmental Elective |
| Course Level: | |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Prof. Dr. SARPER ÖZHARAR |
| Course Objectives: | Theory of Relativity together with Quantum Physics, are fundamental concepts that shaped the 20th century. Therefore, the aim of this class is to give students a new perspective towards the working dynamics of the universe as a whole while using mathematics as a tool. |
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The students who have succeeded in this course; Successful students will be able to: 1- realize there are more than one perspectives to physical events. 2- model mathematical the law of gravity that holds the universe together 3- know that the mass bends the universe 4- know how the speed of light defines the structure of the universe 5- prove mathematically the existence of black holes and practice the mathematics on Einstein’s equations. |
| Special relativity, space-time coordinates and transformations, energy-matter relation |
| Week | Subject | Related Preparation | |
| 1) | Distance in metric spaces, and Euclidian Spaces | ||
| 2) | MINKOWSKI SPACE, COVARIANCE VE CONTRAVARIANCE | ||
| 3) | GENERAL COORDİNATE TRANSFORMS, SPACE-TIME DEPENDENT SPACES | ||
| 4) | COVARIANT DERIVATIVE, AFİN CONNECTIONS | ||
| 5) | UNDERSTANDING CURVES, PARALLEL SHIFTING | ||
| 6) | GEODESIC: DEFINITION AND CONCEPT | ||
| 7) | COVARIANT MAXWELL’S THEORY IN 4 DIMENSIONAL SPACE | ||
| 8) | EXISTENCE OF MATTER AND ENERGY TENSOR | ||
| 9) | NEWTONIAN MECHANICS AND GALILEAN COVARIANT | ||
| 10) | FUNDAMENTALS OF EINSTEIN'S SPECIAL RELATIVITY | ||
| 11) | UNDERSTANDING ALGEBRAIC STRUCTURE OF LORENTZ TRANSFORMATIONS | ||
| 12) | PRINCIPLE OF SPEED OF LIGHT AND RELATIVISTIC INVARIANT | ||
| 13) | TO MAKE AN INVARIANT THEORY UNDER GENERAL COORDINATE TRANSFORMS | ||
| 14) | GEOMETRICAL VIEW ON FORCE OR A SIMPLE INTRODUCTION TO EINSTEIN’S GENERAL RELATIVITY | ||
| Course Notes: | General Relativity, An Introduction for Physicists, M. P. Hobson, G. P. Efstathiou and A. N. Lasenby, Cambridge Univ. Press , 2006 |
| References: | Introducing Einstein’ s Relativity, Ray D’ Inverno, Oxford Univ. Press, 1998 |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | % 0 | |
| Laboratory | % 0 | |
| Application | % 0 | |
| Field Work | % 0 | |
| Special Course Internship (Work Placement) | % 0 | |
| Quizzes | % 0 | |
| Homework Assignments | % 0 | |
| Presentation | % 0 | |
| Project | % 0 | |
| Seminar | % 0 | |
| Midterms | 1 | % 40 |
| Preliminary Jury | % 0 | |
| Final | 1 | % 60 |
| Paper Submission | % 0 | |
| Jury | % 0 | |
| Bütünleme | % 0 | |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 40 | |
| PERCENTAGE OF FINAL WORK | % 60 | |
| Total | % 100 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Special Course Internship (Work Placement) | 0 | 0 | 0 |
| Field Work | 0 | 0 | 0 |
| Study Hours Out of Class | 14 | 6 | 84 |
| Presentations / Seminar | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework Assignments | 0 | 0 | 0 |
| Quizzes | 0 | 0 | 0 |
| Preliminary Jury | 0 | ||
| Midterms | 1 | 30 | 30 |
| Paper Submission | 0 | ||
| Jury | 0 | ||
| Final | 1 | 44 | 44 |
| Total Workload | 200 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution | |
| 1) | Ability to assimilate mathematic related concepts and associate these concepts with each other. | |
| 2) | Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization. | |
| 3) | Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques. | |
| 4) | Ability to make individual and team work on issues related to working and social life. | |
| 5) | Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball. | |
| 6) | Ability to use mathematical knowledge in technology. | |
| 7) | To apply mathematical principles to real world problems. | |
| 8) | Ability to use the approaches and knowledge of other disciplines in Mathematics. | |
| 9) | Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary. | |
| 10) | To be able to link abstract thought that one has to concrete events and to transfer the solutions and examine and interpret the results scientifically by forming experiments and collecting data. | |
| 11) | To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively. | |
| 12) | To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself. |