ECTS - Mathematical Logic
Mathematical Logic (MATH365) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Mathematical Logic | MATH365 | Elective Courses | 3 | 0 | 0 | 3 | 6 |
| Pre-requisite Course(s) |
|---|
| MATH 136 Mathematical Analysis II or MATH 152 Calculus II or MATH 158 Extended Calculus II or Consent of the instructor |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Bachelor’s Degree (First Cycle) |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Question and Answer, Problem Solving. |
| Course Lecturer(s) |
|
| Course Objectives | The objective of the course is to study basic notions of Approximation Theory. Approximation Theory not only provides theoretical foundations for Applied Mathematics, Numerical Analysis, and Scientific Computing, but also gives methods to solve practical problems of computation. The course is for students of mathematical and engineering departments interested in analysis and its applications to numerical computations. |
| Course Learning Outcomes |
The students who succeeded in this course;
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| Course Content | No data provided |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Metric spaces. Normed linear spaces. The space C[a,b]. Inner-product spaces. The Gram-Schmidt process. | [1] Ch. I, pp. 3-16 |
| 2 | Convex sets. Caratheodory’s theorem. | [1] Ch. 1, pp. 16-20 |
| 3 | Convex functions: local and absolute extrema, continuity. Existence and unicity of the best approximation. | [1] Ch. I, pp. 20 - 27 |
| 4 | A minimax solution of a linear system. Inconsistent systems of linear equations with one unknown, their graphical solution. | [1] Ch. 2, pp. 28 – 33 |
| 5 | Characterization of Chebychev solutions. The ascent and descent algorithms. | [1] Ch. 2, pp. 34-37, pp. 45-56 |
| 6 | Lagrange interpolation polynomial. Error formula. Hermite interpolation. | [1] Ch. 3, pp. 57-60, 62-65 |
| 7 | Review and Midterm I | |
| 8 | The Weierstrass approximation theorem. | [1] Ch. 3, pp. 61 - 67 |
| 9 | Monotone operators. Korovkin’s theorem. | [1] Ch. 3, pp. 65-71 |
| 10 | Bernstein polynomials. | [3] Ch. VI, pp. 108-111 |
| 11 | Polynomials of the best approximation. Alternation theorem. Orthogonal systems of polynomials, their properties. | [1] Ch. 3, pp. 72-77, Ch. 4, pp. 101 - 105 |
| 12 | Review and Midterm II | |
| 13 | Uniform and least-squares convergence, Christoffel-Darboux identity, Bessel Inequality | [1] Ch. 4, pp. 115 - 119 |
| 14 | Convergence of Fourier series, Fejer’s theorem. | [1] Ch. 4, pp. 120 - 125 |
| 15 | Review | |
| 16 | Final exam. |
Sources
| Course Book | 1. [1] E.W. Cheney. Introduction to Approximation Theory. Chelsea Publ. |
|---|---|
| Other Sources | 2. [2] G. G. Lorentz, Approximation of Functions, AMS Chelsea publishing, 1986. |
| 3. [3] P. J. Davis, Interpolation and Approximation, Dover Publications, 1975 |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 4 | 20 |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 2 | 40 |
| Final Exam/Final Jury | 1 | 40 |
| Toplam | 7 | 100 |
| Percentage of Semester Work | 60 |
|---|---|
| Percentage of Final Work | 40 |
| Total | 100 |
Course Category
| Core Courses | X |
|---|---|
| Major Area Courses | |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
| # | Program Qualifications / Competencies | Level of Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Acquires skills to use the advanced theoretical and applied knowledge obtained at the mathematics bachelors program to do further academic and scientific research in both mathematics-based graduate programs and public or private sectors. | X | ||||
| 2 | Transplants and applies the theoretical and applicable knowledge gained in their field to the secondary education by using suitable tools and devices. | X | ||||
| 3 | Acquires the skill of choosing, using and improving problem solving techniques which are needed for modeling and solving current problems in mathematics or related fields by using the obtained knowledge and skills. | X | ||||
| 4 | Acquires analytical thinking and uses time effectively in the process of deduction | X | ||||
| 5 | Acquires basic software knowledge necessary to work in the computer science related fields and together with the skills to use information technologies effectively. | X | ||||
| 6 | Obtains the ability to collect data, to analyze, interpret and use statistical methods necessary in decision making processes. | X | ||||
| 7 | Acquires the level of knowledge to be able to work in the mathematics and related fields and keeps professional knowledge and skills up-to-date with awareness in the importance of lifelong learning. | X | ||||
| 8 | Takes responsibility in mathematics related areas and has the ability to work affectively either individually or as a member of a team. | X | ||||
| 9 | Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields. | X | ||||
| 10 | Has the ability to communicate ideas with peers supported by qualitative and quantitative data. | X | ||||
| 11 | Has professional and ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. | X | ||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | |||
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 16 | 3 | 48 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 4 | 10 | 40 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 12 | 24 |
| Prepration of Final Exams/Final Jury | 1 | 18 | 18 |
| Total Workload | 130 | ||