ECTS - Mathematical Logic
Mathematical Logic (MATH365) Course Detail
Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
---|---|---|---|---|---|---|---|
Mathematical Logic | MATH365 | 3 | 0 | 0 | 3 | 6 |
Pre-requisite Course(s) |
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MATH 136 Mathematical Analysis II or MATH 152 Calculus II or MATH 158 Extended Calculus II or Consent of the instructor |
Course Language | English |
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Course Type | N/A |
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) |
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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 |
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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. |
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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 |
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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 |
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Percentage of Final Work | 40 |
Total | 100 |
Course Category
Core Courses | X |
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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 | ||||
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1 | 2 | 3 | 4 | 5 | ||
1 | Skills to understand, compare and paraphrase the basic concepts of law as a jurist following common principles of law. | |||||
2 | Skills to solve problems using a critical point of view when necessary , to determine and analyse the theoretical and implementation problems of law. | |||||
3 | Contribution to understanding, planning, exercising and coordinating the functionss of law, by explaining and practising. | |||||
4 | Skills to understand the strategic, tactical and practical sides of private and public law. | |||||
5 | Skills to understand the local, national, international, universal and supranational sides of private and public law. | |||||
6 | Skills to understand the modern methods and differences of law. | |||||
7 | Skills to participate in/inter disciplinary group works succesfully. | |||||
8 | Skills to adopt open minded behaviors in the way of learning and attempting. | |||||
9 | Skills to assimilate and carry the rules of ethics and profession within the framework of social responsibility | |||||
10 | Skills to use Turkish efficiently in writing and speaking, and have the communication talent that is required by a law related career. | |||||
11 | Skills to approach critically and creativly on the legal and social problems in terms of rule of law and ideal of justice. | |||||
12 | Skills to understand and practice the national and international sides of law through caselaw and judical implementations. | |||||
13 | Skills to prepare/present a written or oral academic study within the framework of acedemic ethic and rules. | |||||
14 | Skills to use vocational information technologies efficiently in solving legal problems. | |||||
15 | Skills to reinforce knowledge of foreign languages and command of legal terminolgy. |
ECTS/Workload Table
Activities | Number | Duration (Hours) | Total Workload |
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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 |