Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
---|---|---|---|---|---|
Matrıx Analysıs | MAT 523 | 0 | 3 + 0 | 3 | 6 |
Ön Koşul Dersleri | Students are assumed to be familiar with Analysis I-II and Linear Algebra I-II |
Önerilen Seçmeli Dersler | |
Dersin Dili | Türkçe |
Dersin Seviyesi | YUKSEK_LISANS |
Dersin Türü | Seçmeli |
Dersin Koordinatörü | Prof.Dr. HALİM ÖZDEMİR |
Dersi Verenler | |
Dersin Yardımcıları | Res. Assist. Emre Kişi and Res. Assist. Tuğba Petik |
Dersin Kategorisi | Alanına Uygun Öğretim |
Dersin Amacı | Linear algebra and matrix theory have long been fundamental tools in mathematical and statistical disciplines as well as applied sciences for example, sociology, education, chemistry, and engineering for research in their own right. The aim of this course is to introduce the reader to the study of matrix theory, a field which with a great deal of justice may be called the arithmetic of higher mathematics. |
Dersin İçeriği | Maximization, minimization, and motivation. Vectors and matrices. Diagonalization and canonical forms. Reduction of general symmetric matrices. The Cayley-Hamilton Theorem for symmetric matrices. Constrained maxima. Functions of matrices. Variational description of characteristic roots. Inequalities. Dynamic programming. |
# | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
---|---|---|---|
1 | He/she consolidates the culture of linear algebra. | Lecture, Question-Answer, Discussion, | Testing, Homework, |
2 | He/she sees some of usefulness and easiness which are supplied by matrix analysis in mathematical analysis. | Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, | Testing, Homework, |
3 | To recognize the necessity of matrix analysis in engineering and other applied sciences. | Question-Answer, Discussion, Drilland Practice, Problem Solving, | Testing, Homework, |
4 | He/she understands diagonalization in matrices. | Question-Answer, Discussion, Drilland Practice, Problem Solving, | Testing, Homework, |
5 | He/she maximizes or minimizes any multivariate function using matrices. | Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, | Testing, Homework, |
6 | He/she analyzes matrix functions | Question-Answer, Discussion, Drilland Practice, Problem Solving, | Testing, Homework, |
7 | He/she finds eigenvalues and eigenvectors of any given matrix | Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, | Testing, Homework, |
8 | He/she understands inequalities of matrices | Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, | Testing, Homework, |
9 | He/she solves various inequalities of matrices problems using packet programs | Question-Answer, Discussion, Drilland Practice, Problem Solving, | Testing, Homework, |
Hafta | Ders Konuları | Ön Hazırlık |
---|---|---|
1 | Maximization, minimization, and motivation | [1] pages 1-12 |
2 | Vectors and matrices | [1] pages 12-32 |
3 | Vectors and matrices (continuation) | [1] pages 12-32 |
4 | Diagonalization and canonical forms | [1] pages 32-44 |
5 | Reduction of general symmetric matrices | [1] pages 44-55 |
6 | Reduction of general symmetric matrices (continuation) | [1] pages 44-55 |
7 | The Cayley-Hamilton Theorem for symmetric matrices | [1] pages 55-73 |
8 | Constrained maxima | [1] pages 73-90 |
9 | Functions of matrices | [1] pages 90-112 |
10 | Variational description of characteristic roots | [1] pages 112-126 |
11 | Inequalities | [1] pages 126-144 |
12 | Inequalities (continuation) | [1] pages 126-144 |
13 | Dynamic programming | [1] pages 144-157 |
14 | Dynamic programming (continuation) | [1] pages 144-157 |
Kaynaklar | |
---|---|
Ders Notu | [1] Bellman, R., Introduction to Matrix Analysis, The Rand Corporation, Philadelphia, 1997. |
Ders Kaynakları | [2] Golub G. H., Van Loan, C. F., Matrix Computations, The Johns Hopkins University Press, London, 1996. [3] Horn, R. A., Johnson, C. R., Matrix Analysis, Cambridge University Press, Cambridge, 1985. |
Sıra | Program Çıktıları | Katkı Düzeyi | |||||
---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | |||
0 | Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise | X | |||||
2 | Student follows the current journals in his/her field and puts forward problems. | X | |||||
2 | Student follows the current journals in his/her field and puts forward problems. | X | |||||
3 | Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics | X | |||||
3 | Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics | X | |||||
4 | Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. | X | |||||
4 | Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. | X | |||||
5 | Student uses different proof methods to come to a solution by analyzing the problems encountered. | X | |||||
5 | Student uses different proof methods to come to a solution by analyzing the problems encountered. | X | |||||
6 | Student determines the problems to be solved within his/her field and if necessary takes the lead. | X | |||||
6 | Student determines the problems to be solved within his/her field and if necessary takes the lead. | X | |||||
7 | Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. | X | |||||
7 | Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. | X | |||||
8 | Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters | X | |||||
8 | Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters | X | |||||
9 | Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. | X | |||||
9 | Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. | X | |||||
10 | Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. | X | |||||
10 | Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. | X | |||||
11 | Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. | X |
Değerlendirme Sistemi | |
---|---|
Yarıyıl Çalışmaları | Katkı Oranı |
1. Ödev | 100 |
Toplam | 100 |
1. Final | 70 |
1. Yıl İçinin Başarıya | 30 |
Toplam | 100 |
AKTS - İş Yükü Etkinlik | Sayı | Süre (Saat) | Toplam İş Yükü (Saat) |
---|---|---|---|
Course Duration (Including the exam week: 16x Total course hours) | 16 | 3 | 48 |
Hours for off-the-classroom study (Pre-study, practice) | 16 | 3 | 48 |
Mid-terms | 1 | 15 | 15 |
Assignment | 1 | 8 | 8 |
Performance Task (Seminar) | 1 | 20 | 20 |
Final examination | 1 | 20 | 20 |
Toplam İş Yükü | 159 | ||
Toplam İş Yükü / 25 (Saat) | 6,36 | ||
Dersin AKTS Kredisi | 6 |