1. Eğitim Bilgi Sistemi
  2. Matematik Pr. (Yl)
  3. Matrıces In Applıed Scıences II (2020 - 2021)
Ders Adı Kodu Yarıyıl T+U Saat Kredi AKTS
Matrıces In Applıed Scıences II MAT 570 0 3 + 0 3 6
Ön Koşul Dersleri Students are assumed to be familiar with Linear Algebra, Probability, Statistics, Generalized and Conditional Inverse, and Applied Matrix Equations.
Önerilen Seçmeli Dersler
Dersin Dili Türkçe
Dersin Seviyesi YUKSEK_LISANS
Dersin Türü Seçmeli
Dersin Koordinatörü Doç.Dr. MURAT SARDUVAN
Dersi Verenler Doç.Dr. MURAT SARDUVAN,
Dersin Yardımcıları Res. Assist. Emre KİŞİ- Res. Assist. Tuğba PETİK
Dersin Kategorisi Diğer
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 some information and facilities related to special types of matrices mainly used in many applied sciences.
Dersin İçeriği Transformation of Random Variables, Multivariate Normal Density; Moments of Density Functions and Excepted Values of Random Matrices, Marginal Density Functions, Expected Values of Quadratic Forms, Expectation of the Elements of a Wishart Matrix, Matrices with Positive Principle Minors and Matrices with Non-Positive Off Diagonal Elements; Nonnegative Matrices; Idempotent Matrices and Tripotent Matrices; Projections and Additional Theorems.
# Ders Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri
1 He/she consolidates the cultures of random variable and multivariate normal density. Lecture, Question-Answer, Discussion, Testing, Homework,
2 He/she sees the concepts of random matrices and their expected values. Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework, Project / Design,
3 He/she recognizes usefulness of quadratic forms with normal density. Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
4 He/she recognizes usefulness of matrices with positive principle minor. Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
5 He/she understands the concept of M-matrices and Z-matrices. Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework, Project / Design,
6 He/she recognizes usefulness of nonnegative matrices. Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
7 He/she recognizes usefulness of idempotent and tripotent matrices. Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Homework,
Hafta Ders Konuları Ön Hazırlık
1 Transformation of Random Variables, Multivariate Normal Density [1] pages 326-334
2 Moments of Density Functions and Expected Values of Random Matrices [1] pages 335-344
3 Marginal Density Functions [1] pages 345-360
4 Expected Values of Quadratic Forms [1] pages 361-368
5 Expectation of the Elements of a Wishart Matrix and Problems [1] pages 369-372
6 Matrices with Positive Principle Minors [1] pages 373-378
7 Matrices with Non-Positive Off Diagonal Elements [1] pages 379-381
8 M- matrices with Positive and Non-positive Principle Minors [1] pages 382-387
9 Z-matrices with Positive and Non-positive Principle Minors [1] pages 388-393
10 Nonnegative Matrices [1] pages 394-417
11 Idempotent Matrices [1] pages 418-429
12 Tripotent Matrices [1] pages 430-434
13 Projections [1] pages 435-438
14 Additional Theorems [1] pages 439-450
Kaynaklar
Ders Notu Graybill, F. A., Introduction to Matrices with Applications in Statistics, United States, 1969.
Ders Kaynakları [1] Searle, S. R., Matrix Algebra Useful For Statistics, Canada, 1982.
[2] Johnson, R. A. and Wichern, D. W., Applied Multivariate Statistical Analysis, Englewood Cliffs, New Jersey, 1982.
[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
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
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
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
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
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. Ara Sınav 50
1. Ödev 50
Toplam 100
1. Yıl İçinin Başarıya 50
1. Final 50
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