MANAGEMENT OF HEALTH (TURKISH)
Bachelor TR-NQF-HE: Level 6 QF-EHEA: First Cycle EQF-LLL: Level 6

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT4052 Commutative Algebra Fall 3 0 3 6
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction: English
Type of course: Non-Departmental Elective
Course Level: Bachelor’s Degree (First Cycle)
Mode of Delivery: Face to face
Course Coordinator :
Recommended Optional Program Components: None
Course Objectives: To provide the necessary background (both computational and theoretical) in commutative algebra to mathematics majors.

Learning Outcomes

The students who have succeeded in this course;
A student who finishes this course successfully will have learned basic concepts of commutative algebra.

Course Content

Abelian groups, rings and fields. Vector spaces and linear transformations. Bases and matrix representations of linear transformations. Polynomial rings. Ideals, prime and maximal ideals. Quotients of polynomial rings. Modules over polynomial rings. Prime and primary ideals. Factorization of ideals in the monoid of ideals. Localizations of ideals. Zero-divisors, integral domains and rings of fractions. Unique factorization domains and Euclidean domains. Radical of an ideal. Nilradical and Jacobson radical of a ring. Operations in the lattice of ideals. Classical Euclidean division algorithm in polynomial algebras. Monomial orderings and division algorithms. Fundamental Theorem of Algebra. Finite generation of ideals in polynomial algebras. Gröbner basis and Buchberger algorithm. Examples and calculations.
Gröbner bazları ve Buchberger algoritması. Örnekler ve hesaplamalar. Gröbner basis and Buchberger algorithm. Examples and calculations. Morphisms between modules. Kernels and images of morphisms. Submodules and quotient modules. Ideals of annihilators. Internal and external sums of modules. Tensor products of modules. Submodule and ideal chains. Artinian and Noetherian rings and modules.

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Abelian groups, rings and fields.
2) Vector spaces and linear transformations. Bases and matrix representations of linear transformations.
3) Polynomial rings. Ideals, prime and maximal ideals. Quotients of polynomial rings. Modules over polynomial rings.
4) Prime and primary ideals. Factorization of ideals in the monoid of ideals. Localizations of ideals.
5) Zero-divisors, integral domains and rings of fractions. Unique factorization domains and Eucledian domains.
6) Radical of an ideal. Nilradical and Jacobson radical of a ring. Operations in the lattice of ideals.
7) A review of covered subjects and the first exam.
8) Classical Euclidean division algorithm in polynomial algebras. Monomial orderings and division algorithms.
9) Fundamental Theorem of Algebra. Finite generation of ideals in polynomial algebras.
10) Gröbner basis and Buchberger algorithm. Examples and calculations.
11) Gröbner basis and Buchberger algorithm. Examples and calculations.
12) A review of covered subjects and the second exam.
13) Morphisms between modules. Kernels and images of morphisms. Submodules and quotient modules. Ideals of annihilators. Examples.
14) Internal and external sums of modules. Tensor products of modules. Submodule and ideal chains. Artinian and Noetherian rings and modules.

Sources

Course Notes / Textbooks: Instructor's own lecture notes.
Atiyah and MacDonald, "Introduction to Commutative Algebra"
References:

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Quizzes 3 % 10
Midterms 2 % 40
Final 1 % 50
Total % 100
PERCENTAGE OF SEMESTER WORK % 50
PERCENTAGE OF FINAL WORK % 50
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Study Hours Out of Class 14 2 28
Quizzes 3 3 9
Midterms 2 10 20
Final 1 26 26
Total Workload 125

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution
1) To have theoretical and practical knowledge required to fulfill professional roles and functions of Management of Health Scşences field. 3
2) To act in accordance with ethical principles and values in management, to learn and implement related regulations and guides. 3
3) To use life-long learning, problem-solving and critical thinking skills. 3
4) To identify the process of management functions (management and organization, public relations, human resources, cost accounting, marketing) in the Management of Health Sciences field. 2
5) To take part in research, projects and activities within sense of social responsibility and interdisciplinary approach. 2
6) To have skills for planning training programs and projects according to health education needs of individual, family and the community. 2
7) To be sensitive to health problems of the community and to be able to offer solutions. 2
8) To be able to use effective communication skills; to take responsibility as a team member in collaboration with other professions. 2
9) To have skills for research, planning and practice about health systems and health information systems field within national and international level. 2
10) To be able to search for literature in health sciences and management and information sources to access to information and use the information effectively. 2
11) To be able to monitor occupational information using at least one foreign language, to collaborate and communicate with colleagues at international level. 2
12) To be a role model with contemporary and professional identity. 2