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COURSE INFORMATION
Course CodeCourse TitleL+P HourSemesterECTS
MAT 512ADVANCED RINGS THEORY II3 + 01st Semester7,5

COURSE DESCRIPTION
Course Level Master's Degree
Course Type Elective
Course Objective The aim of the course is to deal with same complementary knowledge about rings and modüles and to extend students reasoning horizon.
Course Content Rings and Homomorphisms, Ideals, Division Rings and Localization, Rings of Power Series, Product at Polynomial Rings, Modules, Vector Spaces, Projective and Injective Modules, Hom and Duality, Tensor Product, Algebras, Field Extensions, Splitting Fields, Algebraic Closure and Normality, Galaois Group of Polinomials, Finite Fields, Separability, Transcendence Bases, Linear Disjointness and Separability.
Prerequisites No the prerequisite of lesson.
Corequisite No the corequisite of lesson.
Mode of Delivery Face to Face

COURSE LEARNING OUTCOMES
1Learns the structure of the rings and homomorphisms and studies the examples.
2Can set up the structures of ideals and division rings.
3Learns the Rings of Power Series.
4Define the Product at Polynomial Rings.
5Knows the definitions of Modules, Vector Spaces, Projective and Injective Modules, Hom and Duality, Tensor Product, Algebras and prove the theorems.
6Can express and prove the theorems of Field Extensions, Splitting Fields, Algebraic Closure and Normality, Galaois Group of Polinomials, Finite Fields, Separability, Transcendence Bases, Linear Disjointness and Separability.

COURSE'S CONTRIBUTION TO PROGRAM
PO 01PO 02PO 03PO 04PO 05PO 06PO 07PO 08
LO 0015 45  4 
LO 0024 55  5 
LO 0035 45  4 
LO 0045 54  4 
LO 0055 54  5 
LO 0064 54  4 
Sub Total28 2827  26 
Contribution50550040

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
ActivitiesQuantityDuration (Hour)Total Work Load (Hour)
Course Duration (14 weeks/theoric+practical)14342
Hours for off-the-classroom study (Pre-study, practice)14798
Assignments155
Mid-terms11515
Final examination13535
Total Work Load

ECTS Credit of the Course






195

7,5
COURSE DETAILS
 Select Year   


 Course TermNoInstructors
Details 2017-2018 Spring1MUSTAFA AŞCI
Details 2017-2018 Fall1CANAN CELEP YÜCEL
Details 2016-2017 Spring1SERPİL HALICI
Details 2012-2013 Spring1ŞAHİN CERAN
Details 2010-2011 Spring1ŞAHİN CERAN
Details 2009-2010 Spring1ŞAHİN CERAN


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Course Details
Course Code Course Title L+P Hour Course Code Language Of Instruction Course Semester
MAT 512 ADVANCED RINGS THEORY II 3 + 0 1 Turkish 2017-2018 Spring
Course Coordinator  E-Mail  Phone Number  Course Location Attendance
Prof. Dr. MUSTAFA AŞCI masci@pau.edu.tr FEN B0112 %70
Goals The aim of the course is to deal with same complementary knowledge about rings and modüles and to extend students reasoning horizon.
Content Rings and Homomorphisms, Ideals, Division Rings and Localization, Rings of Power Series, Product at Polynomial Rings, Modules, Vector Spaces, Projective and Injective Modules, Hom and Duality, Tensor Product, Algebras, Field Extensions, Splitting Fields, Algebraic Closure and Normality, Galaois Group of Polinomials, Finite Fields, Separability, Transcendence Bases, Linear Disjointness and Separability.
Topics
WeeksTopics
1 Rings.
2 Rings Homomorphisms and Subrings.
3 Integrel Domain and Fields.
4 Ideals.
5 Maximal Ideals and Prime Ideals.
6 Quotient Rings.
7 Isomorphism Theorems.
8 Factorization in Commutative Rings.
9 Midterm Exam.
10 Rings of Quotients and Localization.
11 Modulles and Submodulles.
12 Modulles Homomorphism and Isomorphism Theorems.
13 Free Modulles.
14 Rings of Polynomıals and Formal Power Series.
Materials
Materials are not specified.
Resources
Course Assessment
Assesment MethodsPercentage (%)Assesment Methods Title
Final Exam50Final Exam
Midterm Exam50Midterm Exam
L+P: Lecture and Practice
PQ: Program Learning Outcomes
LO: Course Learning Outcomes